A dual-representation strategy for the virtual assembly of thin deformable objects

Abstract

The two main objectives of virtual assembly are: (1) to train assembly-operators through virtual assembly models, and (2) to simultaneously evaluate products for ease-of-assembly. The focus of this paper is on developing computational techniques for virtual assembly of thin deformable beam and plate-like objects. To meet the objectives of virtual assembly, the underlying computational technique must: (1) be carried out at a high frame-rate (>20 frames/second), (2) be accurate (<5% error in deformation and force estimation), (3) be conducive to collision detection, and (4) support rapid design evaluations. We argue in this paper that popular computational techniques such as 3-D finite element analysis, boundary element analysis and classic beam/plate/shell analysis fail to meet these requirements. We therefore propose a new class of dual representation techniques for virtual assembly of thin solids, where the geometry is retained in its full 3-D form, while the underlying physics is dimensionally reduced, delivering: (1) high computational efficiency and accuracy (over 20 frames per second with <1% deformation error), and (2) direct CAD model processing, i.e., the CAD model is not geometrically simplified, and 3-D finite element mesh is not generated. In particular, a small-size stiffness matrix with about 300 degrees of freedom per deformable object is generated directly from a coarse surface triangulation, and its LU-decomposition is then exploited during real-time simulation. The accuracy and efficiency of the proposed method is established through numerical experiments and a case study.