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