Accession Number : AD0701332

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

Descriptive Note : Technical rept.,

Corporate Author : CALIFORNIA UNIV SAN DIEGO LA JOLLA DEPT OF THE AEROSPACE AND MECHANICAL ENGINEERING SCIENCES

Personal Author(s) : Nemat-Nasser,S. ; Shatoff ,H. D.

Report Date : JAN 1970

Pagination or Media Count : 53

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)

Descriptors :   (*MATERIALS, ELASTIC PROPERTIES), (*ELASTIC PROPERTIES, NUMERICAL ANALYSIS), DEFORMATION, NONLINEAR SYSTEMS, LOADS(FORCES), STRESSES, COMPRESSIVE PROPERTIES, TENSOR ANALYSIS, ITERATIONS

Subject Categories : Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE