Method of Finite Bodies for Mathematical Modeling of the Stress-strain State of Cylindrical Orthotropic Shell with the Reinforced Rectangular Hole

Abstract

An analytical-numerical method (nite bodies) for calculating the stress state of the cylindrical orthotropic shell with a large reinforced rectangular hole is proposed. The shell and reinforcement consist of various materials. The systems of equations that exactly satis es the equilibrium equations of the orthotropic cylindrical shell and the orthotropic reinforced are used. The presentation of the solution is divided into basic and self-balanced states. The nite-body method uses the conditional partition of the three-connected surface of the shell and the reinforcement into simpler doubly-connected and simply connected parts. An algorithm is developed for analytic-numerical solution of boundary-value problems, based on the proposed universal method of reducing the satisfaction of all contact conditions of shell parts and boundary conditions to minimization of the generalized quadratic form. We establish criteria under which the construction of approximate solution coincides with the exact one.