Mathematical modeling of planar physically nonlinear inhomogeneous plates with rectangular cuts in the three-dimensional formulation

Abstract Mathematical models of planar physically nonlinear inhomogeneous plates with rectangular cuts are constructed based on the three-dimensional (3D) theory elasticity, Mises plasticity criterion, and Birger’s method variable parameters. The is developed for arbitrary deformation diagrams, boundary conditions, transverse loads, material inhomogeneities. Additionally, inhomogeneities in form holes any size shape considered. finite element employed to solve problem, convergence this examined. Finally, numerical experiments, influence various their stress–strain states under action static mechanical loads presented discussed. Results show that these imbalances existing plate’s structure lead increased plastic deformation.