Numerical analysis of the stress state of non-thin corrugated cylindrical shells made of continuous-inhomogeneous materials
DOI:
https://doi.org/10.32347/2410-2547.2024.113.108-115Keywords:
corrugated cylindrical shells, discrete Fourier series, linear theory of elasticity, stress state, continuous-inhomogeneous material, spatial modelAbstract
Cylindrical shells of circular and non-circular cross-section are used as structural elements in many branches of economy. To increase the reliability of operation of such elements, continuous non-homogeneous materials are used.
This research investigates non-thin cylindrical shells with corrugated as cross sections made of the continuously inhomogeneous materials. The shells are subjected to internal pressure under conditions of simple support on the ends.The subject of the study is the stressed state of the shells and, as a consequence, the establishment of dependencies between its characteristics and the geometric parameters of the reference surface, the thickness of the shells, and the law of change of the modulus of elasticity of the material.
The aim of the work is numerical analysis of the stress state of shells of such class depending on the amplitude of the corrugation, the thickness of the shells and the law of variation of elastic properties of their material. The solution of the problem is based on reduction of the original three-dimensional boundary value problem for the system of partial differential equations with variable coefficients to a one-dimensional boundary value problem for a system of ordinary differential equations with constant coefficients of higher order. At the same time, the analytical method of separating variables in two coordinate directions is used, together with approximation of functions by discrete Fourier series. The one-dimensional boundary value problem is solved by the stable numerical method of discrete orthogonalization.
An analysis of the stress state of the considered shells was carried out depending on the amplitude of the corrugation, the thickness of the shells and the law of change of the elastic characteristics of the material. It is shown that with a slight deviation of the shape of the cross-section from the circular one, for a certain thickness of the shells, the presence of corrugations can be neglected when choosing the calculation model.In addition, the presence of corrugations causes a redistribution of the values of displacements and stresses in the characteristic sections of the shells, which must be taken into account when calculating the strength and reliability of the structures under consideration.
References
Rozhok L.S., Onishchenko А.M., Garkusha M.V., Bashkevych I.V. Sproshchennia rozrakhunkovoi skhemy pry vyznachenni napruzhenoho stanu netonkykh tsylindrychnykh obolonok zi skladnoiu formoiu poperechnoho pererizu (Simplification of the calculation scheme for determining the stress state of non-thin cylindrical shells with a complex crosssectional shape ellipticity). Strength of Materials and Theory of Structures: Scientificand-technical collected articles. Kyiv: KNUBA. 2022. Issue 109. P. 287–300.
Semenyuk M.P., Trach V.M., Podvornyi A.V. Napruzheno-deformovanyi stan tovstostinnoi anizotropnoi tsylindrychnoi obolonky (Stress–Strain State of a Thick-Walled Anisotropic Cylindrical Shell). Int. Appl.Mech. 2023. 59, No 1. 79–89.
Chen T., Liu J., Zhang R. et al. Electromechanical coupling analysis of geometrically exact functionally graded piezoelectric shells based on weak form quadrature element method. Arch. Appl. Mech. 2024. (https://doi.org/10.1007/s00419-024-02619-0).
Cheng X., Zhang H.,Mu Y. Dynamic Response of Sand Cushion Layer Isolation Concrete Liquid Storage Structure with X-Type Soft Steel-SMA Shock Absorber Considering Long (Short) Period Earthquake. Iran. J. Sci. Technol. Trans. Civ. Eng. 2024. (https://doi.org/10.1007/s40996-024-01486-7).
Draiche K., Tounsi A., Ibrahim K.D. et al. An improved mathematical model for static and dynamic analysis of functionally graded doubly-curved shells. Arch. Appl. Mech. 2024. 94. P. 1589–1611. (https://doi.org/10.1007/s00419-024-02595-5).
Hart E.L., Terokhin B.I. Computer simulation of the stress-strain state of thin plates and cylindrical shells with a circular hole reinforced by an inclusion from functionally graded material. Strength of Materials and Theory of Structures: Scientific-and-technical collected articles. Kyiv: KNUBA. 2023. Issue 110. P. 63–80.
Grigorenko Ya.M., Pozhok L.S. Stress Analysis of Corrugated Hollow Cylinders. Int. App. Mech. 2002. 38, No 12. Р. 1473–1481
Kumar A. Finite Element Approach to Investigate and Mitigate the Lateral Movement of Steel Stack. Int. J. Steel.Struct. 2022. 22. 1395–1401.
MaksimyukYu.V., MartyniukI.Yu., Kozak О.V., Maksimyuk О.V. Numerical analysis of the stressed-deformed state of a tubular element under thermal loading. Strength of Materials and Theory of Structures. Kyiv: KNUBA. 2023. Issue 110. P. 199–206.
Ntayeesh T.J., Arefi M. Higher-order displacement, strain, and stress analyses of origami graphene auxeticmetamaterial-reinforced cylindrical shell. Arch. Civ. Mech. Eng. 2024. 24, 149. (https://doi.org/10.1007/s43452-024-00956-z).
Rozhok L., Sperkach S., Vasil’eva L. Solving of Stress State Problems of Anisotropic Thick Noncircular Cylindrical Shells with Different Nonhomogeneous Structures Based on Discrete Continual Approach. – Selected Problems of Solid Mechanics and Solving Methods. Advanced Structured Materials. Springer Cham, 2024. Vol. 204. Chapter, p. 425 – 441.
Sharifi H. Magneto–thermoelastic behavior of an orthotropic hollow cylinder based on Lord–Shulman and Green–Lindsay theories. Acta Mech. 2024.(https://doi.org/10.1007/s00707-024-03985-0).
Downloads
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
