ESAIM: Control, Optimisation and Calculus of Variations

Table of Contents - July 2005 - Volume 11, Issue 03  

Research Article

Conical differentiability for bone remodeling contact rod models

Figueiredo, Isabel N.a1, Leal, Carlos F.a1 and Pinto, Cecília S.a2

a1 Departamento de Matemática, Universidade de Coimbra, Apartado 3008, 3001-454 Coimbra, Portugal; isabel.figueiredo@mat.uc.pt; carlosl@mat.uc.pt

a2 Departamento de Matemática, Escola Superior de Tecnologia de Viseu, Campus Politécnico 3504-510 Viseu, Portugal; cagostinho@mat.estv.ipv.pt

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.

(Received June 29 2004)

(Online publication July 15 2005)

Key Words:

  • Adaptive elasticity;
  • functional spaces;
  • polyhedric set;
  • rod.

Mathematics Subject Classification:

  • 49J15;
  • 49J20;
  • 74B20;
  • 74K10;
  • 74L15;
  • 90C31