On the formulation and iterative solution of small strain plasticity problems
Open Access
- 1 January 1966
- journal article
- Published by American Mathematical Society (AMS) in Quarterly of Applied Mathematics
- Vol. 23 (4) , 323-335
- https://doi.org/10.1090/qam/99938
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.Keywords
This publication has 16 references indexed in Scilit:
- Finite-difference solution of two variable thermal and mechanical deformation problemsJournal of Spacecraft and Rockets, 1965
- On the numerical solution of problems allowing mixed boundary conditionsJournal of the Franklin Institute, 1964
- Stresses in the Plastic Range Around a Normally Loaded Circular Hole in an Infinite SheetJournal of Applied Mechanics, 1960
- Plastic Stress Concentration at a Circular Hole in an Infinite Sheet Subjected to Equal Biaxial TensionJournal of Applied Mechanics, 1960
- A COMPARISON OF FLOW AND DEFORMATION THEORIES IN PLASTIC TORSION OF A SQUARE CYLINDERPublished by Elsevier ,1960
- STRESS-STRAIN RELATIONS IN PLASTICITY AND THERMOPLASTICITYPublished by Elsevier ,1960
- New concepts in plasticity and deformation theoryJournal of Applied Mathematics and Mechanics, 1959
- On a possible manner of establishing the plasticity relationsJournal of Applied Mathematics and Mechanics, 1959
- On plasticity laws for work-hardening materialsJournal of Applied Mathematics and Mechanics, 1958
- ber die partiellen Differenzengleichungen der mathematischen PhysikMathematische Annalen, 1928