We prove the conical differentiability of the solution to a bone remodeling contact rod model, for given data (applied loads and rigid obstacle), with respect to small perturbations of the cross section of the rod. The proof is based on the special structure of the model, composed of a variational inequality coupled with an ordinary differential equation with respect to time. This structure enables the verification of the two following fundamental results: the polyhedricity of a modified displacement constraint set defined by the obstacle and the differentiability of the two forms associated to the variational inequality.
Keywords: adaptive elasticity, functional spaces, polyhedric set, rod
Figueiredo, Isabel N. ; Leal, Carlos F. ; Pinto, Cecília S. 1
@article{COCV_2005__11_3_382_0,
author = {Figueiredo, Isabel N. and Leal, Carlos F. and Pinto, Cec{\'\i}lia S.},
title = {Conical differentiability for bone remodeling contact rod models},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {382--400},
year = {2005},
publisher = {EDP Sciences},
volume = {11},
number = {3},
doi = {10.1051/cocv:2005011},
mrnumber = {2148850},
zbl = {1085.49005},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv:2005011/}
}
TY - JOUR AU - Figueiredo, Isabel N. AU - Leal, Carlos F. AU - Pinto, Cecília S. TI - Conical differentiability for bone remodeling contact rod models JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2005 SP - 382 EP - 400 VL - 11 IS - 3 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv:2005011/ DO - 10.1051/cocv:2005011 LA - en ID - COCV_2005__11_3_382_0 ER -
%0 Journal Article %A Figueiredo, Isabel N. %A Leal, Carlos F. %A Pinto, Cecília S. %T Conical differentiability for bone remodeling contact rod models %J ESAIM: Control, Optimisation and Calculus of Variations %D 2005 %P 382-400 %V 11 %N 3 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv:2005011/ %R 10.1051/cocv:2005011 %G en %F COCV_2005__11_3_382_0
Figueiredo, Isabel N.; Leal, Carlos F.; Pinto, Cecília S. Conical differentiability for bone remodeling contact rod models. ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 3, pp. 382-400. doi: 10.1051/cocv:2005011
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