Elastic-plastic deformation of geometrically nonlinear plates and shallow shells

In the article, in a geometrically and physically nonlinear formulation, the problem of the stress-strain state of plates and shallow shells on the rectangular plane under pressure loading is solved. The resolving equations of the theory of shallow shells are obtained on the basis of the Genki-Ilyushin deformation theory of the plasticity and the equations of the geometrically nonlinear shell theory, which contain quadratic terms with respect to the angles of rotation of the normals to the middle surface. The geometric parameters of the middle surface are taken in the original undeformed state. The equations are written in the form allowing to perform numerical calculations of problems with allowance for geometric and physical nonlinearities or only with geometric nonlinearity, allow for unloading and secondary plastic deformations.