Application of the finite element moment scheme to the investigation of thin elastic shells of inhomogeneous structure

The work is devoted to the problem of developing a universal method for studying the deformation, buckling, postbuckling behavior and vibrations of thin and medium-thickness shells of complex shape and structure under the action of mechanical and thermal loads. A wide class of shells is considered: of constant and smooth-variable thickness, with ribs and cover plates, channels and cavities, holes, sharp bends of the mid-surface, and with a multilayer structure of the material. The method is based on the positions of the 3D geometrically nonlinear theory of thermoelasticity without the use of simplifying hypotheses of the theory of shells. The development of the computational model is based on the use of a universal isoparametric spatial finite element with multilinear shape functions, which is the same for all sections of the shell with stepwise variable thickness. The governing equations are constructed in accordance with the requirements of the finite element moment scheme. The mid-surface of the shell’s casing is taken as a single reference surface. All matrices of governing equations for a universal spatial multilayer finite element are obtained in explicit form by analytical integration. This speeds up the execution of calculations in the algorithmic implementation of the method. Such an approach, based on a unified methodology, makes it possible to study the behavior of multilayer shells with different geometric features in terms of thickness under complex thermo-mechanical loading.