Strength of Materials and Theory of Structures

Meditations on Equi-Strength, Equi-Stability, Equi-Reliability and Optimal Design

2026-05-14T13:13:47+03:00

Traditional approaches to the design of building structures are considered, which are based on the full use of their resistance and rely on the search for conditions of equi-strength, equi-stability or equi-reliability of system components.

Attention is drawn to the fact that the equi-strength of structural elements tacitly assumes their equal role in ensuring the reliability of the system as a whole, when the failure of at least one element is a critical event. That is, the structure is considered a system with sequentially (in the sense of reliability) connected elements, and this often does not correspond to reality. That is why the optimization conditions do not coincide with the principle of equi-strength. Examples of deliberate deviation from equal strength in order to increase the survivability of structures are given.

The design of equi-stable structures is based on the independence of various forms of loss of stability, but such independence is violated when switching to nonlinear analysis. Then it turns out that structures designed according to the principle of equi-stability have a special tendency to the destabilizing effect of initial imperfections, and here there is a possibility of destruction of structures, which has an avalanche-like character.

It is emphasized that it is quite logical to formulate the same requirements for the reliability of functioning (target reliability levels) for objects of approximately the same degree of responsibility, regardless of the material from which they will be designed and the type of structural scheme. The condition for the equi-probability of the occurrence of design loads is also valid, regardless of the number in the design combination. But the equal reliability of structural elements may not correspond to their functional purpose, which leads to a decrease in overall reliability. A simpler example is ensuring survivability by using key elements with increased reliability.

Comparative analysis of the use of Matlab tools for optimizing parameters with constraints

2026-05-14T13:59:57+03:00

This study suggests focusing on dynamic behavior of the single-sided vibro-impact nonlinear energy sink (SSVI NES) as it moves in direction opposite the obstacle. It can hits the primary structure (PS); its dynamics and efficiency in mitigating the PS vibrations were examined in our previous works. If these impacts are simply ignored, the damper moves in the PS direction over a very large distance, which is unrealistic for this diagram. To prevent such impacts, the connecting spring must have high stiffness. However, when optimizing damper parameters, the requirement to avoid these impacts makes it necessary to set limits not only on the parameters, but also on the relationship between the displacements of bodies, which are variables obtained by integrating the motion equations. The optimization procedures were performed using Matlab platform tools. The approximate damper parameters are determined using the surf program, which constructs an image where the dependence of the objective function value on the relationship between two parameters is displayed in color. The selected approximate parameters should be further optimized; their values can be refined using various Matlab platform tools. We compared the use of fminsearch and fmincon programs, as well as the Ga genetic algorithm, and chose the fminsearch program. Using the fminsearch program with a penalty for violating the constraint conditions gives quite good results and allows us to select several sets of optimized damper parameters. However, the analysis of the efficiency in mitigating the PS vibrations for SSVI NESs with four various sets of optimized parameters showed that such a model with high stiffness of connecting spring could hardly be considered successful.

Non-stationary bending vibration of a helicopter rotor blade under distributed aerodynamic load. Part 2. Forced vibrations of the blade

2026-05-14T14:47:21+03:00

Each technical problem statement requires an adequate physical model. This model must take into account the basic physical properties and bring the physical problem statement closer to the technical problem. Part 1 of this work presents experimental instantaneous photographs of the bending vibrations of a helicopter rotor blade, which are similar to the small bending vibrations of a cantilever-clamped thin plate. It is known that helicopter blades are made rigid. Therefore, to model small bending vibrations, we apply Kirchhoff-Love's hypothesis and Lagrange-Sophie Germain's equation in this work.

Currently, existing approaches to solving the problem of natural bending vibrations of a thin rectangular plate under cantilever clamping conditions lead to uncertainty and non-uniqueness of the solution. Therefore, in Part 2 of this work, in order to obtain a unique solution to the problem, a non-zero distribution of normal forces is set at the two edges of the plate. These forces are taken into account only in the boundary conditions, and the rest of the blade surface is free. Therefore, no forces are added to the right-hand side of the Langrange-Sophie Germain equation. This refinement of the boundary conditions brings the physical formulation of the problem closer to the real technical problem: during rotation, forces act on the blade, causing a lifting force, which determines the load distributed normal to the blade surface.

The change in boundary conditions at the two edges of the blade resulted in the system of linear algebraic equations changing from homogeneous to non-homogeneous. This made it possible to find a unique solution to the problem based on Cramer's rule and to unambiguously determine the desired integration constants. Since the blade motion is periodic, the problem is solved under the condition of a time-harmonic load on the plate.

To obtain an analytical solution of the problem for forced vibrations, the normal coordinate method is used. It allows using the solution of the problem for natural vibrations, its stationary part, and on its basis, obtaining an equation for the normal coordinate that describes the non-stationarity of the general solution of the problem. Using L'Hôpital's rule, the obtained general solution is divided by frequency into non-resonant and resonant regions.

As an example of numerical calculation, the amplitudes of the bending of the natural vibrations of a plate, a helicopter blade, are calculated for different frequencies of its rotation. It was found that the amplitude of the bending has a wave character, slightly increasing towards the outer end of the blade with an increase in the rotation frequency of the helicopter rotor.

A protective shelter sheet steel structural behaviour numerical simulation when hit by a fragment from an impacting UAV

2026-05-14T15:13:02+03:00

It has been determined that, under the conditions of the war of the russian federation against Ukraine, the problem of selecting cost-effective and efficient solutions for the design of protective shelters is highly relevant. A review of the literature has shown that previous studies focused on the behaviour of protective structures subjected to small-arms bullet impacts, while the impact of fragments from strike UAVs has not been considered. It is noted that steel plate protective structures are advantageous due to the high speed of construction. From practical experience in the design of protective shelters, it is known that, due to the limited availability of armored steel plate sizes, plate structures must be designed as multilayer systems.

It is proposed to use single-layer plate structures of greater thickness made of low-alloy steel with lower strength. Numerical modeling of fragment penetration from a strike UAV into steel structures of protective shelters under the conditions of Ukraine was carried out. The size, velocity, and material parameters of the fragment were adopted in accordance with the strike UAV used by the adversary. A dynamic analysis was performed using the finite element method with the ANSYS software package. To model the material behaviour of steel, the Johnson–Cook model was adopted—an empirical material model used to describe the behaviour of metals under large deformations, high strain rates, and elevated temperatures.

Two numerical simulations were conducted for different thicknesses of steel plates for both armored steel and low-alloy steel. The sufficient thickness required to prevent fragment penetration was determined for steel plates made of armored and low-alloy steel. It was established that, instead of multilayer armored steel plate structures, single-layer structures made of low-alloy steel can be used in protective shelters, providing several-fold reductions in material cost. The results of this study make it possible to apply more economical and less labor-intensive structural solutions in the design of protective shelters, with a reduced number of welded assembly connections.

Assessment of the effect of the fluctuating component of wind pressure on a lattice telecommunication tower

2026-05-14T15:50:29+03:00

Abstract. The paper presents a calculation methodology for accounting for the fluctuating component of wind loading in the analysis of a spatial lattice telecommunication tower 50 m high, designed according to a modular concept (2.0 m vertical module) with plan-dimension changes along the height. Unlike the standard approach, where the dynamic coefficient is taken as an input multiplier, a methodology based on the peak response parameter is proposed. In this methodology, the equivalent dynamic coefficient is determined by the criterion of the structure’s peak response (top displacement, base bending moment, or critical axial force), and the distribution of equivalent nodal forces is formed so as to ensure equality of the generalized modal force in the first vibration mode. The matrix form of the equations of motion is given in full as , with derivation of the element stiffness and mass matrices of a spatial truss element and rules for assembling the global matrices. An algorithm is proposed for piecewise formation of the equivalent wind load over the height intervals 0–32, 32–34, 34–44, 44–46, and 46–50 m, converting pressure to forces through the effective projected area of the lattice. The methodology provides a physically justified consideration of the fluctuating component without direct time-history simulation of the wind process and improves the reproducibility of calculation results. In addition, the choice of the first mode as dominant for the along-wind response is substantiated, and procedural checks of load consistency are provided through equality of the generalized modal force. It is shown that the piecewise discretization enables correct consideration of structural transitions and differences in «wind-exposed area» along the height, while the use of the effective projected area reduces subjectivity when modeling permeable lattice systems. A control criterion is proposed: and , which guarantees convergence with respect to the selected response quantity.

Features of Finite Element Modeling for Buckling Analysis of Elastic Shells with Inhomogeneous Structure under Thermomechanical Loads

2026-05-14T16:33:41+03:00

The method for studying the behavior of elastic inhomogeneous shells is based on geometrically nonlinear relationships of the three-dimensional theory of thermoelasticity, the principles of the finite element moment scheme, and the use of a modifiable universal 3d finite element with additional variable parameters. For the analysis of geometrically nonlinear deformation, buckling, post-buckling behavior, and natural vibrations of shells under static thermomechanical loading, an integral approach is employed. A comprehensive study of the stability and natural vibrations of shells subjected to static thermomechanical loading is implemented using a stepwise algorithm. A distinctive feature of the method and the algorithm developed on its basis is the capability to accurately analyze both the pre-buckling and post-buckling states of shell deformation with various thickness features, including ribs, channels, etc. The specificity of the method and algorithm lies in the adopted methodology for prescribing thermomechanical loading as a function. This enables the definition of various loading regimes and the description of complex combined thermomechanical effects on the structure that may be close to real operating conditions. In addition, the developed method provides the capability, in the analysis of nonlinear deformation and buckling of shells to determine solution branching points and to trace adjacent equilibrium branches in the pre-buckling domain. The features of the method and algorithm are demonstrated through a series of specially selected benchmark problems.

Study of the Propagation of Explosive and Impulsive Loads in Soil Environments

2026-05-14T16:57:03+03:00

The paper considers the features of propagation of explosive and impulsive loads in soil media and their influence on the stress-strain state of building structures. It is shown that modern design approaches are often based on the quasi-static representation of explosive loads, which does not fully reflect their dynamic nature and may lead to reduced accuracy of calculations. The time characteristics of a blast wave, including the positive and negative phases, are analyzed, and analytical relationships for determining overpressure and load impulses are presented. The application of the Friedlander equation and simplified triangular approximations for engineering calculations is discussed.

Special attention is paid to the propagation of wave processes in soil masses, including longitudinal, transverse, and surface waves, as well as to the influence of the physical and mechanical properties of soils on wave attenuation and transformation. It is established that the nature of energy transfer from an explosion largely depends on the interaction conditions between the explosive source and the soil medium, the depth of charge placement, and the structural heterogeneity of the soil. It is shown that in the case of buried explosions, a significant part of the energy is transferred into the soil, generating intense wave processes that may substantially affect structures.

The nonlinear elastoplastic behavior of soils under dynamic loading is analyzed, which is accompanied by the development of plastic deformations, compaction, and decompaction processes. The necessity of considering these effects in modeling the dynamic response of the “soil–structure” system is emphasized. Taking into account the negative phase of the blast wave and the nonlinear properties of soils makes it possible to improve the reliability of computational models and to ensure a more accurate assessment of structural performance under extreme loading conditions.

Zonal method for contact interaction modeling in the semi-analytical finite element method

2026-05-14T22:38:11+03:00

This paper presents a comprehensive investigation of contact interaction modeling capabilities within the Semi-Analytical Finite Element Method for prismatic structures. The classical SAFEM formulation assumes material property invariance along the longitudinal coordinate, which leads to the appearance of non-physical tensile stresses in contact opening zones. To address this issue, a zonal method is proposed, based on partitioning the longitudinal axis into zones and iteratively determining the distribution of elastic moduli depending on the presence or absence of contact in each zone.

Particular attention is given to the modification of the stiffness matrix assembly procedure, where integration along the longitudinal coordinate for contact elements is performed zonally using different elastic moduli. In contact zones, the full material modulus is applied, while in opening zones a significantly reduced modulus is used to simulate the absence of interaction. The modulus distribution is determined iteratively by solving the problem, computing gaps at zone centers, and updating material properties until convergence is achieved.

Verification of the method was carried out on a benchmark problem of a flange connection of two plates, with results compared against calculations performed in the LIRA-SAPR software package. The results demonstrated high agreement between the zonal method and the three-dimensional FEM formulation: the discrepancy in displacements does not exceed 2.4%, and in stresses — 1.04%. At the same time, the computational efficiency of the zonal method is significantly higher due to the reduced problem dimensionality and the possibility of parallelizing calculations for different expansion terms.

The obtained results confirm the feasibility and effectiveness of the zonal method for modeling contact interaction in prismatic structures. This approach allows for accurate representation of opening zones while maintaining high computational efficiency, making the method suitable for a broad class of engineering problems, including flange connections, multilayer composites, and other cases of unilateral contact.

Using the finite element method to determine the possibility of application and improvement of organizational and technological solutions for localization of destroyments caused by influences not foreseeed during design

2026-05-18T10:32:59+03:00

The article examines the impact of off-design loads on the structures of an industrial building that was damaged but retained its overall stability.

The generalized predictive and computational model is considered as a simplified transition from the physical system of an industrial building to a mathematical model used to assess the current state of structures and predict the possible development of damage. An effective approach to building such a model involves the use of the finite element method (FEM), which allows for the formalization of complex spatial systems by dividing them into components of simple geometry. The predictive and computational model, built based on FEM, provides the ability not only to analyze the current state of damaged structures, but also to predict their further behavior under the influence of variable loading conditions. This allows it to be used as a tool for making informed technical decisions in the process of eliminating the consequences of off-design impacts.

An algorithmic sequence of actions for building an information and mathematical predictive and calculation model (using the example of a reinforced concrete truss of an industrial structure) in the environment of a calculation complex is proposed, which allows assessing the change in the technical condition of structural elements after the action of an off-design impact.

An example of a corresponding calculation of a predictive and calculation model of a truss with a span of 24 m is given, the main tasks of which were: checking the absence of general destruction of its structure in the event of loss of an element at different stages of temporary reinforcement using an assembly platform and steel risers; determining the efficiency of unloading a damaged truss with this reinforcement, taking into account the limitation of the total allowable load transmitted by the risers to the assembly platform.

A significant advantage (in the required total effort in the unloading risers) of the one-rise variant compared to two was found. This advantage increases from approximately 5% to 3 times when changing the location of the missing truss element from the edge to the middle of the truss.

The planned level of truss unloading can be fully achieved with the use of a single riser for two of the four damage patterns and 88% for the other two. The options using 2 risers are significantly less effective (33-85% of the planned level of unloading).

No cases of total truss failure were identified for any option and at any stage of the calculation.

Methodology for creating a mobile crushing plant taking into account the stress-deformed state of its structural elements

2026-05-18T11:07:27+03:00

Due to the growing requirements for the quality of building materials, as well as the expansion of the scope of their use, the task of reducing energy costs for the processes of manufacturing building materials arises. The main areas of reducing energy costs are optimization or improvement of the designs of individual machines included in technological lines, technological lines themselves, the processes of extracting materials for construction and their delivery to the consumer. On the other hand, Ukraine is experiencing a sharp increase in the volume of construction waste, which is associated with large-scale destruction of infrastructure and housing stock, reconstruction and dismantling of dilapidated structures. Recycling construction waste allows you to reduce future construction costs and also solves environmental safety problems. A large number of current problems in the production and processing of building materials are solved by mobile crushing and sorting plants. Mobile crushing and sorting plants designed for crushing and separating rocks, construction waste or other bulk materials directly at the place of extraction or processing. Such complexes can function as independent units or as elements of entire plants, while ensuring flexible adaptation to production conditions. Mobile crushing plants combine high productivity, autonomy, mobility and economic feasibility, ensuring minimal loss of time and fuel while maintaining the quality of crushing and sorting. One of the most important advantages of mobile crushing plants compared to stationary machine designs is a significant reduction in logistics costs associated with transporting raw materials to the crushing site. In addition to direct savings in fuel and transport resources, reducing logistics provides a number of indirect benefits. First of all, the technological cycle time is reduced. This, in turn, increases the company's cash flow and reduces the need for intermediate warehouses. An important advantage is the reduction in infrastructure construction and maintenance costs. For stationary crushers, it is necessary to build concrete foundations, access roads, overpasses, loading hoppers, and also provide for the supply of communications. Another aspect that has a financial impact is the reduction of downtime related to weather conditions and road conditions.

The paper performs a criterion-based assessment of mobile crushing and screening plants, builds models of technological schemes for single-stage crushing and two-stage crushing, which include the designed mobile crushing plant, and provides calculations of the parameters of the mechanical mode of the jaw crusher, the running gear, and the hydraulic system. Based on the load scheme of the structural elements of the jaw crusher, the stress-strain state of the eccentric shaft and the spacer plate was determined using the finite element method.

Research of technology for creating external waterproofing by injection of underground structure

2026-05-18T11:56:41+03:00

Given the security situation in Ukraine, some underground structures and premises are used as simple shelters to protect the population from explosions and shrapnel. Certain requirements are imposed on the maintenance of such structures, namely: the structure must be protected from the effects of ground, surface and technical water by means of waterproofing. If the waterproofing is damaged or missing, the structures lose their operational properties and collapse. In addition, high humidity has a negative impact on the people inside. There are three common methods for repairing or installing waterproofing: excavating the structure and applying waterproofing from the outside, installing waterproofing from the inside, or installing external waterproofing using the injection method. To ensure sustainable development with the aim of reducing the impact on the environment and human health, the third method of waterproofing is the most acceptable. Given the wide choice of materials and their properties, it is advisable to study the effectiveness of the technology of waterproofing by injecting material outside the structure (externally). To this end, a series of experimental laboratory studies were carried out, which revealed the influence of soil moisture on the material's ability to increase in volume, spread and adhere to the structure. The waterproofing properties of the material were also tested. Based on the results obtained, practical recommendations were formulated for the use of improved technology for external waterproofing of underground structures. The optimal level of soil moisture for waterproofing was established. Further research directions were outlined for the installation of external horizontal waterproofing of reinforced concrete structures.

Construction of 3D models for additive manufacturing based on three-periodic surfaces of the Fourier polynomia

2026-05-18T12:36:43+03:00

With advances in 3D printing, the construction of increasingly intricate designs has become possible. Metamaterials and devices based on tri-periodic minimal surfaces (TPMS) have proven useful in various applications, including tissue engineering, acoustics, and heat exchange. These surfaces have minimal average curvature at every point, although certain studies show that minimality in a strictly geometric sense is not necessary or even desirable for some applications.

This paper proposes an algorithm for Fourier polynomial approximation combined with interpolation that enables the construction of generic tri-periodic surfaces (TPS), which are not minimal but appear more governable. In the context of tri-periodic implicit surfaces construction, the interpolating property of the polynomial allows setting the expected function values in points directly, while the approximating property allows for an unlimited number of non-strict guiding points. Such points can be obtained by discretizing curves and surfaces. This enables both explicit and implicit control over the shape of a TPS within the same algorithm.

The implicit level of control enables the creation of 3D-models applicable in all fields where TPMS are already in use. The explicit level of control ensures that such models can be produced using additive manufacturing technologies. Not to become too broad, this particular paper only discusses the applicability of Fourier-based 3-periodic surfaces in heat exchangers design, and printability of the models based on these surfaces in laser powder bed fusion (LPBF) and electron beam melting (EBM) additive manufacturing processes.

Features of the calculation of a flat sheet as a membrane element of a combined retaining wall

2026-05-18T14:41:49+03:00

The construction of underground structures is one of the key trends in modern construction, with additional consideration given to the threat posed by an aggressor state. This inevitably involves the excavation of deep pits, which requires the installation of costly retaining wall structures, particularly in water-saturated soils. An effective design for a combined flexible retaining wall is proposed, incorporating a flat sheet pile that functions within the system under tension as a membrane element, also serving as an anti-seepage curtain.

Classical elasticity theories are used to model the behaviour of flat sheet piles: the Kirchhoff–Love theory for thin plates, the Mindlin–Reissner theory for elements of intermediate thickness, and the Föppl–von Kármán theory for cases involving significant deflections and geometric non-linearity. The choice of theory depends on the ratio of the membrane thickness to its characteristic dimensions and on the type of loading. Combining analytical solutions with numerical methods, in particular the finite element method (FEM), ensures the accuracy and reliability of the results.

The effect of membrane thickness on deflections, axial forces and the convergence of numerical algorithms was investigated. It was found that as the thickness increases from 2 to 20 mm, deflections decrease from 147,3 to 65,6 mm, whilst the maximum axial force Nx increases from 491,29 to 904,5 kN/m. Thicker membranes are characterised by greater stiffness, lower deformation and faster convergence of calculations. For thin membranes (2–6 mm), the application of the Föppl–von Kármán theory is necessary, whilst for medium thicknesses (8–12 mm), a balance between permissible deflections and load-bearing capacity is advisable. For thick membranes (14–20 mm), the use of the Mindlin–Reissner theory, taking into account shear effects, is recommended. The optimal thickness range of 8–12 mm ensures acceptable deflections, sufficient load-bearing capacity and material savings.

Modelling in the LIRA-FEM software package is based on the displacement-based finite element method. The membrane is treated as a shell with minimal bending stiffness, where membrane forces dominate. The use of the Kirchhoff–Love and Föppl–von Kármán theories allows the effect of geometric stiffening to be taken into account, whilst the application of physically-based geometric non-linearity ensures realistic results. The study involved modelling a steel membrane 6 m high, 5 m wide and 10 mm thick under trapezoidal soil pressure. Three modelling variants were considered: geometric non-linearity only, a shell with full stiffness, and physical-geometric non-linearity. The comparison showed that taking physical non-linearity into account allows the bearing capacity to be correctly estimated and the safety factor to be accurately assessed.

Thus, an integrated approach combining analytical models and numerical methods makes it possible to establish a multi-level methodological framework for the design and calculation of composite retaining wall structures incorporating flat sheet piles (membrane elements). This ensures the accuracy of calculations and the reliability of results for modern engineering practice.

Method for determining the penetrating ability of small arms bullets into protective equipment

2026-05-18T15:12:43+03:00

Adoption of foreign and new domestic types of weapons and ammunition requires conducting a large amount of experimental research. However, the short-term nature of the processes that occur with ammunition on the trajectory complicates direct measurements of the quantities that characterize them, forcing the use of complex measuring and recording equipment. In this context, mathematical modeling of the processes of external ballistics and aerodynamics of ammunition movement comes to the fore.

The mathematical modeling method allows to significantly reduce the time and reduce the total cost of ammunition for their testing. Modeling methods, based on mathematical calculations and formulas, allow you to determine the future trajectory of ammunition based on a minimum set of parameters and in a short time. This method makes it possible to accelerate the compilation of temporary firing tables for the use of ammunition and accelerates their arrival to units that directly perform tasks in the combat zone.

Mathematical modeling methods allow us to obtain dependencies for determining the level of protection of military personnel when performing assigned tasks by units, taking into account the fact that the effectiveness of measures to ensure the protection of personnel depends on the type of protective barriers, effect of small arms bullets depends on their mass, shape, and bullet speed at the moment of encountering a protective obstacle.

The development of a scientific and methodological apparatus for conducting research to determine the parameters of new weapons and increase the ballistic protection of personnel from small arms remains an urgent scientific task.

The paper examines the process of interaction of a bullet with various types of protective environments. A method for determining the penetration ability of small arms bullets into protective equipment and models for determining the depth of bullet penetration into various types of obstacles are proposed. The results of calculations of the penetration depth of a bullet from an AK-74 assault rifle into various types of protective environments are presented. Further improvement of armor protection designs can be achieved by developing new technical solutions using the proposed method for determining the penetration ability of small arms bullets into protective equipment.

Aprobation of a methodology for modeling progressive collapse using the example of a real-world accidental impact on a construction site

2026-05-18T15:44:51+03:00

In this article, the authorsexamine the issues associated with traditional approaches to determining resistance to progressive collapse, as regulated by national and international standards, which are based on the principle of independence from the type of threat. This is achieved by modeling the sudden removal of a single column or other vertical load-bearing structure from the structural model. According to statistical studies of progressive collapse cases, this approach is plausible; however, it does not fully reflect real collapse scenarios, in particular, it does not account for the nature of the cause of the structural failure and its impact on adjacent elements.

To improve the predictive accuracy and reliability of the analysis, it is proposed to expand the traditional modeling approach by considering more complex and realistic damage scenarios. Based on the results of a series of verification numerical calculations, an effective methodology for determining the resistance of buildings and structures to progressive collapse is proposed. The method is based on a dynamic approach (direct integration of the equations of motion over time) and consists of six sequential stages.

To validate the methodology, the results of modeling the progressive collapse of a steel-framed building of consequence class CC3, which sustained local damage due to a real emergency impact (UAV strike), are presented. A comparative analysis was conducted of the calculation results obtained using the traditional standard method of sudden removal of a single element and the refined approach based on reproducing the actual damage pattern. The main focus was on investigating the effect of dynamic unloading of the structural system caused by the instantaneous destruction of lightweight enclosure elements and the roof by a blast wave. The obtained data confirm the high consistency of the refined model with the actual condition of the structure and allow for an objective assessment of the remaining service life of the damaged structures to inform decisions regarding their further restoration.

Application of additive technologies in the construction of energy-efficient buildings with a positive energy balance

2026-05-18T16:30:18+03:00

The article is dedicated to the development of additive technologies, using 3D frames from concrete bags, for the formation of energy-efficient housing structures with a positive energy balance. The advantages of lining 3D-laminated shells with highly efficient thermal insulation materials (PU, ecowool, mineral wool, EPS) in the context of reduced heat loss, increased energy efficiency and fluidity wakefulness. A three-tier research methodology is described - laboratory testing, digital modeling (Revit, Rhinoceros, Grasshopper, Energy Plus) and implementation on a real everyday life with the parameters of the future. The robot examines current approaches to the development of modern 3D technology as one of the promising directions for the post-war renovation of the housing stock of Ukraine. It has been shown that the use of additive technologies makes it possible to significantly speed up the work cycle, reduce the wastage of materials, increase the level of automation of everyday processes and ensure flexibility architectural and planning solutions. Particular attention is paid to ensuring energy efficiency through the integration of thermal insulation materials into the structure of 3D-laminated wall elements, as well as the integration of structural systems from renewed energy sources. The results of the study of the optimal technological parameters of 3D frames, the terms of pressing concrete mixes for 3DPC, the thermal insulation characteristics of wall elements, the modeling of the generation of electrical energy from solar panels are presented. Power station with a varied number of solar panels, technical and economic efficiency of 3D technology compared to traditional technology. Optimal parameters for the hand process have been established, ranging from the relationship between the height of the ball and the diameter of the printer nozzle, the fluidity of the hand and the characteristics of inter-ball adhesion. The results of experimental studies of thermal insulation authorities of various types of insulation materials were compiled and the most effective design solutions were identified to meet the Energy+.

Research of the influence of defects on the dynamic behavior of layered spherical shell structures

2026-05-18T18:18:02+03:00

The linear transient dynamic processes of three-layer spherical shell structures with discrete-symmetric rib-reinforced filler in the presence of annular discontinuities in the reinforcing ribs of these structures were studied. Numerical calculations of normal deformations and von Mises stresses of the bearing layers of spherical structures, determining their stress-strain state, were performed using the finite element method.

The equation of motion of a three-layer spherical shell with a discrete-inhomogeneous filler was obtained. The stress-strain state of three-layer spherical structures under the action of an axisymmetric internal impulse load was studied. The results of the values of the first five natural frequencies of the considered structures are presented.

The studies made it possible to determine the significance of the influence of defects in the form of annular discontinuities on the characteristics of the stress-strain state of three-layer spherical shells in the presence and absence of an interlayer filler under different boundary conditions.

The influence of structural defects on the characteristics of the stress-strain state of three-layer hemispherical shells with a discretely symmetric lightweight, rib-reinforced filler under internal impulse loading under various boundary conditions was analyzed. Circular breaks in the reinforcing ribs of the structures were modeled as defects. To analyze the elements of the elastic structure, the model of the theory of shells and rods of Tymoshenko was used under independent static and kinematic hypotheses for each layer. The equation of motion was obtained using the Hamilton-Ostrogradsky variational principle. A corresponding finite element model of the hemispherical structure was created, which reflects the relationship between the potential energy of deformations in the shell and the potential of applied forces.

The results of calculations of normal deformations and von Mises stresses in the load-bearing layers, obtained by the finite element method, for shells with defects under various boundary conditions are compared with the corresponding values for three-layer hemispherical shells in a defect-free state. The conducted studies of three-layer hemispherical shells show that circular discontinuities in the reinforcing ribs of the structure change the values and distribution of the characteristics of the stress-strain state, but have a negligible effect on the change in the values of the natural frequencies of the structure.

Use of the Green's function method in the hyperbolic heat conduction theory and non-Fourier analysis of non-stationary thermoelastic fields (moving) deformed media/bodies and composite materials

2026-05-18T18:38:33+03:00

The work develops precisely solvable models of pulse optics for dispersive, dissipative deformed media (bodies) and composite materials during their laser processing with short wave pulses. Unsteady thermoelastic fields excited by video pulses in these media (bodies) and materials are presented analytically thanks to exact periodic and unsteady solutions of thermoelasticity equations obtained directly in the time domain outside the limits of Fourier series by analogy with the well-known results of A.B. Schwarzburg.

This study also obtained a hyperbolic heat conduction equation for a moving body and a solution to this equation in a cylindrical coordinate system using Green's functions. The solution obtained in this work corresponds to the hyperbolic theory of heat conduction, which takes into account the finiteness of the heat propagation velocity and allows for a more accurate assignment of strength standards for parts operating under thermodynamic stresses, and in technological processes, for example, in the problem of temperature field distribution in cylindrical samples during their processing with a grinding tool, to optimize the processing mode parameters.

Geometric modeling of solar radiation zones on curved airport terminals coverings during their reconstruction

2026-05-18T19:22:39+03:00

The article considers the current problem of energy-efficient modernization of large transport hubs through optimization of the use of solar energy. The object of the study is the processes of formation of insolation zones on complex curved surfaces of coatings of modern airport terminals using solar-receiving devices.

The authors analyze the specifics of the reconstruction of existing terminals, where changing the roof configuration may be limited by load-bearing structures.The geometry is selected at the pre-design stage, taking into account the requirements for the location of the building relative to the runway (runway), passenger flow conditions, structural safety, and architectural and economic factors.

A geometric modeling algorithm based on discrete geometry and computer-aided design methods is proposed. This allows for accurate calculation of the solar radiation intensity at each point of a curved roof, taking into account geographical coordinates and seasonal changes.Two types of surfaces were selected for analysis - an ellipsoid of revolution and a hyperbolic paraboloid. The developed model allows you to determine the most effective areas for placing photovoltaic panels (BIPV systems) and solar heating systems.Graphical and analytical dependences of the distribution of radiation fluxes were obtained, which allow minimizing overheating of premises in the summer and maximizing heat gain in the winter.

The proposed approach to determining effective solar radiation zones allows optimizing the shape of the airport terminal's coverage at the pre-design stage. This ensures a balance between urban planning constraints (orientation relative to the runway) and energy independence requirements.

If the selected geometry does not provide sufficient insolation, the algorithm involves iteratively searching for shape options or changing the functional purpose of the solar system (for example, switching from full energy supply to hot water supply only).

Underestimation of Vertical Stresses in Soil Foundations Using Analytical Methods: Numerical Substantiation Considering Nonlinear Base Behavior

2026-05-18T20:31:58+03:00

raditional methods for foundation subgrade analysis are frequently based on linear-elastic models, which may lead to inaccurate estimations of the compressible thickness, particularly under high load intensities. This study aims to quantify the error of the analytical corner point method in comparison with advanced nonlinear constitutive soil models across diverse geotechnical conditions. To achieve this, a series of numerical experiments using the finite element method (FEM) was conducted for a reinforced concrete raft foundation with dimensions of 1.8×2.6 m. Two types of subgrades were analyzed: sandy soil (E=30 MPa) and clayey soil (E=15 MPa). Calculations were performed using various constitutive models, with a primary focus on the Hardening Soil Small Strain (HSsmall) model, which accounts for strain-dependent stiffness degradation.

The research results verify the hypothesis of "vertical stress concentration" within nonlinear models. It was established that the geometry of the "stress bulb" undergoes significant transformation depending on the soil type: in clayey subgrades, a more intensive stress penetration depth is observed compared to the predictions of the elastic solution. Furthermore, a redistribution of contact pressures in the central and corner zones of the raft was recorded. It is proven that the error of the analytical method increases proportionally to the load magnitude and the decrease in the soil's deformation modulus. The simulation results demonstrate the necessity of implementing correction factors for the standard tabular stress distribution coefficients α. The application of the HSsmall model provides the most reliable representation of the stress-strain state (SSS), which is critical for avoiding the underestimation of stresses in the deeper layers of the foundation base.

Structural design under blast loading: from simplified models to advanced dynamic analysis

2026-05-18T20:47:41+03:00

Relevance. In the context of the full-scale war of russia against Ukraine, the issues of ensuring the reliability and survivability of buildings and structures under blast loading caused by aerial attack means, missile and artillery strikes, and other damaging factors are of particular relevance.

Modern engineering practice provides the use of several principal methods for analyzing structures under blast wave effects, among which the most widely applied are the quasi-static method, the impulse (shock impulse) method, and the direct integration method of the equations of motion.

Despite the availability of these methods, their practical application in the design of protective structures is complicated by the lack of generalized recommendations for selecting an appropriate calculation method depending on loading conditions, structural configuration, and the consequence class of the facility.

The aim of this study is to systematize existing methods for analyzing building structures under the action of blast waves, to examine their advantages and limitations, and to improve approaches to modeling loads and the dynamic response of structures.

Results. The work summarizes the main methods of calculating building structures for the effects of an blast-shock wave, the shock impulse method, and the method of direct integration of equations of motion, which allowed us to determine their areas of effective application. It was established that the quasi-static method is advisable to use at the initial stages of design to obtain engineering estimates, while the method of direct integration of equations of motion provides the most accurate results in a detailed analysis of the operation of structures under the action of a blast-shock wave. The results of the study can be used to improve the regulatory framework in the field of designing structures for special impacts.

Analysis of the optimal speed-based start-up mode of the tower crane swing mechanism under control limitations

2026-05-18T21:38:16+03:00

A comparative analysis of the optimal starting mode of the tower crane slewing mechanism in terms of speed under asymmetric (task 1) and symmetric (task 2) constraints on optimal control is presented in a scientific article. A two-mass dynamic model was used for the research, whose motion in time is described by a system of two second-order differential equations. In the course of further research, the system of two second-order differential equations was reduced to a single fourth-order differential equation. After performing the appropriate transformations, the fourth-order differential equation was presented in Cauchy form and the initial and final conditions of motion were given, under which the load oscillations will be eliminated after the turning mechanism reaches a steady speed.The optimisation task itself was reduced to the task of unconditional minimisation of a complex integral-terminal functional, where the terminal component is responsible for the fulfilment of the final boundary conditions, and the integral component is responsible for the speed of the mechanism. A series of 54 experimental studies (27 for each of the tasks under investigation) was planned, in which the independent factors were the length of the flexible suspension (which was 10, 15 and 20 metres), the load projection (which was 5, 15 and 20 m), and the load mass (which was 500, 2000 and 5000 kg).During the theoretical studies, the main assessment was carried out according to the following indicators: the duration of the system acceleration to the steady-state speed value; the maximum deviation of the flexible suspension of the load from the vertical; the maximum and root mean square values of the power in the drive and the acceleration of the load.The results of the analysis showed that when using asymmetric constraints for optimal control (task 1), the acceleration time of the studied system to a steady state speed increases compared to symmetric constraints (task 2) in the range from 1.23 to 15. 28 %, and the maximum values of kinematic characteristics decrease from 5.46 to 42.85 % and energy indicators from 0.48 to 27.83 %.

An innovative methodology for restoration and strengthening of reinforced concrete structures via concrete overlay and its CAD-implementation during repairs and reconstruction

2026-05-19T19:15:10+03:00

he present work introduces an innovative methodology for the restoration and strengthening of reinforced concrete structures through concrete layering, based on the application of advanced Hilti post-installed rebar and shear stud systems. The proposed approach enables the realization of full monolithic connectivity at the "old-to-new" concrete interface, ensuring effective shear force transfer in accordance with international technical reports EOTA TR 066 and TR 069. This methodology offers extensive possibilities for strengthening flexural and compression elements during building reconstruction, allowing for a significant reduction in embedment depth and optimization of material consumption without compromising structural integrity. Particular emphasis is placed on the integration of calculation algorithms into a unified digital environment through specialized software and modern CAD/BIM systems. Such digital implementation ensures a seamless design process: from processing non-destructive testing data of existing reinforcement to the automated generation of detailed 3D models of reinforced nodes within a CAD-environments. The adoption of this methodology minimizes risks and errors, guarantees the precision of reinforcement geometric parameters, and ensures high operational reliability of restored structures under complex loading conditions. The proposed solution serves as a versatile tool for engineers seeking to combine cutting-edge construction technologies with the advantages of automated design to enhance the longevity of the building stock.

Kinematic synthesis of a combined lambda-type mechanism

2026-05-19T19:31:25+03:00

The paper considers the process of kinematic synthesis of a combined lambda-type mechanism with an interval of quasi-linear motion of the coupler point, which belongs to third-class straight-line guiding mechanisms. The relevance of the study is determined by the widespread application of lambda-type mechanisms in modern mechanical engineering, where they enable the realization of complex motion trajectories with a relatively simple design and convenient control. The proposed combined mechanism provides motion of the coupler point in both forward and return strokes along a quasi-linear trajectory, which significantly expands its functional capabilities.

In the course of the research, the deviation of the quasi-linear trajectory from an ideal straight line was analyzed. It was established that the maximum nonlinearity is only 1%, which indicates high accuracy of the realized motion. In addition, it was determined that the maximum length of the quasi-linear interval reaches 400% of the crank length, which is a significant indicator for mechanisms of this class and confirms the efficiency of the selected kinematic scheme.

Based on the performed synthesis, optimal geometric parameters of the combined lambda-type mechanism were determined, under which full correspondence of the coupler point trajectory to the straight-line interval of the base mechanism is ensured. A distinctive feature of the proposed solution is the preservation of straight-line motion in both forward and return strokes, which creates the prerequisites for a significant increase in the productivity of machines and mechanisms using this kinematic structure.

The obtained results can be used in the design of highly efficient mechanical engineering systems, where motion accuracy, compact design, and increased operating speed are essential.

Research of the stress-deformed state of a protective shell structure upon impact of shell fragments

2026-05-19T20:51:03+03:00

Modeling of influence of shell fragments on the protective structure state is difficult and not sufficiently studied. This is due to the presence of wide spectrum of structural decisions of the constructions and different types of ammunitions. Ammunitions have different physical and technical characteristics, such as: a diameter, length and mass of the shell; a type and mass of explosive in TNT equivalent; a type and mechanical characteristics of shell material; time of detonation; amount and mass of fragments with maximal flight length and velocity. The amount of fragments depends on a construction a shell, which is increased with the increase of shell caliber, power of explosive, coefficient of filling and diminishing of strength and viscosity of shell metal. Therefore, in connection with the probabilistic parameters of shell fragments, kind and dispersion area on the surface of protective construction, it is necessary to apply the methods of probability theory and experimental test data. In article the stress-deformed state of the protective shell structure upon impact of shell fragments was investigated. Characteristics of shell fragments and their distributing on the affected construction area according to empiric formulas and experimental test data were determined. Static and dynamic behavior of protective shell structure upon impact of shell fragments was investigated in the software of finite element analysis NASTRAN. The nonlinear static problem and static stability of shell structure taking into account elastic-plastic property of its material were solved by the Newton-Raphson method and the Lanczos method respectively. The dynamic calculation of protective shell structure contained determination of forms and frequencies of natural vibrations using the Lanczos method and investigation of forced vibrations by the Newmark method. Characteristics of the stress-deformed state of protective shell structure and realizations of its reactions on the action of shell fragments were received. The presented numeral method simplified the process of modeling of shell fragments action on the protective construction and allowed to research its stress-deformed state.

Features of the distribution of stresses in the soil base of piles depending on the method of their placement in the plan

2026-05-19T21:16:31+03:00

The improvement of existing methods for calculating new structures and their elements in accordance with current regulatory documents in the field of construction is much slower than the development of production technologies. This, in turn, limits the implementation of modern technical solutions and technologies, and also complicates the creation of optimal conditions for their effective use and calculation. For example, calculations of piles and pile foundations for bearing capacity and base deformations according to DBN V.2.1-10-2009. Amendment 1 does not provide a sufficient level of accuracy and reliability due to a number of factors: the use of averaged tabular values of soil resistance, failure to take into account the state of the soil along the length of the pile, its origin and compression pressure, the use of deformation characteristics of soils obtained from the results of field tests, etc.

The paper presents the results of an analytical study of the spatial distribution of vertical stresses in the soil base in the zone located under the lower end of the driven hanging piles of square cross-section 30x30cm in size with their different location in the plan. The construction of stresses was based on mathematical modeling of the distribution of stresses in the soil base developed by the Department of Geotechnics of the KNUBA for a single pile, which allows obtaining satisfactory results in comparison with experimental data, as well as a pile bush of two piles with different positions of the pile in the plan. The construction of the nature of the stress distribution in the horizontal plane below the pile tip was carried out using theoretical solutions based on experimental field studies of deformations of the base of sandy and clayey soils in field and laboratory conditions. Special attention is paid to the influence of the pile placement configuration on the change in the shape, size and area of the zones of the stressed state in the soil environment from the transfer of load by the lateral surface and the lower end of the pile. A comparative analysis of the geometric characteristics of conditional foundations determined by different methods, in particular, based on classical theoretical provisions and modern analytical approaches, has been performed. The results obtained allow a deeper understanding of the mechanism of interaction of piles with the base, and can also serve as a basis for refining calculation models when designing pile foundations, taking into account the spatial effect and the influence of the pile bush configuration.

Research on the influence of soil base stiffness reduction on the stress-strain state of the “base-structure” system

2026-05-19T21:26:18+03:00

This article investigates the complex influence of rheological processes, specifically consolidation and viscous creep of the soil skeleton, on the evolution of the stress-strain state of the spatial "soil base - foundation - structure" system over time. The relevance of the work is driven by the need for accurate forecasting of post-construction settlements to ensure the operational reliability of buildings, especially under complicated geological conditions. Using the "LIRA-SAPR" software package and the "MONTAZ+" subsystem, a methodology for the staged modeling of changing equivalent soil stiffness was implemented. The theoretical foundation of the numerical model is the classical linear hereditary creep theory of Boltzmann-Volterra, utilizing the exponential relaxation kernel of Maslov-Arutyunyan. This justified the application of a transitional stiffness coefficient K, which non-linearly degrades from 1.0 (instantaneous elastic state at the moment of external load application) to differentiated values of K_∞ (ranging from 0.85 for sands to 0.65 for weak clays depending on their physical nature) after the completion of hydrodynamic consolidation processes. The research encompassed several representative computational scenarios: 1) load on a foundation slab without accounting for superstructure spatial stiffness; 2) joint operation of a three-story reinforced concrete frame with a homogeneous soil base; 3) joint spatial operation of the building with heterogeneous geology, complicated by the presence of lenses of weak soil (using various schemes for differentiating rheological properties). The modeling results conclusively prove that ignoring the spatial stiffness of the load-bearing frame leads to an overestimation of maximum absolute settlements by more than 28%. At the same time, incorporating the frame into joint operation with a time-degrading base generates a load-relieving effect in the central zone of the slab (the "hanging" effect), with a subsequent redistribution of contact pressure to the periphery. It was established that using a traditional averaged creep coefficient for all layers artificially overestimates stabilized settlements. The correct application of differentiated coefficients, which takes into account the ability of low-compressibility sands to maintain long-term stiffness, demonstrates a significantly softer redistribution of forces in load-bearing elements. The obtained regularities expand the understanding of the mechanics of interaction between structures and visco-elastic bases and prove the absolute necessity of considering the time factor during the design stage to prevent progressive collapse.

Analysis of the stress-strain state of a reinforced concrete collector considering soil-structure interaction

2026-05-19T21:50:37+03:00

The paper analyzes the stress-strain state (SSS) of a rectangular reinforced concrete collector, constructed during the development of the Syretsko-Pecherska metro line in Kyiv. The study aims to verify design solutions by performing duplicate calculations and comparing simplified engineering approaches with a comprehensive 2D model that accounts for the "soil-structure" interaction. Three calculation schemes were employed to evaluate the SSS: a continuum 2D model in "Midas GTS NX" software (considering the "soil-structure" system as a single unit) and simplified 2D/3D models in "Lira-SAPR" software using subgrade reaction coefficients. The study accounted for dead loads (soil weight, pavement) and live loads from vehicles ("NK-100", "qA15") across six load combinations. Significant discrepancies were found between the results of the refined and simplified models. Simplified methods were shown to lead to a substantial underestimation of forces in critical zones. Specifically, bending moments in the collector's top slab were 15–24% higher in the span and 4.5 times higher in the corner joints compared to simplified analytical results. This is because the continuum model accounts for the actual geometry of the joints and the complex mechanism of stress redistribution within the soil mass surrounding a rigid structure. The study confirms that simplified models based on an elastic foundation lead to incorrect distribution of internal forces along the frame perimeter. For high-precision calculations of deep-seated reinforced concrete collectors, numerical modeling in a continuum formulation is recommended to ensure the reliability of reinforcement solutions.

Optimization of bidirectional data exchange processes between BIM-platforms and structural analysis software using visual programming tools

2026-05-19T22:01:41+03:00

The implementation and use of software focused on BIM technologies in the design activities of construction organizations require additional costs and a rather long transition period. In the absence of economic incentives and customers' interest in using BIM technologies, there is an impression of a lack of practical justification for their use by design organizations. However, there are a number of advantages underlying these technologies, consisting in the ability to create and operate a large database of a construction object, which in turn opens up the possibility of automating modeling processes. The paper considers approaches to automating modeling processes depending on the tools used.

The main focus of the work is on highlighting the possibilities of improving information exchange processes between software suites based on BIM technologies (Autodesk Revit) and computational software based on the finite element method (SCAD Office) using visual programming. This allows solving various types of tasks to accelerate and improve the quality of analytical models based on information models and creates opportunities for the computational software to provide feedback to the information model in the Revit environment. Two algorithms are presented, implemented by means of visual programming in the Dynamo environment. The first one allows to automatically supplement the original analytical model with foundation elements and adjust it if necessary to ensure its connectivity. The second one allows to automatically update the sections of metal structures based on information obtained in the SCAD Office environment.

Deep Well Trajectory Optimization Using the Lagrange problem

2026-05-21T19:30:14+03:00

In the conditions of the modern oil and gas industry, the construction of wells of various types is carried out, including vertical, two-dimensional and three-dimensional directional, as well as branched wells. The selection and formation of the trajectory of the well is a complex engineering and technical task and is carried out taking into account the depth and geological structure of the oil and gas-bearing deposit, the physical and mechanical properties of rocks, the degree of their hardness, structural heterogeneity, permeability and other geological and technological factors.

The set of these parameters has a decisive influence on the technical and economic indicators of drilling, in particular the final cost of well construction and its operational productivity.

In order to increase the overall efficiency of the functioning of wells, reduce the costs of drilling them, and increase the mechanical speed of drilling, methods of optimal nonlinear control are widely used in the practice of drilling operations. The use of these methods makes it possible to more accurately control the process of formation of the well trajectory, to adapt the drilling parameters to the changing geological conditions and, as a result, to achieve higher indicators of economic and technological effectiveness.

Using the application of differential geometric correlations, a nonlinear mathematical model of the well contour was developed in the form of a system of nonlinear ordinary differential equations. Different objective functions are selected, reflecting the full integral curvature of the well axis, its length and the cost of its penetration; additional restrictions separating permitted and prohibited areas are selected. Trajectory curvature and torsion functions are used as control variables. Discrete continuous correlations are considered, as well as non-linear programming methods are applied.

Based on the method of projection of the gradient (antigradient) of the objective function onto linearized constraints on the plane, a step-by-step algorithm for approaching the optimal state has been developed. Newton's method is used for correcting corrupted constraints at each step of calculations. The results of the numerical analysis are discussed.

Fundamental analysis of the dynamics of discrete-continuous rotary systems of tracked machines with mechatronic control systems

2026-05-21T19:53:30+03:00

When constructing a model of tracked machines, it is not possible to limit oneself to discrete parameters – masses and rigidities – if the shafts of the rotary system have significant masses and lengths. In long shaft lines, wave processes may occur under the action of external disturbances applied to the discrete masses of the system. The complexity of analyzing wave processes in discrete-continuous systems that arise in them when operating modes change forces us to look for simpler solution methods that still give satisfactory results in terms of accuracy. One such method is to replace the discrete-continuous model with a discrete one, which differs slightly in its dynamic properties from the original. In this case, the finite element method is used, into which each section of the shaft with discrete masses concentrated on it can be divided, and the shaft itself is a distributed mass. In this regard, there is a need to formulate a criterion that allows establishing an equivalent system of discrete masses that replace the discrete-continuous system. A similar task is the analysis of dynamic processes occurring in hydromechanical systems, which include long pipelines and large masses of hydraulic mechanism links.

The paper presents equations of motion for a tracked vehicle shaft with distributed mass, analyzes a weighted shaft with masses at its ends, and determines the natural frequencies of a multi-mass rotary system of a tracked vehicle, taking into account the shaft mass. The Prager method was used to find the natural numbers of the system. The results of calculating the amplitudes of shaft vibrations can be used to find the maximum values of the moments of elastic forces of the shaft sections. The change in the moment of elastic forces has a beating character. Each of the natural frequencies of a system with several degrees of freedom corresponds to a certain form of vibration, therefore, at close values of natural frequencies, there is a continuous transition from one form of vibration to another and, accordingly, a periodic exchange of energy between individual sections of the system while maintaining their energy constant. Control over the movement of the system in transient processes (start-up) can be carried out by mechatronic control systems.

Methodical aspects of application of visual aids when teaching the «Kinematic Analysis» module to engineering students

2026-05-21T20:38:05+03:00

Structural mechanics is one of fundamental disciplines in training future specialists. Laws of mechanics are often complex for students because to understand them they need to have the preliminary mathematical background and the spatial imagination. It is often difficult for students to understand the physical nature of deformation processes looking only at drawings and theoretical calculations that they see and perform on paper or the university board. The integration of traditional teaching methods and innovative visual aids into the educational process can help students to understand the material more easily and to learn it more effectively. This paper examines some methodical aspects of the practical effectiveness of application of such visual aids as construction sets in «Structural Mechanics» classes at higher education institutionswhen teaching the «Kinematic Analysis» module to students studying in civil engineering. Construction sets can be considered as visual aids for modeling that can be useful students and instructors. Models assembled from construction sets can help the instructor:demonstrate methods of connecting disks using simple examples directly within the classroom; explain why the specific number of connecting devices is the minimum requirement for connecting the certain number of disks; explain why specific links arrangements cause the system to become instantaneously unstable; explain the relationship between real and virtual hinges; explain interconnections between disk connection methods when representing certain elements of the analytical model as others. Learning the kinematic analysis within the structural mechanics with application of construction sets can help students: to improve the spatial imagination; to understand how various connecting devices work in the analytical model; to understand methods of connecting discs and joints and their interconnections among themselves; to transform schemes from paper drawings into visual models; to promote the understanding principles of combining various elements into the complex construction structure.

Survivability assessment of shell structures under blast loads

2026-05-21T20:52:06+03:00

Shell structures in the form of vertical steel storage tanks for petroleum products constitute a critical element of modern industrial infrastructure and are designated as strategic facilities. Ensuring their survivability under blast loads represents a pressing engineering challenge. In the context of blast resistance, the notion of survivability should be interpreted with an understanding that the complete preservation of a thin-walled shell structure under extreme impact is practically unattainable. The article regards the survivability of thin-walled vertical steel tanks subjected to impulsive loading generated by a surface blast. The consequences of such loading depend not only on its spatial characteristics but also on the mechanical and geometrical properties of the structures. The classification of the load regime - whether impulsive or quasi-static - is determined by the ratio between the load duration τ and the fundamental vibration period T of the structure. For any mechanical system, it is possible to construct graphical dependencies in which each point defines the decisive boundary between impulsive and quasi-static regimes as a function of the fundamental frequency f, distance R, and TNT-equivalent charge mass W. For given f, R, and W, such graphs make it possible to determine whether dynamic effects dominate the response. Finite-element models have been developed to simulate potential damage scenarios for the cylindrical shell of a 20000 m³ tank exposed to blast loading. Three scenarios have been considered: minor plastic strains; the onset of wall fracture; and severe failure of the frontal sector of the tank. The predicted structural response corresponds well to experimentally observed failure modes that occur under surface blast conditions for thin-walled cylindrical shells. Numerical simulations have been conducted for various combinations of R and W. Obviously, only the first scenario is fully consistent with the engineering concept of survivability. For this regime, the structural integrity and operability of the tank are preserved, and von Mises stresses remain within or near the elastic limit of the material. Survivability is considered assured if, for any point on the shell surface, the maximum von Mises stress does not exceed the yield stress. This criterion implicitly constrains the possibility of a local buckling.

Some aspects of the restoration of transport infrastructure facilities

2026-05-21T21:19:38+03:00

This article examines issues related to the restoration of transportation infrastructure, specifically: the acquisition of land parcels for the construction of transportation facilities and the selection of optimal structural designs for road bridges. As of early 2022 (prior to the full-scale invasion), Ukraine’s bridge infrastructure had a stable structure and was undergoing active modernization as part of the “Great Construction” program (2020–2021). Due to the full-scale invasion, Ukraine’s transportation infrastructure has suffered unprecedented damage. As of early 2026, the total number of destroyed or damaged bridges and overpasses exceeded 346 (in government-controlled territories). On state roads, specifically on key routes, 157 bridges were destroyed. To ensure logistics, approximately 100 temporary crossings and modular bridges were constructed. In order to select rational bridge structures, that will be built to replace the destroyed ones, the structural systems in which its elements damage does not lead to the destruction in whole and the structure will be capable to restoration were studied and proposed. These are structures in which the failure of its elements leads to formation of such systems of the damaged structure that would be geometrically stable. Two key variants have been proposed: an arch bridge system and a truss bridge system with polygonal bottom chord along the outline of an arch. By analyzing the internal force diagrams for initial analytical models and the considered destruction cases, the conclusion about the most acceptable system was drawn. Since bridges are linear transport infrastructure objects, for the construction of which authorities have the right to purchase private land plots with the owner’s consent, the issues of land alienation for the construction and reconstruction of bridges in Ukraine and the legislative acts regulating these actions were examined.

Flexible architectural and structural prefabricated frame system of residential buildings of the "RAPL" type

2026-05-21T21:32:37+03:00

The article is devoted to the development of prefabricated, frame frame-plate systems for housing construction in Ukraine. As a result of the preliminary analysis of frame systems, shortcomings were identified in both industrial prefabricated housing construction and monolithic and frame - this is a narrow gap between transverse load-bearing walls or pylons, which does not allow for reconstruction, design with planning options.In wartime, under the influence of explosive shells, as well as in difficult engineering and geological conditions and seismic areas, insufficient stability of structures is revealed, brittle destruction of nodal connections of floor slabs with columns occurs. Therefore, the "RAPL" system was developed for housing construction for ordinary and difficult conditions, which ensures the strength and stability of load-bearing structures, is economical, allows free and diverse use of the area of apartments and is suitable for the prospective development of housing construction, taking into account the possibilities of reconstruction of the building. The “RAPL” system is suitable for use in difficult operating conditions, it is the safest structural and frame system of the frame type with loop joints between columns and crossbars. Loop joints are the most important part of the frame frame design, which do not require welding. The “RAPL” system uses pre-stressed reinforcement in the frames with anchoring to the outer columns, which greatly improves the operation of structures, especially in seismic zones and during shell explosions. Such an architectural and structural system provides flexibility in architectural and planning solutions.

Dynamic analysis of the slewing mechanism of a jib crane with a payload suspension in the form of a double pendulum

2026-05-21T21:42:27+03:00

Gripper devices with weights close to the payload weight are used when jib cranes perform installation work on complex structures. For such cases, the flexible payload suspension is represented by a double mathematical pendulum model. The paper deals with the dynamics of the slewing mechanism of a jib crane with a flexible payload suspension in the form of a double pendulum. The purpose of this study is to construct a mathematical model and perform a dynamic analysis of the jib crane slewing mechanism with a double mathematical pendulum payload suspension. The slewing mechanism is represented by a dynamic model with four degrees of freedom (4-DoF). Based on this model, a mathematical model of the jib crane slewing mechanism is constructed using Lagrange equations of the second kind, forming a system of second-order ordinary differential equations. In this model, the driving torque of the electric motor is described by its dynamic mechanical characteristic. As a result of numerical solving of the equations, the kinematic, dynamic, and energy characteristics of the jib crane slewing mechanism are determined. The study investigates the main movement of the drive mechanism, as well as high-frequency oscillations of drive elements and low-frequency oscillations of the payload and gripper on the flexible suspensionIt is revealed that the dynamics of the slewing mechanism depend on the nature of the driving torque change, while low-frequency oscillations of the payload and gripper practically do not dampen and continue throughout the entire movement cycle.

To reduce dynamic loads and high-frequency vibrations in the drive transmission mechanism, as well as low-frequency vibrations of the gripping device and load on a flexible suspension, it is recommended to select modes of smooth change of the drive torque during start-up and braking, which ensure the desired movement of the load on a flexible suspension.

Influence of non-homogeneity parameters on the stress state of long non-thin cylindrical elliptical shells

2026-05-21T22:00:26+03:00

Cylindrical shells of circular and non-circular cross-section are used as structural elements in many industries, as well as computational models in the study of the properties of newly created materials that can increase the operational capabilities of these structural elements.

This research investigates long non-thin cylindrical elliptical shells made of a continuously non-homogeneous material, the elastic properties of which vary along the thickness. The shells are under the action of internal pressure under conditions of hinged fastening of the ends.

The subject of research is the stressed state of the shells and, as a result, the establishment of dependencies between its characteristics and the parameters of the law of change of the moduluselasticity of the material.

The purpose of the work is to conduct a numerical analysis of the stressed state of shells of this class depending on the law of change of the elastic properties of the material. The problem is solved using a spatial model of the linear theory of elasticity based on the method of approximation of functions by discrete Fourier series. In this case, an analytical method of separation of variables in two coordinate directions is used, with parallel use of approximation of functions by discrete Fourier series and a stable numerical method of discrete orthogonalization.

The stress state of the considered shells is analyzed depending on two parameters of the law of change of elastic properties of the material along the thickness.

Assessment of the stress-strain state of a retaining wall taking into account its spatial rigidity in dense urban development conditions

2026-05-21T22:17:34+03:00

In the context of modern construction development, especially in densely populated urban areas, the use of deep excavations has become an integral part of the construction of multi-level car parks, bomb shelters, high-rise buildings, etc. Excavations often reach depths of more than 7-10 metres, which requires the development and implementation of engineering protection measures to prevent soil collapse and reduce the impact on existing buildings. One of the most common structural solutions is the construction of retaining walls from bored piles. In order to select effective parameters for retaining walls and take into account the impact of excavation and enclosing structures on existing buildings, it is necessary to conduct a comprehensive analysis of the stress-strain state of the elements of the ‘soil - retaining walls - existing buildings’ system using numerical modelling.

The study evaluates the impact of numerical modelling methodology on determining the stress-strain state (SSS) of the elements of the ‘soil – retaining walls – existing buildings’ system for the construction of a deep excavation in the dense urban development of Kyiv. The results of flat (2D) and spatial (3D) finite element models (FEM) are compared with empirical data from geodetic monitoring (additional settlements of existing buildings and horizontal displacements of retaining wall piles).

The modelling was implemented in the Plaxis software package using the Hardening Soil Model (HSM) elastic-plastic model with the Coulomb-Mohr strength criterion, which takes into account the nonlinear dependence of soil deformation characteristics on stress levels. The modelling takes into account the following sequential stages: formation of the initial stress-strain state of the soil base during its sedimentation, change in stresses due to loading from the foundations of previously constructed structures, and the effects of soil unloading during the development of deep excavations.

The results of the modelling allow us to conclude that the use of spatial FEM makes it possible to more comprehensively assess the stress-strain state of the elements of the ‘soil – retaining walls – existing buildings’ system, taking into account the factor of spatial rigidity.

A conceptual model for quality assessment of frame strengthening during building reconstruction

2026-05-21T22:42:06+03:00

The strengthening of frame buildings during reconstruction is a complex engineering task that requires the coordinated consideration of structural reliability, technological efficiency, and long-term sustainability. In practice, the selection of structural-technological solutions is often based on expert judgment and fragmented criteria, which limits transparency and increases uncertainty in decision-making, especially under constrained reconstruction conditions.

This paper proposes a conceptual model for quality assessment of frame strengthening as a core component of a decision support system. The model is based on a systemic and life-cycle-oriented approach and integrates three interacting groups of criteria: reliability, efficiency, and sustainability. Quality is interpreted as an integral result of the interaction between these criteria rather than as a single performance indicator.

The proposed structure formalizes the hierarchy of criteria and indicators, allowing the assessment process to account for structural performance, technological feasibility, resource efficiency, environmental impact, and organizational stability throughout the life cycle of the building. The model does not represent a comparative optimization algorithm but provides a methodological framework for ensuring logical consistency and transparency in the evaluation and substantiation of strengthening solutions.

The developed conceptual model creates a theoretical basis for further implementation of digital decision support tools, multi-criteria analysis methods, and BIM-based quality management systems in building reconstruction projects.

Semi-analytical finite element method for solving three-dimensional problems of thermo-visco-elasto-plasticity of prismatic bodies with material damage consideration

2026-05-21T22:55:49+03:00

The paper presents a methodology for solving three-dimensional problems of thermo-visco-elastoplasticity of prismatic bodies using the semi-analytical finite element method. An approach to modeling geometrically complex heterogeneous structures subjected to spatially and temporally varying mechanical and thermal loads is described. It is noted that accounting for nonlinear deformation processes, such as plasticity and creep, requires step-by-step iterative algorithms. The use of nonhomogeneous skew prismatic finite elements is proposed, in which the formulas account for the variability of the metric tensor. This makes it possible to significantly reduce the number of unknowns and improve the accuracy of approximating the stress–strain state. An algorithm for solving thermo-visco-elastoplastic problems has been developed, which includes two iterative cycles: an inner cycle for solving the system of linear equations and an outer cycle for the nonlinear problem. The approach is based on the Newton–Kantorovich iterative procedure. A distinctive feature of the method is the use of displacement extrapolation at the current step based on the results of the previous step, which ensures faster convergence. An example of modeling the deformation of a non-uniformly heated cube is presented. For this example, the semi-analytical finite element method results showed a discrepancy of less than 5% compared with known reference data, confirming the reliability of the method. The analysis shows that the maximum stresses are concentrated in the center of the cube, where a state close to hydrostatic compression is realized, while plastic deformations reduce the stress level by up to 35%. The application of the algorithm with displacement extrapolation made it possible to reduce the number of iterations by more than half and decrease computational costs by 1.5–3 times. The obtained results confirm the efficiency and accuracy of the proposed approach for three-dimensional thermo-visco-elastoplastic problems of complex prismatic bodies.

Physics-Informed Neural Networks for Analysis of Spatial Beam Structures: A Kinematic Decomposition Approach

2026-05-21T23:09:44+03:00

The design of critical steel structures faces a persistent dilemma between computational speed and physical fidelity. While classical 1D beam elements are computationally efficient, they often fail to capture complex spatial effects like non-uniform torsion and cross-sectional distortion, whereas detailed 3D solid finite element models (FEM) offer reference accuracy but come at a prohibitive computational cost, making them unsuitable for real-time generative design or multi-objective optimization. This study proposes a novel Physics-Informed Neural Network (PINN) architecture designed to function as a real-time “AI-Surrogate” capable of predicting the stress-strain state of spatial members with the accuracy of a high-fidelity 3D FEM model but at analytical speeds. The proposed approach utilizes a Kinematic Decomposition strategy, separating the displacement field into a macroscopic “spine” behavior and a field of local cross-sectional deformations. This effectively reduces the dimensionality of the problem and allows for training on a compact dataset of 10,000 samples. To address the “linearization trap” and the vanishing gradient problem associated with predicting higher-order derivatives (curvature and bi-moments), we introduce a Coordinate Scaling technique. This method normalizes the derivative space, ensuring numerical stability and physical consistency of the solution. Validated against nonlinear 3D solid FEM simulations (Ansys), the model demonstrates high precision, achieving a Mean Absolute Error (MAE) of 0.08 mm for deflections and 0.2 mrad for torsion angles. Furthermore, the specialized physics-informed loss function successfully minimizes the curvature error to 1.510^–4 m^–2, ensuring the accurate recovery of internal forces. The results confirm that the proposed PINN architecture effectively bridges the gap between the speed of beam theories and the accuracy of volumetric models. The introduced Coordinate Scaling method proves critical for learning differential relationships in mechanics, paving the way for the next generation of real-time structural analysis tools.

Modelling of momentless thin-walled shells of revolution by vector rational parametric curves of the second degree

2026-05-22T10:11:26+03:00

The completed scientific research proposed the use of vector rational parametric curves of the second degree for modelling of momentless thin-walled shells of revolution with the determination of meridian and hoop forces under axisymmetric loading. This approach represents the dissemination of progressive experience in design of complex technical objects in the domestic aviation industry. The appropriate mathematical apparatus was presented and its application was demonstrated. The obtained results were compared with the corresponding ones available in the literature. The greater flexibility and productivity of vector parametric geometric modelling tools compared to conventional algebraic ones has been substantiated. The generalizing nature of the developed methodology was demonstrated in relation to the existing development of individual models for spherical, conical, ellipsoidal, paraboloidal, hyperboloidal, toric and other middle surfaces of thin-walled shells. This further emphasizes the effectiveness of the presented mathematical apparatus and its suitability for implementation in the environment of computer information technologies. In addition to theoretical achievements, the proposed method also has important practical significance, illustrated by the example of the domes of Orthodox temples and chapels. The highlighted issue is relevant for the current historical stage of Ukraine's development, associated with military actions on its territory. The latter determines the destruction of these facilities, the need for their restoration and the construction of new ones. These circumstances are also caused by the growing number of people turning to higher powers for help. The presented approach successfully implements the desired variety of shapes and sizes of the analyzed architectural structures in accordance with the requirements of ensuring the individuality of Christian sacred buildings. The presented tools are appropriate at the stage of preliminary design, when a significant number of dome variants are considered for the purposes of comprehensive optimization, and detailed processing of each of them requires significant costs or is impossible due to the lack of necessary information. The discussed topic deserves further development by extending it to more complex operation cases, in particular under the action of non-axisymmetric loads.

Multi-layeredspatial–hierarchical model of protected zones in buildings and structures

2026-05-22T10:27:08+03:00

The growth of military threats and increased risks for the civilian population make the problem of increasing the level of security of buildings and integrating protective functions into their spatial structure more urgent. Traditionally, the issue of population protection is considered mainly in the context of creating specialized protective structures or increasing the strength of individual structural elements. At the same time, the spatial and structural organization of a building as a factor in the formation of potentially protected zones has not been studied sufficiently.

The purpose of the study is to develop a multi-level structural and spatial model of protected zones in the structure of residential and public buildings.

The study uses methods of analyzing scientific sources, comparative analysis of international regulatory documents and generalizing the practice of organizing protective spaces in different countries. The results of studies of the impact of explosive loads on buildings, the principles of increasing the resistance of structures to dynamic impacts, as well as international experience in integrating protected spaces into the structure of buildings are analyzed. Particular attention is paid to regulatory requirements and practical solutions used in NATO countries, in particular in Israel, Singapore, Finland, Switzerland, Norway and the United Kingdom.

As a result of the study, a concept of a multi-level structural-spatial model of protected zones in a building was formed, which is based on the differentiation of the internal space of the building depending on its location relative to the external shell and the structural core. The proposed model involves the allocation of several spatial levels of protection: the external shell of the building, transitional (buffer) zones, internal spaces and the structural core.

The role of the structurally separated core of the building as the central element of the system of protected zones is substantiated, as well as the value of transitional spatial layers, which can perform the function of an additional structural barrier between the external environment and the internal zones of the building.

For an analytical assessment of the potential level of protection of different parts of the building, a space protection index is proposed, which takes into account the spatial location of the room, the number of structural barriers, the characteristics of the enclosing structures and the proximity to the structural core of the building.

The proposed model is universal in nature and can be used for the analysis of residential and public buildings, as well as used as a theoretical basis for further research into the architectural typology of protected spaces and the development of recommendations for improving the security of buildings in the face of modern military risks.

Optimal design of the stability of a minimum surface shell on a rectangular contour with accounting for geometric nonlinearity under thermo-stress loading

2026-05-22T10:42:41+03:00

The field of optimal design for spatial thin-walled structures has been developing since the 1950s. In general, when studying optimal design, one must determine all optimized strength characteristics based on the second group of limit states. These strength characteristics include: strength, stability, deflections, and deformations in spatial thin-walled structures. The implementation of optimal design with these strength characteristics occurs simultaneously with the weight of the spatial thin-walled structure.

Multi-criteria parametric optimization is achieved by incorporating two objective functions simultaneously into the mathematical framework and research methodology for spatial thin-walled structures. These include weight or volume, and strength characteristics. Such objective functions include: weight and strength, weight and stability, weight and deflections, and weight and forced or natural frequencies of vibration of a spatial thin-walled structure. The specificity of such studies lies in the fact that when investigating these objective functions, it is necessary to employ three different types of calculations.

Optimal design problems can be formulated in both linear and nonlinear settings. Nonlinear formulations include geometric and physical ones. This scientific article examines the geometric nonlinear formulation, which allows for the consideration of actual displacements and stresses when determining the bifurcation point. The instability coefficient λ is, in fact, the bifurcation point of the minimal surface.

The use of this algorithm leads to a new approach in the design of building structures. This type of optimal design offers significant economic benefits when creating future structures. This approach can be applied not only to shell structures but also to beam and plate structures. An important aspect is the material, which must be isotropic; this includes metals and composites.

The analysis of the objective function is shown in Figure 1.14. We were able to reduce the weight of the minimal surface shell from 52,593 kg to 40,391 kg, which represents a 23.12% reduction. At the same time, we were able to redistribute the thickness of the minimal surface shell to the loaded zones, which made it possible to reduce the buckling coefficient λ from 2.58 to 1.06. This significant result was achieved through a geometrically nonlinear formulation of the problem. Automation, in the optimal design approach, makes it possible to determine the required thickness of the minimal surface shell.

Research on the impact of diesel generator fire on building structures of enclosed spaces

2026-05-22T11:17:41+03:00

Actuality. Violation of operating rules and underestimation of real temperature regimes of fires in generator stations lead to an increase in fire hazard and the risk of loss of load-bearing capacity of building structures. Insufficient consideration of real temperature regimes of fires in diesel generator stations makes it difficult to ensure fire resistance and operational reliability of buildings and structures. In this regard, there is a need for scientifically substantiated research into the thermal effects of diesel generator fires to form effective and safe spatial planning and design solutions. Purpose. Study of the nature of the development of a diesel generator fire in a closed room by combining numerical modeling and full-scale fire tests to determine critical temperature regimes and thermal loads on building structures in order to substantiate the fire safety requirements of generator station premises. Main results. The work experimentally and numerically investigated the temperature regime of a diesel generator fire in a closed room, established critical thermal loads and dangerous zones that can lead to the loss of the bearing capacity of metal, reinforced concrete and brick structures. Comparison of the results of full-scale fire studies and computer modeling in the FDS environment showed their consistency with a deviation of 12-15%, which confirms the possibility of using numerical modeling to substantiate the fire resistance requirements of generator station premises. Established the spatial-temporal dependencies of the change in the temperature regime of a diesel generator fire in a closed room depending on the height and distance from the combustion center, and also determined critical temperature ranges for different zones of the room. Quantitative dependencies of thermal loads on enclosing and supporting structures on the diesel fuel combustion scenario were obtained, which allow predicting the loss of fire resistance of structures and justifying the requirements for their fire resistance class and fire zoning of generator station premises. Conclusions. As a result of the conducted numerical and full-scale fire studies, it was established that fires of diesel generator sets in closed rooms are characterized by rapid development and formation of critical temperature regimes, capable of leading to the loss of the bearing capacity of building structures in a short time. The obtained results confirm the feasibility of using computer modeling together with experimental studies for the scientific substantiation of fire safety requirements and fire resistance of generator station premises in buildings of various functional purposes.

Сomparative analysis of methods for determining the parameters of small-sized vibration installations

2026-05-22T12:06:58+03:00

The article discusses modern approaches to determining the main parameters of small-sized vibrating pads, which are widely used in the construction industry for compaction of concrete mixtures and the formation of products with specified physical and mechanical properties. The relevance of the study is due to the need to increase the efficiency of vibration equipment while reducing energy consumption, material consumption and dimensions of installations.

The main attention is paid to the analysis of existing methods for calculating the dynamic characteristics of vibration sites, in particular, the determination of the amplitude of vibrations, the frequency of excitation, accelerations of the working platform and the parameters of vibration exciters. Analytical, empirical and numerical approaches to modeling oscillatory processes, including the application of methods of the theory of oscillations and finite elements, are considered. It has been established that traditional analytical dependencies do not always take into account the influence of design features and real operating conditions, which can lead to deviations between the calculated and experimental data.

The paper conducts a comparative analysis of various calculation methods, identifies their advantages and limitations in terms of accuracy, labor intensity and the possibility of practical application. Particular attention is paid to the influence of the loading mass, the rigidity of elastic elements and the parameters of the excitatory force on the efficiency of the vibrating platform. It is shown that the most promising are combined approaches that combine analytical calculations with numerical modeling and experimental verification of results.

The results obtained can be used in the design and modernization of small-sized vibration units, as well as for optimizing their operating modes, taking into account specific technological conditions. The practical significance of the study is to improve the quality of compaction of concrete mixtures, reduce energy costs and ensure the reliability of equipment operation.

Thus, the analysis allows us to form reasonable recommendations for the choice of effective methods for calculating the parameters of small-sized vibration platforms and determines the directions of further scientific research in this area.

Theoretical and experimental bases for ensuring thermal and acoustic resistance of structural elements of buildings and shielding of electromagnetic radiation emission

2026-05-22T12:48:59+03:00

An applied mathematical apparatus has been developed for predicting the thermal and acoustic resistance of building elements and the effectiveness of electromagnetic radiation shielding. Thermal resistance calculations take into account the influence of solar radiation and convective heat exchange on the outer surface of buildings. This makes it possible to rationalise the thermal protection of buildings and their energy efficiency. To predict the acoustic resistance of building structural elements, a multifactorial model of sound transmission through a protective layer has been improved, which has reduced the calculation error compared to known solutions. An applied calculation tool has been developed to predict the effectiveness of shielding electromagnetic radiation with building and facing materials. It is based on the relationships of electrodynamics of continuous media and is most suitable for multicomponent materials compared to semi-empirical formulas. Verification of the results obtained indicates an acceptable convergence of theoretical and experimental data. Given the presence of certain assumptions and simplifications in the calculations, in practical activities, a certain margin of effectiveness must be included in the protective properties of the designed materials and structures.

Analysis of the stress-strain state of a cylindrical multilayer shell of a protective structure under explosive loads

2026-05-22T13:12:55+03:00

The work involves modeling and analyzing of the stress state of shell bodies of a multilayer structure under quasi-static and dynamic loads. The quasi-static and non-stationary stress-strain state of heterogeneous building elements of structures made of significantly different structural materials is investigated.

Testing of the applied calculation methods is performed by comparing the results of solutions obtained for a two-dimensional and three-dimensional model of a multilayer cantilever beam.

The response of a cylindrical multilayer coating of a protective structure to an explosive load in a quasi-static and non-stationary setting is analyzed. In quasistatic statement displacement and complex stress state was explored and most loaded points were defined. A layer-by-layer strength assessment of a heterogeneous structure is performed using the Tsai-Wu strength criterion.

When modeling an explosive load in a non-stationary setting, the phases of positive and negative pressure are taken into account. An analysis of the oscillations that occur in the structure under such loads is performed. The damping of vibrations is modeled using Rayleigh damping. The dynamics of changes in displacements and stresses at selected points of the structure are described. There were defined frequency and decrement of free vibrations after load removal.

Research on the influence of rare-earth and alkaline-earth micro-additions on the visco-plastic properties and brittle strength of cold-resistant low-alloy steel

2026-05-22T13:28:30+03:00

It has been established that one of the most effective additional reserves for improving the deformation capacity and fracture toughness of pipe steel under static and cyclic loading is cost-effective modification by microadditions containing rare-earth and alkaline-earth elements or their compounds. This approach is especially important when the potential for improving mechanical and viscoplastic properties by traditionally used alloying elements, such as nickel, molybdenum, titanium, vanadium, niobium, etc., has been fully exhausted.

At the same time, alloying pipe steels with these elements often fails to ensure high and stable mechanical properties, particularly under operating conditions in aggressive corrosive environments of oil and gas fields in Ukraine. Under alternating loading conditions, the service life of industrial pipelines in such environments is significantly reduced. For example, the service life of pipelines used for wastewater injection into wells at several oil fields in Western Ukraine is only 2–3 years instead of the planned 10–15 years.

Optimal concentrations of modifying additions have been determined, the introduction of which into low-alloy steel during the melting process leads to a significant increase in viscoplastic properties, brittle strength, and fracture toughness of the metal (in wt.%): cerium – 0.01–0.03; yttrium – 0.01–0.025; barium – 0.007–0.015; calcium – 0.001–0.0025; zirconium – 0.02–0.04. It has been established that the introduction of modifying additions within the specified concentration ranges promotes an increase in the fracture toughness of low-alloy steel over a wide temperature range from +20 to −60 °C.

The controlling role of globular non-metallic inclusions (mainly oxides and oxysulfides) in the process of brittle fracture of cold-resistant steels economically alloyed with Ni, Mo, V, and Nb has been demonstrated. Such inclusions contribute to microstructural refinement, while rare-earth and alkaline-earth elements, as well as zirconium, additionally influence the formation of second-phase particles, namely non-metallic inclusions. Non-metallic inclusions are considered to be sources of submicrocrack initiation at grain boundaries, thereby limiting the increase in the metal’s toughness reserve. It has been established that the presence of the above-mentioned non-metallic inclusions prevents the full realization of the beneficial effect of nickel, molybdenum, and vanadium on the level of brittle strength, despite grain refinement and an increase in the viscoplastic characteristics of the metal (KCV, K₁C, δC).