Minimum stress optimal design with the level set method

This paper is devoted to minimum stress design in structural optimization. We propose a simple and efficient numerical algorithm for shape and topology optimization based on the level set method coupled with the topological derivative. We compute a shape derivative, as well as a topological derivati...

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Bibliographic Details
Published in:Engineering analysis with boundary elements 2008-11, Vol.32 (11), p.909-918
Main Authors: Allaire, Grégoire, Jouve, François
Format: Article
Language:English
Subjects:
Boundary element method
Derivatives
Design engineering
Level set method
Mathematical analysis
Mathematical models
Mathematics
Numerical Analysis
Optimization
Shape derivative
Stresses
Topological derivative
Topology
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Summary:This paper is devoted to minimum stress design in structural optimization. We propose a simple and efficient numerical algorithm for shape and topology optimization based on the level set method coupled with the topological derivative. We compute a shape derivative, as well as a topological derivative, for a stress-based objective function. Using an adjoint equation we implement a gradient algorithm for the minimization of the objective function. Several numerical examples in 2-d and 3-d are discussed.
ISSN:0955-7997
1873-197X
DOI:10.1016/j.enganabound.2007.05.007