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Implicit constraint handling for shape optimisation with POD-morphing. (English. French summary) Zbl 1348.74284
Summary: In the former paper [B. Raghavan et al., “POD-morphing: an a posteriori grid parametrization method for shape optimization”, Eur. J. Comput. Mech. 19, No. 5–7 (2010; doi:10.3166/ejcm.19.671-697)], we have introduced an original morphing approach based on Proper Orthogonal Decomposition (POD) of shapes, designed to replace parametrized CAD models in structural optimization. Here, we expand the method to interpolate exclusively between admissible instances of structural shapes, thus permitting a global understanding of the design domain and also reducing the size of the optimisation problem. The result is a bi-level reparametrization approach for structural geometries based on Diffuse Approximation in a properly chosen locally linearized space, and the geometric parameters are replaced with the smallest set of variables needed to represent a manifold of admissible shapes for a chosen precision. We demonstrate the approach in a typical shape optimisation problem.

74P10 Optimization of other properties in solid mechanics
65D17 Computer-aided design (modeling of curves and surfaces)
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