Reliable solutions of problems in the deformation theory of plasticity with respect to uncertain material function
type: Item
instance of: scholarly article
title: Reliable solutions of problems in the deformation theory of plasticity with respect to uncertain material function
zbMATH Open document ID: 0870.65095
author: I. Hlaváček
published in: Applications of Mathematics
publication date: 1997-08-07T00:00:00Z
full work available at URL: https://eudml.org/doc/32961
review text: 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.
reviewed by: Jan Chleboun
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 74C99
Mathematics Subject Classification ID: 74B20
zbMATH DE Number: 1046559
zbMATH Keywords: deformation theory of plasticity
zbMATH Keywords: physically nonlinear elasticity
zbMATH Keywords: uncertain data
MaRDI profile type: Publication
cites work: Q5612126
cites work: Reliable solutions of elliptic boundary value problems with respect to uncertain data
cites work: Q4169334
cites work: Q3657579
cites work: Q3094428
OpenAlex ID: W2624673457
DOI: 10.21136/AM.1996.134337
description: scientific article; zbMATH DE number 1046559