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Volumetric expressions of the shape gradient of the compliance in structural shape optimization

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arxiv 1701.05762 v1 pith:6VRIJHL7 submitted 2017-01-20 math.OC cs.NAmath.NA

Matteo Giacomini , Olivier Pantz , Karim Trabelsi This is my paper · ORCID
classification math.OCcs.NAmath.NA
keywords shapeexpressionsgradientcomplianceelasticitylinearproblemvolumetric
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In this article, we consider the problem of optimal design of a compliant structure under a volume constraint, within the framework of linear elasticity. We introduce the pure displacement and the dual mixed formulations of the linear elasticity problem and we compute the volumetric expressions of the shape gradient of the compliance by means of the velocity method. A preliminary qualitative comparison of the two expressions of the shape gradient is performed through some numerical simulations using the Boundary Variation Algorithm.

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