期刊
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
卷 32, 期 11, 页码 926-935出版社
ELSEVIER SCI LTD
DOI: 10.1016/j.enganabound.2007.12.007
关键词
Topological derivative; Shape sensitivity analysis; Topology design; Asymptotic analysis
资金
- CNPq/FAPERJ-PRONEX [E-26/ 171.199/2003]
- CONICET
- CAPES
The topological derivative gives the sensitivity of the problem when the domain under consideration is perturbed by the introduction of a hole. Alternatively, this same concept can also be used to calculate the sensitivity of the problem when, instead of a hole, a small inclusion is introduced at a point in the domain. In the present paper we apply the Topological-Shape Sensitivity Method to obtain the topological derivative of inclusion in two-dimensional linear elasticity, adopting the total potential energy as the cost function and the equilibrium equation as a constraint. For the sake of completeness, initially we present a brief description of the Topological-Shape Sensitivity Method. Then, we calculate the topological derivative for the problem under consideration in two steps: firstly we perform the shape derivative and next we calculate the limit when the perturbation vanishes using classical asymptotic analysis around a circular inclusion. In addition, we use this information as a descent direction in a topology design algorithm which allows to simultaneously remove and insert material. Finally, we explore this feature showing some numerical experiments of structural topology design within the context of two-dimensional linear elasticity problem. (c) 2008 Elsevier Ltd. All rights reserved.
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