Investigation of nonlinear deformation, buckling and natural vibrations of elastic shells under thermomechanical loads using a universal three-dimensional finite element
DOI:
https://doi.org/10.32347/2410-2547.2025.114.35-43Keywords:
shell of inhomogeneous structure, universal 3D finite element, geometrically nonlinear deformation, buckling, natural vibrations, finite element moment schemeAbstract
The article presents the fundamentals and features of the method for solving static problems of nonlinear deformation, buckling, post-buckling behavior and natural vibrations of a wide class of thin elastic inhomogeneous shells of various shapes and structures under the action of thermomechanical loads. The method is developed from the unified positions of the three-dimensional geometrically nonlinear theory of thermoelasticity based on the finite element method. A universal 3D finite element is used. The distinctive feature of the finite element is the presence of its additional variable parameters. This approach allowed for the use of a single universal finite element in all sections when modeling shells with different inhomogeneities. On this basis, a unified model has been developed that takes into account the geometric features of the structural elements and the multilayer structure of a material of the thin shells (constant or piecewise variable thickness, ribs, cover plates, channels, holes, sharp bends in the middle surface, layers, etc.). The algorithm for solving the shell buckling problem finds the branching points and allows obtaining adjacent deformation modes in their neighborhood. A method for the integrated solution of problems of stability and natural vibrations of shells under the action of thermomechanical loads has been developed. Based on this approach, the loss of stability is determined by static and dynamic criteria. The efficiency of the method is demonstrated by a numerical example. The method is used to identify the branching point of the solution on the load-deflection curve for panels of different curvatures.
References
Zenkevich O. Metod konechnykh elementov v tekhnike (Finite element method in engineering). – M.: Mir. – 1975. – 541 p. (Метод конечных элементов в технике). – М.: Мир. – 1975. – 541 с. (in Russian)
Sakharov A.S., Kislookiy V.N., Kirichevsky V.V. et al. Metod konechnykh elementov v mekhanike tverdykh tel (Finite element method in solid mechanics). – K.: Vishcha school. Head. publishing house, 1982. – 480 p. (in Ukrainian)
Bathe K.-J., Wilson E.L. Numerical methods in finite element analysis. – Prentice-Hall Inc., Englewood Cliffs, N.J., 1976. – 528 p.
Reddy J.N. Theory and Analysis of Elastic Plates and Shells, Second Edition – CRC Press, 2006. – 568 p.
Rikards R.B. Metod konechnykh elementov v teorii obolochek i plastin (Finite Element Method in the Theory of Shells and Plates). – Riga: Zinatne, 1988. – 284 p. (in Russian)
Lukianchenko O., Kostina O. The Finite Element Metod inProblems of the Thin Shells Theory - LAP LAMBERT Academic Publishing, Beau Bassin, Mauritius, 2019 – 134 p.
Karpilovsky V.S. Metod konechnykh elementov i zadachi teorii uprugosti (Finite element method and problems of elasticity theory). – Kyiv: "Sofia A", 2022. - 275 p. (in Russian)
Bazhenov V.A., Solovei N.A. Nonlinear Deformation and Buckling of Elastic Inhomogeneous Shells under Thermomechanical Loads // International Applied Mechanics. 2009. Vol. 45, No 9. P 923–953.
Bazhenov V.A., Krivenko O.P., Solovei M.O. Neliniine deformuvannia ta stiikist pruzhnykh obolonok neodnoridnoi struktury (Nonlinear deformation and stability of elastic shells with inhomogeneous structure). – K.: ZAT «Vipol», 2010. – 316 p. ISBN: 978-966-646-097-7 (in Ukrainian)
Guz A.N. Osnovy trekhmernoy teorii ustoychivosti deformiruyemykh tel (Fundamentals of three-dimensional theory of stability of deformable bodies). – K.: Vishcha shkola. – 1986. – 511 p. (in Russian)
Cinefra M. Formulation of 3D finite elements using curvilinear coordinates // Mechanics of Advanced Materials and Structures, pp, 1-10 (2020).
Podvornyi A.V., Semenyuk N.P., Trach V.M. Stability of Inhomogeneous Cylindrical Shells Under Distributed External Pressure in a Three-Dimensional Statement // Int. Appl. Mech. 53, 623–638 (2017).
Kolyano Yu.M. Metody teploprovodnosti i termouprugosti neodnorodnogo tela (Methods of thermal conductivity and thermoelasticity of a heterogeneous body). – Kyiv: Nauk. dumka. – 1992. – 280 p. (in Russian)
Grigorenko Ya.M., Vasilenko A.T. Zadachi statiki neodnorodnykh obolochek (Problems of statics of inhomogeneous shells). – Moscow: Nauka. Chief editor of physical and mathematical literature. – 1992. – 336 p. (in Russian)
Kryvenko, O.P., Lizunov, P.P., Vorona, Y.V., Kalashnikov, O.B. Modeling of Nonlinear Deformation, Buckling, and Vibration Processes of Elastic Shells in Inhomogeneous Structure // International Applied Mechanics. 2024. – 60 (3). 464- 478. https://doi.org/10.1007/s10778-024-01298-2.
Krivenko O.P., Lizunov P.P., Kalashnikov O.B. Momentna skhema skinchennykh elementiv u zadachakh termostiykosti i vlasnykh kolyvan pruzhnykh neodnoridnykh obolonok: Monohrafiya (Moment scheme of finite elements in problems of thermal stability and natural oscillations of elastic inhomogeneous shells: Monograph). – Kyiv: Publishing house “Karavela”, 2024. – 179 p. ISBN 978-966-969-168-2 (in Ukrainian).
Amenzade Yu.A. Teoriya uprugosti. Uchebnik dlya universitetov (Theory of elasticity. Textbook for universities). Moscow: Higher School, 1976. 272 p. (in Russian)
Novatsky V. Teoriya uprugosti (Theory of elasticity). Moscow: Mir, 1975. 872 p. (in Russian)
Rabotnov Yu.N. Mekhanika tverdogo deformiruyemogo tela (Mechanics of a solid deformable body). - Moscow: Nauka, 1988. 712 p. (in Russian)
Valishvili N.V. Metody rascheta obolochek vrashcheniya na ETSVM (Methods for calculating shells of revolution on a digital computer). - M.: Mashinostroenie, 1976. - 278 p. (in Russian)
Volmir A.S. Ustoychivost' deformiruyemykh sistem (Stability of deformable systems). - M.: Nauka, 1967. - 984 p. (in Russian)
Loss of stability and buckling of structures: theory and practice / Ed. J. Thompson and J. Hunt (Poterya ustoychivosti i vypuchivaniye konstruktsiy: teoriya i praktika / Pod red. Dzh. Tompsona i Dzh. Khanta). - M.: Nauka, 1991. - 424 p. (in Russian)
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