Inelastic stress analyses at finite deformation through complementary energy approachesA new hybrid-stress finite element algorithm, suitable for analyses of large, quasistatic, inelastic deformations, is presented. The algorithm is based upon a generalization of de Veubeke's (1972) complementary energy principle. The principal variables in the formulation are the nominal stress rate and spin, and the resulting finite element equations are discrete versions of the equations of compatibility and angular momentum balance. The algorithm produces true rates, time derivatives, as opposed to 'increments'. There results a boundary value problem (for stress rate and velocity) and an initial value problem (for total stress and deformation). A discussion of the numerical treatment of the boundary value problem is followed by a detailed examination of the numerical treatment of the initial value problem, covering the topics of efficiency, stability, and objectivity. The paper is closed with a set of examples, finite homogeneous deformation problems, which serve to bring out important aspects of the algorithm.
Document ID
19840030461
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Atluri, S. N. (Georgia Institute of Technology Atlanta, GA, United States)
Reed, K. W. (Georgia Inst. of Tech. Atlanta, GA, United States)