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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.
@article{COCV_2002__7__135_0,
author = {Figueiredo, Isabel N. and Leal, Carlos F.},
title = {Sensitivity analysis of a nonlinear obstacle plate problem},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {135--155},
publisher = {EDP-Sciences},
volume = {7},
year = {2002},
doi = {10.1051/cocv:2002006},
mrnumber = {1925024},
zbl = {1042.49038},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002006/}
}
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 PY - 2002 SP - 135 EP - 155 VL - 7 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002006/ DO - 10.1051/cocv:2002006 LA - en ID - COCV_2002__7__135_0 ER -
%0 Journal Article %A Figueiredo, Isabel N. %A Leal, Carlos F. %T Sensitivity analysis of a nonlinear obstacle plate problem %J ESAIM: Control, Optimisation and Calculus of Variations %D 2002 %P 135-155 %V 7 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002006/ %R 10.1051/cocv:2002006 %G en %F COCV_2002__7__135_0
Figueiredo, Isabel N.; Leal, Carlos F. Sensitivity analysis of a nonlinear obstacle plate problem. ESAIM: Control, Optimisation and Calculus of Variations, Tome 7 (2002), pp. 135-155. doi: 10.1051/cocv:2002006
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