Singular perturbations in optimal control problem with application to nonlinear structural analysis
type: Item
instance of: scholarly article
title: Singular perturbations in optimal control problem with application to nonlinear structural analysis
zbMATH Open document ID: 0870.49003
published in: Applications of Mathematics
publication date: 1997-08-07T00:00:00Z
full work available at URL: https://eudml.org/doc/32952
review text: The author considers an optimal control problem for a singularly perturbed elliptic variational inequality. The control appears in coefficients, in the right-hand side, and in the convex set of admissible spaces. The existence of an optimal control and the convergence to a solution of the limit (unperturbed) problem is proven. Some approximations are proposed and studied, as well. The theory is applied to an equilibrium of an elastic membrane perturbed by a small elasto-plastic bending rigidity and resting above a rigid inner obstacle. The role of the control (design variable) is played here by a transversal loading and the obstacle function. Employing standard finite elements, approximate solution is proposed for the above problem of a membrane, but the obstacle is restricted to the boundary of the domain only.
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 35J85
zbMATH DE Number: 1046551
zbMATH Keywords: optimal control of variational inequalities
zbMATH Keywords: elasto-plastic plate
zbMATH Keywords: singular perturbation
author: Jan Lovíšek
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1046551