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

Abstract

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)

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1976
Accession Number
ADA031238

Entities

People

  • C. T. Reddy
  • J. Tinsley Oden
  • L. C. Wellford Jr.

Organizations

  • University of Texas at Austin

Tags

Communities of Interest

  • Energy and Power Technologies
  • Space

DTIC Thesaurus Topics

  • Banach Space
  • Boundary Layer
  • Boundary Value Problems
  • Computational Fluid Dynamics
  • Computational Science
  • Difference Equations
  • Differential Equations
  • Elastic Materials
  • Finite Element Analysis
  • Fluid Flow
  • Fluid Mechanics
  • Hyperelastic Materials
  • Mechanical Properties
  • Mechanics
  • Partial Differential Equations
  • Shock Waves
  • Wave Propagation

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)