Automated Mesh Deformation for Computer-Aided Design Models That Exhibit Boundary Topology Changes

Abstract

This paper describes an automated approach to deform the analysis mesh applied to a CAD model in response to a change in the shape of the CAD model during the shape optimization process. It is an advance over existing techniques because it works even when the boundary topology of the CAD model changes during the shape change, which other approaches cannot generally accommodate. To achieve the deformation, an analysis topology representation is created for each model, such that there is a one-to-one mapping between the analysis topology representing the models before and after the shape change. The surface mesh is deformed using constrained Delaunay triangulation and it is shown how the domain mesh can be updated based on the surface mesh deformation calculated. Here the approach used is Linear Elasticity.

Mesh and Geometry Manipulations for Optimization and Inverse Design

“…This method can accommodate large displacements, and the matching of B-Rep topology between the models is facilitated by the implementations of virtual topology [13], using the structure provided by [14] and As-Rigid-As-Possible (ARAP) [15] parametrization of virtual supersets to transfer nodal positions. As a result, faces appearing or disappearing as a result of parametric perturbations can be processed [16]. In the example shown in Fig.…”