Implicit constraint handling for shape optimisation with POD-morphing - Raghavan, Balaji; Xiao, Manyu; Breitkopf, Piotr; Villon, Pierre (European Journal of Computational Mechanics, 2012)
In the former paper, 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 bilevel 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.