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Reliable solutions of problems in the deformation theory of plasticity with respect to uncertain material function. (English) Zbl 0870.65095
Modified summary: Maximization problems are formulated for a class of 3D quasistatic problems in the deformation theory of plasticity with respect to an uncertainty in the material function. The admissible set of material functions is defined via a compact subset of the space \(C^{(1)}([0,1])\) and a continuous monotone mapping transforming the real axis into the segment \((0,1)\). Continuous cost functionals are considered to measure some quantity of a deformed plastic body (e.g. averaged local displacements or stresses). Maximization problem reads: find an admissible function which maximizes the cost functional, i.e. find “the worst case” from engineering point of view.
Approximation problems are introduced on the basis of cubic Hermite splines (material function) and finite elements (displacements). The solvability of both continuous and approximate maximization problems is proved and some convergence analysis is presented, too.
Reviewer: J.Chleboun (Praha)

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations
35R30 Inverse problems for PDEs
74C99 Plastic materials, materials of stress-rate and internal-variable type
74B20 Nonlinear elasticity
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