Simplified engineering analysis via medial mesh reduction

ABSTRACT

Numerous simplification methods have been proposed for speeding up engineering analysis/ simulation. A recently proposed medial axis reduction is one such method, that is particularly well suited for analyzing thin solids, wherein a governing equation is reduced to the medial axis, leading to significantly smaller stiffness matrices. However, this method involves the non-trivial computation of a piece-wise C¹ continuous medial axis that must closely approximate the exact medial axis.In this paper, we propose a new medial mesh reduction that is computationally more efficient than medial axis reduction in that it only requires a C⁰ continuous tessellation of the medial axis. However, the proposed method retains all the advantages of the explicit medial axis reduction including automation and guaranteed numerical convergence. Furthermore, as the medial mesh converges to the exact medial axis, the computed solution also converges to the exact dimensionally reduced solution. These claims are substantiated through numerical experiments in 2-D and 3-D.

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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.5 Computational Geometry and Object Modeling
          Subjects: Curve, surface, solid, and object representations

Additional Classification:
  J. Computer Applications
  J.2 PHYSICAL SCIENCES AND ENGINEERING
      Subjects: Engineering
  J.6 COMPUTER-AIDED ENGINEERING
      Subjects: Computer-aided design (CAD)

General Terms:
Algorithms, Design, Theory

Keywords:
CAD, CAE, dimensional reduction, engineering analysis, medial axis transforms, medial mesh, mid-plane