Mathematical Modeling of the Deformation of Nonlinear Plates and Shallow Shells

Abstract

The paper discusses the deformation of plates and shallow shells, taking into account the geometric nonlinearity and plastic deformations under variable loading. In the case of an elastoplastic material, unloading, secondary plastic deformations material compressibility are taken into account. Geometric and physical relations and solving nonlinear differential equations of the theory of flexible shallow shells of elastoplastic material are given for an arbitrary loading cycle. The relationship between the intensity of stresses and strains, using the generalized Masing principle, allows one to investigate the deformation of flexible plates and shells of cyclically ideal, hardened and softened materials. In the expressions for the internal forces and internal moments, additional forces and additional moments are taken into account, as well as the history of loading of shallow plates and shells on the previous n-1-th loading.