On the partial difference equations of mathematical physics
IBM Journal of Research and Development
| Hi-index | 31.45 |
A numerical technique is developed for the study of stress wave propagation in axisymmetric layered elastic-plastic solids. Although the theory of wave propagation in layered media is well established, analytic solutions of significant problems are possible only for linearly elastic cases. The underlying continuum is discretized into a finite number of discrete points consisting of mass points, at which displacements, velocities, and accelerations are defined, and stress points, at which the stress and strain tensors are defined. The equations of motion and the strain-displacement relations can be derived directly from this model and can be shown to be central finite difference analogs of the corresponding continuum equations. A noniterative scheme is used to integrate the equations of motion of the model numerically. The stability of this numerical scheme is investigated in detail. Convergence of the numerical scheme is also demonstrated by comparing solutions obtained by decreasing mesh sizes.