Features of the Wave Field in a Finite Body with a Noncentral Hole

摘要

In the article, in a linear formulation, it is solved the problem of the propagation of nonstationary stress waves in a rectangular region, containing within itself a noncentral rectangular hole. The wave process is caused by applying an external dynamic load on the front edge of a rectangular area, and its lateral boundaries are free of stresses. The lower boundary of a rectangular region is rigidly fixed, and the contour of a rectangular hole is free of stresses. The problem is solved using a numerical method of spatial characteristics. On the basis of the numerical method developed in the work, the calculated finite-difference relations of dynamic problems at the corner points of a rectangular hole are obtained, where the first and second derivatives of the unknown functions have a discontinuity of the first kind. Dynamic stress fields in an elastic body with a noncentral rectangular hole are analyzed. The concentration of dynamic stresses in the neighborhood of the corner points of a rectangular hole has been studied.