Calculation of the Thermoelastoplastic Nonaxisymmetric Stress-Strain State of Layered Orthotropic Shells of Revolution

The methods for determining the nonaxisymmetric thermoelastoplastic stress-strain state of layered orthotropic shells of revolution are developed. It is assumed that the layered package deforms without mutual slippage or separation of layers. The problem is solved using the geometrically nonlinear theory of shells based on the Kirchhoff-Love hypotheses. In the isotropic layers, plastic deformations may appear, whereas the orthotropic layers deform in the elastic region. It is assumed that the mechanical properties of the materials are temperature-dependent. The thermoplasticity equations are presented in a form corresponding to the method of additional deformations. The order of the system of partial differential equations obtained is reduced with the help of trigonometric series in the circumferential coordinate. The resulting systems of ordinary differential equations are solved by the Godunov technique of discrete orthogonalization. The nonaxisymmetric thermoelastoplastic stress-strain states of layered shells of revolution are considered as examples.