The Bubnov-Galerkin method in the nonlinear theory of hollow, flexible multilayer orthotropic shells
The existence of solutions of a strongly nonlinear system of differential equations describing, in the framework of the kinematic Timoshenko model adopted for the whole packet in toto, the behaviour of a flexible, multilayer shell whose very layer is made of an inhomogeneous orthotropic material, is proved. To obtain an approximate solution of the problem in question, a procedure is proposed and justified, using the Bubnov- Galerkin method based on constructing an auxiliary quasilinear system of equations. A similar approach makes is possible to extend the method of studying the convergence of the BG method to strongly nonlinear systems of elliptic type equations, and to achieve the convergence of the sequence of approximate solutions to the exact solution in a space of any prescribed degree of smoothness, without imposing additional constraints on the initial data of the problem.
strongly nonlinear system of differential equations
auxiliary quasilinear system of equations
scientific article; zbMATH DE number 3976542