Automatic finite element mesh generation over domains comprised of multiply connected, intersecting, rigid body-movable subdomains for the automation of parametric conceptual design

A novel approach for the automatic generation and refinement of finite element meshes over nonconvex domains subdivided by multiply connected, rigid body movable subdomains has been developed. Unlike most traditional approaches to mesh generation, a combination of computational geometry and geometric modeling has been employed to implement parametric computer-aided design based on the finite element method. Nonconvexity of an overall three dimensional domain is handled by combining convex geometric primitives as subdomains for the construction of an initial three dimensional domain. A clipping algorithm is employed for determining intersections and boundary points between subdomains following their rigid body movements. Triangulated surfaces of three dimensional subdomains are used to calculate the intersection points. As an application of this approach to parametric redesign, a series of two and three dimensional meshes that model a human hip joint prosthesis in two different positions relative to the pelvis, have been developed.