Investigation of static and dynamic behavior of anisotropic inhomogeneous shallow shells by spline approximation method

Abstract

The present report proposes an efficient approach to solving within the framework of the classic and refined models the stress-strain problems of shallow shells as well as the problems on free vibrations. In accordance with the approach the initial system of partial differential equations is reduced to one-dimensional problems by using approximation of the solution in terms of basic splines in one coordinate. The boundary-value problems obtained and eigenvalue boundary-value problems for systems of ordinary differential high-order equations are solved by the stable numerical method of discrete ortogonalization.