NUMERICAL SOLUTION OF SHALLOW SPHERICAL SHELLS

Abstract

A numerical method of determining displace ments and stresses in a uniformly thin shallow spherical shell with general shape of the boun dary and boundary conditions of practical impor tance is studied. The partial differential equa tions for the shell are derived from the varia tional principle in a form so as to yield a real symmetric matrix on discretisation. The use of the variational principle also leads to a better insight into the boundary conditions which are discussed in detail. The matrix of finite difference equations derived as approximations of the partial differen tial equations has been proved to be symmetric and positive definite in some of the physically significant cases of boundary conditions. This ensures the success of successive over-relaxation iterative methods of solution of the finite difference equations on a high speed digital computer. The method is illustrated by solving a few problems of shallow spherical shells with circular and rectangular boundaries, for in these cases the results could be compared with known analytical solutions. A chapter-wise summary of the thesis is given in section 1.4 of Chapter I (Introduction).