Numerical solution of a boundary-value problem of elasticity theory for a body with an inclusion

Abstract

We consider the problem of steady-state oscillations of a plane body with an inclusion. A solution algorithm is constructed. Computational experiments are described, which establish the applicability of the proposed procedure for analyzing the effect of defects inside the body on wave fields excited by ultrasonic sources.Problems of nondestructive ultrasonic testing involve analyzing the effect of various defects inside the body on the wave fields excited by special sources. In this paper, we consider the plane problem of steady-state oscillations of a rectangular body f~ = {x = (x 1, x2):0 _< x 1 -< 1, 0 _< x 2 _< d} (see Fig. 1) with a rectangular inclusion 91. The inclusion is an elastic body whose characteristics are different from those of the main body. The method of summation identities on a nonuniform grid is applied to construct a difference scheme for the problem. The system of grid equations is solved by the Seidel method.