Method of equivalent strength conditions in calculations of bodies with inhomogeneos regular structure

Plates, beams and shells with a non-uniform and micro-uniform regular structure are widely used in aviation and rocket and space technology. In calculating the strength of elastic composite structures using the finite element method (FEM) it is important to know the error of the approximate solution for finding where you need to build a sequence of approximate solutions that is connected with the procedure of crushing discrete models. Implementation of the procedure for grinding (within the micro-pass) discrete models of composite structures (bodies) requires large computer resources, especially for discrete models with a microinhomogeneous structure. In this paper, we propose a method of equivalent strength conditions (MESC) for calculating elastic bodies static strength with inhomogeneous and microinhomogeneous regular structures, which is implemented via FEM using multigrid finite elements. The calculation of composite bodies’ strength according to MESC is limited to the calculation of elastic isotropic homogeneous bodies strength using equivalent strength conditions, which are determined based on the strength conditions set for composite bodies. The MESC is based on the following statement. For all composite bodies V0 , which are such a homogeneous isotropic body V b and the number of p , if the safety factor nb of the body Vb satisfies the equivalent conditions of strength 2 pn1(1 ) nb (1 ) pn2 (1 ) , the safety factor n0 of the body V0 meets the defined criteria for strength n1 n0 n2 , where n1 , n2 specified, the safety factor n0 ( nb ) complies with the accurate (approximate) solution of elasticity theory problem is built for body V0 (body Vb ); (n2 n1) / (n2 n1) ; is the upper b error estimation of the maximum equivalent body stress V b , corresponding to approximate solution. When constructing equivalent strength conditions, i. e when finding the equivalence p coefficient, a system of discrete models is used, dimensions of which are smaller than the dimensions of the basic composite bodies models. The implementation of MESC requires small computer resources and does not use procedures for grinding composite discrete models. Strength calculations for bodies with a microinhomogeneous structure using MESC show its high efficiency. The main procedures for implementing the MESC are briefly described.