An approach to the numerical solution of two-dimensional problems of plate and shell theory with variable parameters

Abstract

Here Zi = 2~ (a, ~) (a I ~ a ~ a2; ~, ~ ~ ~ ~_) are the desired resolving functions, r is a linear function in ~kzj/~flk; fi(~ ' fl) are free terms and ~, fl are orthogonal curvilinear coordinates. For open shells (plates) boundary conditions on the contour lines ~ = coast; fi = coast are appended. For shelis closed in one direction the boundary conditions'in this direction are replaced by periodicity conditions. Before going over to an exposition of the proposed approach, let us examine the fundamental aspects of the method of integral relations in application to the solution of the calls of problems under consideration (2, 3, 9). The solution of the boundary value problem consists of two stages. In the first stage the initial scheme of the partial differential equations is approximated by a system of ordinary differential equations satisfying the boundary conditions on a part of the shell contour.