A difference scheme for the mixed boundary-value problem of strong bending of shallow shells (Q1122398)

We consider the system of nonlinear differential equations which describes strong bending of thin shallow shells in terms of displacements. We examine the most complex case of mixed boundary conditions, when part of the shell boundary is rigidly fixed and the rest of the boundary is free. We show that if the tangential loads are sufficiently small, then the boundary-value problem is soluble. Uniqueness conditions of the solution are also investigated. A difference scheme is proposed for approximate solution of the problem. The scheme is constructed approximating an integral identity by a summation identity. It is shown that the conditions of existence and uniqueness of the solution are the same for the difference scheme and for the original problem. If the uniqueness conditions are satisfied and the solution is sufficiently smooth, then the accuracy of the scheme is \(O(h^ 2)\).