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.

在这项工作中，构建了由多模量材料制成的物理非线性板和梁的数学模型。我们的考虑基于 3D 塑性变形理论、von Mises 塑性准则和 Birger 开发的弹性理论的可变参数方法。所提出的理论和计算算法能够解决三种类型的边界条件、边缘条件和任意横向载荷分布的问题。该问题通过有限元法（FEM）求解，并对其收敛性和结果的可靠性进行了研究。基于数值实验，阐述和讨论了梁和板材料在横向载荷作用下的多模量特性对其应力应变状态的影响。