Reliable solutions of problems in the deformation theory of plasticity with respect to uncertain material function
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.
scientific article; zbMATH DE number 1046559