Conical differentiability for bone remodeling contact rod models

Isabel N. Figueiredo; Carlos F. Leal; Cecília S. Pinto

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

  • Volume: 11, Issue: 3, page 382-400
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Figueiredo, Isabel N., Leal, Carlos F., and Pinto, Cecília S.. "Conical differentiability for bone remodeling contact rod models." ESAIM: Control, Optimisation and Calculus of Variations 11.3 (2010): 382-400. <http://eudml.org/doc/90769>.

@article{Figueiredo2010,
abstract = { 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. },
author = {Figueiredo, Isabel N., Leal, Carlos F., Pinto, Cecília S.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Adaptive elasticity; functional spaces; polyhedric set; rod.; adaptive elasticity; rod; variational inequality},
language = {eng},
month = {3},
number = {3},
pages = {382-400},
publisher = {EDP Sciences},
title = {Conical differentiability for bone remodeling contact rod models},
url = {http://eudml.org/doc/90769},
volume = {11},
year = {2010},
}

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
DA - 2010/3//
PB - EDP Sciences
VL - 11
IS - 3
SP - 382
EP - 400
AB - 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.
LA - eng
KW - Adaptive elasticity; functional spaces; polyhedric set; rod.; adaptive elasticity; rod; variational inequality
UR - http://eudml.org/doc/90769
ER -

References

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  12. J. Sokolowski and J.-P. Zolesio, Introduction to Shape Optimization, Shape Sensitivity Analysis. Springer-Verlag, New York, Springer Ser. Comput. Math.16 (1992).  
  13. L. Trabucho and J.M. Viaño, Mathematical Modelling of Rods, P.G. Ciarlet and J.L Lions Eds. North-Holland, Amsterdam, Handb. Numer. Anal.4 (1996) 487–974.  
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