On solving the geometrically nonlinear and linear problems of transverse bending of a hinged fixing sandwich plate with transversally soft core

Abstract

The study of the problem of finding the stress-strain state of a sandwich plate with a transversally soft core under the action of a transverse load in a one-dimensional geometrically nonlinear formulation was carried out. A generalized formulation of the problem in the form of an operator equation is proposed. The properties of the operator of the equation are established, which make it possible to use the general results of the theory of monotone operators in the study of correctness. To find the stress-strain state of the plate, a two-layer iterative method is proposed with lowering the nonlinearity on the lower layer. A finite-dimensional approximation of the problem and the iterative method was carried out. The convergence of finite-dimensional approximations and the iterative method has been studied. For the numerical implementation of the proposed approximate methods, a software package has been developed in the Matlab environment. Based on it, numerical experiments were carried out.