X-CAD: Optimizing CAD Models with Extended Finite Elements

摘要

We propose a novel generic shape optimization method for CAD modelsbased on the eXtended Finite Element Method (XFEM). Our method worksdirectly on the intersection between the model and a regular simulation grid,without the need to mesh or remesh, thus removing a bottleneck of classicalshape optimization strategies. This is made possible by a novel hierarchicalintegration scheme that accurately integrates finite element quantities withsub-element precision. For optimization, we efficiently compute analyticalshape derivatives of the entire framework, from model intersection to integrationrule generation and XFEM simulation. Moreover, we describe adifferentiable projection of shape parameters onto a constraint manifoldspanned by user-specified shape preservation, consistency, and manufacturabilityconstraints. We demonstrate the utility of our approach by optimizingmass distribution, strength-to-weight ratio, and inverse elastic shape designobjectives directly on parameterized 3D CAD models.