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Conical differentiability for bone remodelingcontact rod models

Published online by Cambridge University Press:  15 July 2005

Isabel N. Figueiredo ,
Carlos F. Leal  and
Cecília S. Pinto
Isabel N. Figueiredo
Affiliation:
Departamento de Matemática, Universidade de Coimbra, Apartado 3008, 3001-454 Coimbra, Portugal; isabel.figueiredo@mat.uc.pt; carlosl@mat.uc.pt
Carlos F. Leal
Affiliation:
Departamento de Matemática, Universidade de Coimbra, Apartado 3008, 3001-454 Coimbra, Portugal; isabel.figueiredo@mat.uc.pt; carlosl@mat.uc.pt
Cecília S. Pinto
Affiliation:
Departamento de Matemática, Escola Superior de Tecnologia de Viseu, Campus Politécnico 3504-510 Viseu, Portugal; cagostinho@mat.estv.ipv.pt
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Abstract

We prove the conical differentiability of the solution to a boneremodeling contact rod model, for given data (applied loads andrigid obstacle), with respect to small perturbations of the crosssection of the rod. The proof is based on the special structure ofthe model, composed of a variational inequality coupled with anordinary differential equation with respect to time. Thisstructure enables the verification of the two followingfundamental results: the polyhedricity of a modified displacementconstraint set defined by the obstacle and the differentiabilityof the two forms associated to the variational inequality.

Keywords

Adaptive elasticityfunctional spacespolyhedric setrod.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 11 , Issue 3 , July 2005 , pp. 382 - 400
Copyright
© EDP Sciences, SMAI, 2005

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