Investigation of nonlinear deformation, buckling and natural vibrations of elastic shells under thermomechanical loads using a universal three-dimensional finite element

The article presents the fundamentals and features of the method for solving static problems of nonlinear deformation, buckling, post-buckling behavior and natural vibrations of a wide class of thin elastic inhomogeneous shells of various shapes and structures under the action of thermomechanical loads. The method is developed from the unified positions of the three-dimensional geometrically nonlinear theory of thermoelasticity based on the finite element method. A universal 3D finite element is used. The distinctive feature of the finite element is the presence of its additional variable parameters. This approach allowed for the use of a single universal finite element in all sections when modeling shells with different inhomogeneities. On this basis, a unified model has been developed that takes into account the geometric features of the structural elements and the multilayer structure of a material of the thin shells (constant or piecewise variable thickness, ribs, cover plates, channels, holes, sharp bends in the middle surface, layers, etc.). The algorithm for solving the shell buckling problem finds the branching points and allows obtaining adjacent deformation modes in their neighborhood. A method for the integrated solution of problems of stability and natural vibrations of shells under the action of thermomechanical loads has been developed. Based on this approach, the loss of stability is determined by static and dynamic criteria. The efficiency of the method is demonstrated by a numerical example. The method is used to identify the branching point of the solution on the load-deflection curve for panels of different curvatures.