Mathematical modeling of physically nonlinear 3D beams and plates made of multimodulus materials

• Published in: Acta mechanica Vol. 232; no. 9; pp. 3441 - 3469
• Main Authors: Krysko, A. V., Awrejcewicz, J., Bodyagina, K. S., Zhigalov, M. V., Krysko, V. A.
• Format: Journal Article
• Language: English
• Published: Vienna Springer Vienna 01.09.2021; Springer; Springer Nature B.V
• Subjects: Algorithms; Boundary conditions; Classical and Continuum Physics; Control; Dynamical Systems; Engineering; Engineering Fluid Dynamics; Engineering Thermodynamics; Finite element analysis; Finite element method; Graphite; Heat and Mass Transfer; Hypotheses; Lateral loads; Load; Load distribution (forces); Mathematical models; Original Paper; Plastic properties; Plates; Solid Mechanics; Stress analysis; Stress concentration; Theoretical and Applied Mechanics; Transverse loads; Vibration
• ISSN: 0001-5970; 1619-6937
• DOI: 10.1007/s00707-021-03010-8

In this work, mathematical models of physically nonlinear plates and beams made from multimodulus materials are constructed. Our considerations are based on the 3D deformation theory of plasticity, the von Mises plasticity criterion and the method of variable parameters of the theory of elasticity developed by Birger. The proposed theory and computational algorithm enable for solving problems of three types of boundary conditions, edge conditions and arbitrary lateral load distribution. The problem is solved by the finite element method (FEM), and its convergence and the reliability of the results are investigated. Based on numerical experiments, the influence of multimodulus characteristics of the material of the beam and the plate on their stress–strain states under the action of transverse loads is illustrated and discussed.