STRUCTURAL AND MULTI-FUNCTIONAL OPTIMIZATION USING MULTIPLE PHASES AND A LEVEL-SET METHOD

In this work we adress the problem of structural and multi-functional shape and topology optimization using several elastic materials in a fixed working domain. The description and the evolution of the interfaces between the different phases is done using the level-set method. We use a smooth Hooke’s tensor, instead of a discontinuous one. The continuous case can be seen as an approximation of the sharp interface case, and in this context, the signed distance function corresponding to each interface is used for modeling the smooth Hooke’s tensor. A directional shape derivative is calculated for the objective function to minimize. We show 2d results for compliance minimization, as well as an example of multi-functional optimization, coupling structural and thermal problems.

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