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On the solution of a finite element approximation of a linear obstacle plate problem

Luis Fernandes, Isabel Figueiredo, Joaquim Júdice (2002)

International Journal of Applied Mathematics and Computer Science

In this paper the solution of a finite element approximation of a linear obstacle plate problem is investigated. A simple version of an interior point method and a block pivoting algorithm have been proposed for the solution of this problem. Special purpose implementations of these procedures are included and have been used in the solution of a set of test problems. The results of these experiences indicate that these procedures are quite efficient to deal with these instances and compare favourably...

On the Stefan problem with energy specification

Pierluigi Colli (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Vengono trattati due problemi di Stefan con la specificazione dell'energia. Dapprima si fornisce una formulazione debole di un problema unidimensionale ad una fase studiato in [4]: si dimostra un risultato di esistenza. In seguito si considera un problema di Stefan pluridimensionale e multifase in cui viene assegnata l'energia totale del sistema ad ogni istante; si mostra l’esistenza e l’unicità della soluzione per due formulazioni provando inoltre l’equivalenza fra queste.

Optimal control of a frictionless contact problem with normal compliance

Arezki Touzaline (2018)

Commentationes Mathematicae Universitatis Carolinae

We consider a mathematical model which describes a contact between an elastic body and a foundation. The contact is frictionless with normal compliance. The goal of this paper is to study an optimal control problem which consists of leading the stress tensor as close as possible to a given target, by acting with a control on the boundary of the body. We state an optimal control problem which admits at least one solution. Next, we establish an optimality condition corresponding to a regularization...

Optimal Control of Obstacle Problems: Existence of Lagrange Multipliers

Maïtine Bergounioux, Fulbert Mignot (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We study first order optimality systems for the control of a system governed by a variational inequality and deal with Lagrange multipliers: is it possible to associate to each pointwise constraint a multiplier to get a “good” optimality system? We give positive and negative answers for the finite and infinite dimensional cases. These results are compared with the previous ones got by penalization or differentiation.

Optimal control problems for variational inequalities with controls in coefficients and in unilateral constraints

Igor Bock, Ján Lovíšek (1987)

Aplikace matematiky

We deal with an optimal control problem for variational inequalities, where the monotone operators as well as the convex sets of possible states depend on the control parameter. The existence theorem for the optimal control will be applied to the optimal design problems for an elasto-plastic beam and an elastic plate, where a variable thickness appears as a control variable.

Optimal design of cylindrical shell with a rigid obstacle

Ján Lovíšek (1989)

Aplikace matematiky

The aim of the present paper is to study problems of optimal design in mechanics, whose variational form are inequalities expressing the principle of virtual power in its inequality form. We consider an optimal control problem in whixh the state of the system (involving an elliptic, linear symmetric operator, the coefficients of which are chosen as the design - control variables) is defined as the (unique) solution of stationary variational inequalities. The existence result proved in Section 1...

Optimal design of laminated plate with obstacle

Ján Lovíšek (1992)

Applications of Mathematics

The aim of the present paper is to study problems of optimal design in mechanics, whose variational form is given by inequalities expressing the principle of virtual power in its inequality form. The elliptic, linear symmetric operators as well as convex sets of possible states depend on the control parameter. The existence theorem for the optimal control is applied to design problems for an elastic laminated plate whose variable thickness appears as a control variable.

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