ABSTRACT
Applied methods of mathematical modeling, on the basis of which adequate mathematical models and effective calculation technologies that investigate peculiarities of nonlinear deformation of nonhomogeneous thin-walled constructions at different types of static and dynamic loading taking into account geometrical and physical nonlinearity are developed, are represented. One-layer and multilayer shell structures made of both traditional and perspective composite materials are considered. When describing deformation processes for thin-walled structures, mathematical models developed on the basis of Kirchhoff-Love and Timoshenko-Reissner hypothesis are used. Geometrical nonlinearity is considered within the framework of mean-bending theory relations and for taking into account physical nonlinearity relations of deformation plasticity theory with Mises yield criterion supposing elastic unloading are used. Thin-walled shells weakened by cutouts of different forms are considered as well. On external and internal boundaries (cut-out contours) of the shell, different variants of boundary conditions are realized. As loads acting on the shell, a system of boundary and surface loads of general and local character is considered. When solving an original integral-differential problem numerically, the method of finite differences is used for discretization in space and time coordinates. Applying variational-difference method for constructing mesh analogs of equilibrium and motion equations results in conservative difference schemes even for multiconnected regions with complex form of the boundaries. For numerical solutions of stationary problems, the quasi-dynamic form of establishment method is used, which develops calculation algorithms of the same type for solving both static and dynamic problems of nonlinear theory of shells. Relations for determination of the optimal values of iteration process parameters are represented, as is the original technology of critical value of time step significantly decreasing computing time when solving nonlinear problems of shells theory on the basis of explicit difference schemes numerically.
