Sensitivity Analysis of a Nonlinear Obstacle Plate Problem

Isabel N. Figueiredo; Carlos F. Leal

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 7, page 135-155
  • ISSN: 1292-8119

Abstract

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We analyse the sensitivity of the solution of a nonlinear obstacle plate problem, with respect to small perturbations of the middle plane of the plate. This analysis, which generalizes the results of [9,10] for the linear case, is done by application of an abstract variational result [6], where the sensitivity of parameterized variational inequalities in Banach spaces, without uniqueness of solution, is quantified in terms of a generalized derivative, that is the proto-derivative. We prove that the hypotheses required by this abstract sensitivity result are verified for the nonlinear obstacle plate problem. Namely, the constraint set defined by the obstacle is polyhedric and the mapping involved in the definition of the plate problem, considered as a function of the middle plane of the plate, is semi-differentiable. The verification of these two conditions enable to conclude that the sensitivity is characterized by the proto-derivative of the solution mapping associated with the nonlinear obstacle plate problem, in terms of the solution of a variational inequality.

How to cite

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Figueiredo, Isabel N., and Leal, Carlos F.. "Sensitivity Analysis of a Nonlinear Obstacle Plate Problem." ESAIM: Control, Optimisation and Calculus of Variations 7 (2010): 135-155. <http://eudml.org/doc/90616>.

@article{Figueiredo2010,
abstract = { We analyse the sensitivity of the solution of a nonlinear obstacle plate problem, with respect to small perturbations of the middle plane of the plate. This analysis, which generalizes the results of [9,10] for the linear case, is done by application of an abstract variational result [6], where the sensitivity of parameterized variational inequalities in Banach spaces, without uniqueness of solution, is quantified in terms of a generalized derivative, that is the proto-derivative. We prove that the hypotheses required by this abstract sensitivity result are verified for the nonlinear obstacle plate problem. Namely, the constraint set defined by the obstacle is polyhedric and the mapping involved in the definition of the plate problem, considered as a function of the middle plane of the plate, is semi-differentiable. The verification of these two conditions enable to conclude that the sensitivity is characterized by the proto-derivative of the solution mapping associated with the nonlinear obstacle plate problem, in terms of the solution of a variational inequality. },
author = {Figueiredo, Isabel N., Leal, Carlos F.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Plate problem; variational inequality; sensitivity analysis.; plate problem; sensitivity analysis; proto-derivative},
language = {eng},
month = {3},
pages = {135-155},
publisher = {EDP Sciences},
title = {Sensitivity Analysis of a Nonlinear Obstacle Plate Problem},
url = {http://eudml.org/doc/90616},
volume = {7},
year = {2010},
}

TY - JOUR
AU - Figueiredo, Isabel N.
AU - Leal, Carlos F.
TI - Sensitivity Analysis of a Nonlinear Obstacle Plate Problem
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 7
SP - 135
EP - 155
AB - We analyse the sensitivity of the solution of a nonlinear obstacle plate problem, with respect to small perturbations of the middle plane of the plate. This analysis, which generalizes the results of [9,10] for the linear case, is done by application of an abstract variational result [6], where the sensitivity of parameterized variational inequalities in Banach spaces, without uniqueness of solution, is quantified in terms of a generalized derivative, that is the proto-derivative. We prove that the hypotheses required by this abstract sensitivity result are verified for the nonlinear obstacle plate problem. Namely, the constraint set defined by the obstacle is polyhedric and the mapping involved in the definition of the plate problem, considered as a function of the middle plane of the plate, is semi-differentiable. The verification of these two conditions enable to conclude that the sensitivity is characterized by the proto-derivative of the solution mapping associated with the nonlinear obstacle plate problem, in terms of the solution of a variational inequality.
LA - eng
KW - Plate problem; variational inequality; sensitivity analysis.; plate problem; sensitivity analysis; proto-derivative
UR - http://eudml.org/doc/90616
ER -

References

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