Analysis of structures with arbitrary kinematic boundary conditions by the semi-analytical finite element method
DOI:
https://doi.org/10.32347/2410-2547.2023.111.140-146Keywords:
finite element method (FEM), semi-analytical finite element method (SAMSE), stress-strain state, elastic deformation, bending of hinged square plate, cylindrical panel, elastic equilibrium of prismatic beam, thick square plate clamped along the contourAbstract
The successful application of FEM to the analysis of structures is largely due to the efficiency of the use of modern software packages, in connection with which the role of program systems that implement the solution process increases. The correct organization of the computing complex, the choice of optimal algorithms for solving systems of linear and nonlinear equations largely determine the possibilities of the method in terms of the structural complexity of the objects under consideration, the accuracy of the results obtained, and the complexity of setting nonlinear problems. Therefore, there is an increased interest in the development of fairly universal computing complexes based on FEM. One of the effective software complexes is the "Strength" system, designed to conduct comprehensive research in the field of mechanics of a deformable solid, the basic principles of construction of which are used in this work in the implementation of a semi-analytical version of the FEM.
In this work, solutions of a significant number of control problems of deformation of massive and thin-walled prismatic bodies under different boundary conditions and loads are obtained. In the process of solving new problems, the estimation of the convergence of results was carried out on the basis of a sequential increase in finite elements and contained terms of decomposition, an increase in the accuracy of systems of linear and nonlinear equations, and the accuracy of satisfaction with natural boundary conditions was checked. The developed effective method for solving new complex problems of deformation of prismatic bodies is implemented in the form of complex programs and can be used in design and construction practice in construction, mechanical engineering and other fields of technology.
References
Bazhenov V. A. Semi-analytical method of finite elements in problems of continuous destruction of spatial bodies: Monograph / [Bazhenov V. A., Gulyar O. I., Piskunov S. O., Sakharov O. S.]. – Kyiv: Karavela, 2014.– 235 p.
Batoz, Dutt. Further exploration of two simple shell elements. – Rocketry and astronautics, 1972, № 2, p.172-173.
Vabishchevich M.O. Solution of nonlinear contact problems of deformation of nodal connections of steel structures /Vabishchevich M.O., Storchak D.A // Strength of Materials and Theory of Structures: Scientific-&-Technical collected articles – Kyiv: KNUBA, 2021. – Issue 108. – p 178-188.
Zuev B.I. et al. Comparison of some models of finite elements in the analysis of thin-walled spatial structures.– In: Finite Element Method in Structural Mechanics. Gorky: GSU Publ., 1975, p. 149-163.
Bazhenov V. A. Finite element method in problems of deformation and destruction of bodies of rotation under thermoforce load / [Bazhenov V.A., Piskunov S.O., Maksymyuk Yu.V.] – Kyiv : Karavela Publishing House, 2018.– 316 p.
Bazhenov V. A. Semi-analytical method of finite elements in spatial problems of deformation, destruction and shape change of bodies of complex structure / [Bazhenov V.A., Maksym'yuk Yu.V., Martynyuk I.Yu., Maksym'yuk O.V.] - Kyiv: "Caravela" publishing house, 2021. - 280 p.
Solodey I.I. Analysis of algorithms for solving geometrically nonlinear problems of mechanics in the scheme of the semi-analytical method of finite elements/ Solodey I.I., Kozub Yu.G., Strygun R.L., Shovkivska V.V. // Strength of Materials and Theory of Structures: Scientific-&-Technical collected articles – Kyiv: KNUBA, 2021. – Issue 109. – p. 109-119.
Stasenko I.V., Kulikov Yu. A. Comparative analysis of finite elements for a circular cylindrical shell.– Izv. Universities. Mashinostroenie Publ., 1974, no. 8, p. 162-164.
Timoshenko S.P., Voinovsky-Krieger S. Plastinki i obolochki [Plates and shells]. Moscow, Nauka Publ.,1966.– 456 p.
Bennes G., Dhatt G., Gironn I.M. and Rohichad. Curved triangular elements for the analysis of shell. – Proc. and conf on Matrik Methods in stractural Mechanics, Ohio, 1968, p.617-640.
Clough R.W., Tohnson C.P. Afinite element approximation for the analysis of this shelss. – Inst. T. Solids structs., 1968, v.4, № 1, p.43-60.
Cowper G.R., Lindberg G.M., Olson M.D. A shallow shell finite element of triangular shape. – Inst. T. Solids structs., 1970, № 8, p.1133-1156.
Dupuis G.A., Hibbitt H.D., Mc Namara S.F., Marcal P.V. Nonlinear material and geometric behavior of shell structures. – Comput. and struct., 1972, № 1, p.117-121.
Pyskunov S.О., Shkryl O.O., Maksimyuk Yu.V. Determination of crack resistance of a tank with elliptical crack // Strength of Materials and Theory of Structures: Scientific-&-Technical collected articles – Kyiv: KNUBA, 2021. – Issue 106. – P. 14-21.
Sabir F.B., Look A.G. A curved cylindrical shell-finite element. Int. – I. Mech. Sci., 1972, v.14, № 2, p.47-58.
Schultchen E., Ulonska H., Wurmnest W. Statische Berechnung von Rototionskqrpern unter Beliebiger nichtrotations-symmetrischer Belastung mit dem Programmsustem ANTRAS – Rot. – Techn. Mitt. Krupp. Forsch., 1977, № 2, p.113-126.
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.
