A CONSISTENT NUMERICAL METHOD FOR THE SOLUTION OF NONLINEAR ELASTICITY PROBLEMS AT FINITE STRAINS.

Abstract

Based on an absolute minimum principle for small deformations superimposed on a finitely deformed, stable configuration of an elastic solid, a consistent numerical method is developed for a step-by-step incremental solution of large deformation problems which include material as well as geometric nonlinearities (finite rotations and strains). The Lagrangian and Eulerian formulations are presented and compared. Piecewise linear displacement fields are considered, where tetrahedral elements of arbitrary dimensions for the three-dimensional problems, and triangular elements for the plane strain problems are used. Both compressible and incompressible elastic materials are considered, and explicit results are given. Two numerical examples are worked out in detail to illustrate the results. Finally, the incremental method is combined with an iterative scheme, whence an effective method which provides more accurate results with less computational efforts is obtained. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1970
Accession Number
AD0701332

Entities

People

  • H. D. Shatoff
  • S. Nemat-nasser

Organizations

  • University of California, San Diego

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Displacement
  • Elastic Materials
  • Elastic Properties
  • Materials
  • Physical Properties
  • Rotation
  • Three Dimensional

Fields of Study

  • Mathematics

Readers

  • Computational Fluid Dynamics (CFD)
  • Structural Dynamics.