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Multivariable approach to the finite difference solution of elasto‐plastic problems
Author(s) -
Brown David K.
Publication year - 1976
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620100208
Subject(s) - plane stress , multivariable calculus , mathematics , boundary value problem , plane (geometry) , stress (linguistics) , stress field , field (mathematics) , mathematical analysis , tension (geology) , deformation (meteorology) , geometry , materials science , structural engineering , finite element method , engineering , composite material , linguistics , philosophy , control engineering , pure mathematics , ultimate tensile strength
The solutions of plane elasto‐plastic problems usually use one or two field variables—namely a stress functions or the displacements. The use of three, four or five field variables is investigated and it is concluded that the three stresses from the best basis for a multivariable approach. Attempts to solve the governing equations with an initial value technique were exhaustively tried and discarded in preference to a boundary value or elliptical technique. The problem solved to check the method is that of a hole in plane strain uniaxial tension. Effective plastic strain distributions are plotted, along with stress and strain concentration data and distributions of the mean to effective stress ratio. Comparison is made between solutions produced using incremental and deformation theories.