期刊
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
卷 84, 期 6, 页码 733-756出版社
WILEY
DOI: 10.1002/nme.2922
关键词
topological derivative; sensitivity analysis; multi-scale modelling; level set domain representation; synthesis of microstructures
资金
- The Royal Society [JP080066]
- Brazilian research funding council, CNPq [382485/2009-2]
This paper proposes an algorithm for the synthesis/optimization of microstructures based on an exact formula for the topological derivative of the macroscopic elasticity tensor and a level set domain representation. The macroscopic elasticity tensor is estimated by a standard multi-scale constitutive theory where the strain and stress tensors are volume averages of their microscopic counterparts over a representative volume element. The algorithm is of simple computational implementation. In particular, it does not require artificial algorithmic parameters or strategies. This is in sharp contrast with existing microstructural optimization procedures and follows as a natural consequence of the use of the topological derivative concept. This concept provides the correct mathematical framework to treat topology changes such as those characterizing microstuctural optimization problems. The effectiveness of the proposed methodology is illustrated in a set of finite element-based numerical examples.Copyright (c) 2010 John Wiley & Sons, Ltd.
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