Modeling of nonlinear behaviour of three-dimensional bodies and shells of average thickness by finite element method

The work is devoted to the fundamentals of the technique of numerical investigation of the nonlinear behavior of three-dimensional bodies oriented to the application of the finite element method. The first section is devoted to the formulation of the problem, the introduction of finite deformations in the Lagrangian coordinate system, and the description of the Cauchy and Piola-Kirchhoff tensors. The second section describes the resolving equations obtained from the principle of virtual displacements. In the third section, we consider the test problem of the bending of a square plate, and compare the results with other authors.