Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On the formulation and iterative solution of small strain plasticity problems

Author: Kerry S. Havner
Journal: Quart. Appl. Math. 23 (1966), 323-335
DOI: https://doi.org/10.1090/qam/99938
MathSciNet review: QAM99938
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Abstract | References | Additional Information

Abstract: This paper is concerned with a general method of formulation and iterative solution of small displacement plasticity problems, using the Hencky-Nadai hardening law as mathematical model for the material behavior. Beginning with a minimum energy principle for small thermal-mechanical strains under simple external loading, quasi-linear partial differential equations are formulated and a method of iteration by successive solutions is proposed. A finite-difference discretization of the equations (in two dimensions) is obtained through minimization of the total potential energy function, leading to positive definite symmetric matrices for general boundary configurations.

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Additional Information

DOI: https://doi.org/10.1090/qam/99938
Article copyright: © Copyright 1966 American Mathematical Society

American Mathematical Society