Analytical and numerical method of finite bodies for calculation of cylindrical orthotropic shell with rectangular hole

To solve the boundary-value problem for cylindrical orthotropic shell with sizeable rectangular hole we suggest analytical and numerical method of finite bodies. For determination of the stress state of orthotropic thin-walled cylinder we use a system of equations that exactly satisfies the equilibrium equations of orthotropic cylindrical shell. Representation of the solutions is divided into basic and self-equilibrium state. For some loads of shell we build the basic stress state. We obtain a countable number of resolving functions that exactly satisfy the equation shell and describe the self-equilibrium stress state. We develop the algorithm of the analytical and numerical solutions of boundary-value problem based on approximation of the stress state of the shell by finite sum of resolving functions and propose universal way of reduction of all conditions of the contact parts of the enclosure and the boundary conditions to minimize the generalized quadratic forms. We establish criteria under which the construction of approximate solutions coincides with the exact one.