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Multi‐grid solutions to the elastic plastic torsion problem in multiply connected domains
Author(s) -
Hoppe Ronald H. W.
Publication year - 1988
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.1620260308
Subject(s) - mathematics , linear complementarity problem , torsion (gastropod) , grid , discretization , mathematical analysis , obstacle , mathematical optimization , geometry , nonlinear system , medicine , physics , surgery , quantum mechanics , political science , law
The elastic plastic torsion problem for an elastic, perfectly plastic cylinder with multiply connected cross section twisted around its longitudinal axis is formulated as an obstacle problem for an associated stress potential, the obstacle being defined in terms of a generalized distance function. Based upon the reformulation of the obstacle problem as an equivalent linear complementarity problem, the latter is discretized by means of finite difference techniques, and a monotonically convergent iterative scheme for its numerical solution is developed. At each step of the iteration the solution of a reduced system of discrete Poisson equations is required which is done by applying multi‐grid techniques with respect to a hierarchy of grid‐point sets. Combined with a suitably chosen nested iteration process this results in a computationally very efficient algorithm for the approximate solution of the elastic plastic torsion problem.