Investigation of wave processes in a rectangular region with discontinuous boundary conditions
Keywords:velocity, stress, load, discontinuity, plane deformation, concentration of stresses, numerical solution
In the work in linear formulation the problem of propagation of nonstationary stress waves in an elastic single-supported construction, which is a rectangular strip, is solved. Formulated in terms of stresses and velocities the mixed problem is modeled numerically by means of an explicit difference scheme through counting, based on the method of spatial characteristics. The wave process is caused by applying of an external dynamic load on the front boundary of the rectangular region, and the lateral boundaries of the region are stress-free. At the lower boundary of the rectangular region, inhomogeneous boundary conditions are given, where the middle part of the boundary is rigidly fixed, and its lateral sections are free of stresses. Namely at the points of their conjugation, where the boundary conditions change jump-like, the method is proposed for obtaining resolving equations for finding required functions. The concentration of dynamic stresses in the neighborhood of discontinuity of boundary conditions is investigated. The results of the study are brought to numerical solution.