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Sensitivity Analysis of a Nonlinear Obstacle Plate Problem

Published online by Cambridge University Press:  15 September 2002

Isabel N. Figueiredo  and
Carlos F. Leal
Isabel N. Figueiredo
Affiliation:
Departamento de Matemática, Universidade de Coimbra, Apartado 3008, 3000 Coimbra, Portugal; isabelf@mat.uc.pt.
Carlos F. Leal
Affiliation:
Departamento de Matemática, Universidade de Coimbra, Apartado 3008, 3000 Coimbra, Portugal; carlosl@mat.uc.pt
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Abstract

We analyse the sensitivity of the solution of a nonlinear obstacle plateproblem, with respect to small perturbations of the middle planeof the plate. This analysis, which generalizes the results of [9,10]for the linear case,is done by application of an abstract variationalresult [6], where the sensitivity of parameterized variationalinequalities in Banach spaces, without uniqueness of solution, is quantified in terms of a generalizedderivative, that is the proto-derivative. We prove that the hypothesesrequired by this abstract sensitivity result are verified forthe nonlinear obstacle plate problem. Namely, the constraint set definedby the obstacle is polyhedric and the mapping involved in the definitionof the plate problem, considered as a function of the middle planeof the plate, is semi-differentiable. The verification of these two conditionsenable to conclude that the sensitivity ischaracterized bythe proto-derivative of the solution mapping associatedwith the nonlinear obstacle plate problem, in terms of thesolution of a variational inequality.

Keywords

Plate problemvariational inequalitysensitivity analysis.

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 7 , 2002 , pp. 135 - 155
Copyright
© EDP Sciences, SMAI, 2002

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