The correctness of boundary value problems in the theory of momentless thin elastic shells of positive curvature and their solution by the mesh method

Abstract

THREE types of boundary value problems of the theory of momentless thin elastic shells of positive curvature are considered, and for each problem sufficient conditions for its correctness are indicated. Using inequalities proving the stability of the problems, we demonstrate the possibility of solving them by the mesh method. A difference system of equations is obtained by minimization of a quadratic functional (of the least-squares functional type) in a class of functions defined on a net.