Numerical Analysis of the Stress-Strain State of a Body with Thin Inclusion by the Domain Decomposition Method

Abstract

We consider a mathematical model of elastic body with thin inclusion or coating in the form of a thin elastic shell. It is shown that the corresponding Steklov–Poincaré operator of the mathematical model possesses the properties guaranteeing the existence and uniqueness of a weak solution of the boundary-value problem. We propose a method of solution based on the domain decomposition algorithm with the use of the boundary-element and finite-element methods. We prove the convergence of the iterative domain decomposition method and present the results of numerical experiments.