Multi-grid solutions to the elastic plastic torsion problem in multiply connected domains. (English) Zbl 0703.73091

Summary: 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.


74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
74S20 Finite difference methods applied to problems in solid mechanics
65F10 Iterative numerical methods for linear systems
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
49M25 Discrete approximations in optimal control
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