The Topological Asymptotic for PDE Systems: The Elasticity Case
- 1 January 2001
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Control and Optimization
- Vol. 39 (6), 1756-1778
- https://doi.org/10.1137/s0363012900369538
Abstract
The aim of the topological sensitivity analysis is to obtain an asymptotic expansion of a design functional with respect to the creation of a small hole. In this paper, such an expansion is obtained and analyzed in the context of linear elasticity for general functionals and arbitrary shaped holes by using an adaptation of the adjoint method and a domain truncation technique. The method is general and can be easily adapted to other linear PDEs and other types of boundary conditions.Keywords
This publication has 8 references indexed in Scilit:
- The shape and topological optimizations connectionComputer Methods in Applied Mechanics and Engineering, 2000
- On the Topological Derivative in Shape OptimizationSIAM Journal on Control and Optimization, 1999
- Identification of conductivity imperfections of small diameter by boundary measurements. Continuous dependence and computational reconstructionInverse Problems, 1998
- Mechanical inclusions identification by evolutionary computationRevue Européenne des Éléments Finis, 1996
- Computation of high order derivatives in optimal shape designNumerische Mathematik, 1994
- Optimal bounds on the effective behavior of a mixture of two well-ordered elastic materialsQuarterly of Applied Mathematics, 1993
- Identification of small inhomogeneities of extreme conductivity by boundary measurements: a theorem on continuous dependenceArchive for Rational Mechanics and Analysis, 1989
- Conception optimale ou identification de formes, calcul rapide de la dérivée directionnelle de la fonction coûtESAIM: Mathematical Modelling and Numerical Analysis, 1986