Wave field in a strip with symmetric located holes

Abstract

In the linear formulation, the problem of the propagation of unsteady stress waves in an elastic body with symmetrically located rectangular holes is considered. Formulated in terms of stresses and velocities, the mixed problem is modeled numerically using an explicit difference scheme of the end-to-end calculation based on the method of spatial characteristics. The wave process is caused by applying an external dynamic load on the front border of the rectangular region, and the side boundaries of the region are free of stresses. The lower boundary of the rectangular region is rigidly fixed. The contour of symmetrically arranged rectangular openings is free of stress. Based on the numerical technique developed in this work, the calculated finite - difference relations of dynamic problems are obtained at the corner points of a rectangular hole, where the "smoothness"of functions "familiar"to dynamic problems is violated. At these corner points, the first and second derivatives of the desired functions suffer a discontinuity of the first kind. The isoline presents the results of changes in wave fields in an elastic body with symmetrically located rectangular holes. The concentration of dynamic stresses in the vicinity of the corner points of a rectangular hole is investigated. By numerical implementation, the stability of computational algorithms for a sufficiently large time is established.