TY - JOUR

T1 - Analyses of large quasistatic deformations of inelastic bodies by a new hybrid-stress finite element algorithm

AU - Reed, K. W.

AU - Atluri, S. N.

N1 - Funding Information:
This work was supportedb y the NASA-Lewis Research Center under grant NAG3-38 to Georgia Tech. The authors gratefully acknowledget his support. Appreciation is expressedt o Ms. Brenda Bolinger for her help in preparingt his manuscript.

PY - 1983/9

Y1 - 1983/9

N2 - A 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 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 complete separation of the boundary value problem (for stress rate and velocity) and the initial value problem (for total stress and deformation); hence, their numerical treatments are essentially independent. After a fairly comprehensive discussion of the numerical treatment of the boundary value problem, we launch into 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.

AB - A 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 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 complete separation of the boundary value problem (for stress rate and velocity) and the initial value problem (for total stress and deformation); hence, their numerical treatments are essentially independent. After a fairly comprehensive discussion of the numerical treatment of the boundary value problem, we launch into 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.

UR - http://www.scopus.com/inward/record.url?scp=0020824578&partnerID=8YFLogxK

U2 - 10.1016/0045-7825(83)90094-4

DO - 10.1016/0045-7825(83)90094-4

M3 - Article

AN - SCOPUS:0020824578

VL - 39

SP - 245

EP - 295

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

IS - 3

ER -