A Study of Convergence and Stability of Finite Element Approximation of Shock and Acceleration Waves in Nonlinear Materials.

摘要

This report summarizes the recent work on the development of discontinuous finite element methods for the analysis of shock waves in nonlinear elastic materials. A class of one-dimensional finite elements is introduced in which the local interpolation functions consist of the usual piecewise linear functions and some additional functions which have discontinuities. In this way it is possible to model the local displacement field in terms of the values of the displacement at each node and two additional terms in which the shock strength and the location of the shock within an element are used as parameters. The corresponding variational formulation contains the required jump conditions. For a specific class of material a priori error estimates are derived and the scheme is implemented and applied to a number of representative examples. (Author)