Modeling of Nonlinear Deformation, Buckling, and Vibration Processes of Elastic Shells in Inhomogeneous Structure

The basics of the method for studying the processes of nonlinear deformation, buckling, and natural vibrations of thin elastic shells under thermomechanical loading are presented. The shells can have a complex shape of the midsurface, smooth and stepwise variable thickness, holes, and a multilayer material structure. The method is based on the geometrically nonlinear relations of the three-dimensional theory of thermoelasticity, the use of the moment scheme of finite elements, and the developed universal spatial finite element. The method makes it possible to simulate the behavior of shells with different thickness features using a single universal finite element. The modal characteristics of the shell are determined taking into account the prestressed deformed state. The reliability and efficiency of the proposed approach are shown.