Topological sensitivity analysis for elliptic differential operators of order 2m

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:256

Article

Amstutz, Samuel¹  Novotny, Antonio Andre²  Van Goethem, Nicolas^3,4 

[1] Univ Avignon, Fac Sci, Lab Math Avignon, F-84000 Avignon, France

[2] Coordena Matemat Aplicada & Computac, Lab Nacl Computa Cientif LNCC MCTI, BR-25651075 Petropolis, RJ, Brazil

[3] SISSA, I-34136 Trieste, Italy

[4] Univ Lisbon, Fac Ciencias, Dept Matemat, CMAF, P-1649003 Lisbon, Portugal

关键词: Topological sensitivity analysis;    Topological derivative;    Elliptic operator;    Polarization tensor;    Degenerate polarization tensor;   

DOI  :  10.1016/j.jde.2013.12.005

来源: Elsevier

【 摘 要 】

The topological derivative is defined as the first term of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of a singular domain perturbation. It has applications in many different fields such as shape and topology optimization, inverse problems, image processing and mechanical modeling including synthesis and/or optimal design of microstructures, fracture mechanics sensitivity analysis and damage evolution modeling. The topological derivative has been fully developed for a wide range of second order differential operators. In this paper we deal with the topological asymptotic expansion of a class of shape functionals associated with elliptic differential operators of order 2m, m >= 1. The general structure of the polarization tensor is derived and the concept of degenerate polarization tensor is introduced. We provide full mathematical justifications for the derived formulas, including precise estimates of remainders. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free