Meshing Curved Wire-Frame Models Through Energy Minimization and Packing of Ellipses

International Journal for Numerical Methods in Engineering, John Wiley & Sons, Num 46, pp.1221-1236, 1999

MESHING
RESEARCH
CORNER

Kenji Shimada
Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, U.S.A. Email:shimada@cmu.edu

Abstract
In the initial phase of structural part design, wire-frame models are sometimes used to represent the shapes of curved surfaces. Finite Element Analysis (FEA) of a curved surface requires a well shaped, graded mesh that smoothly interpolates the wire frame. This paper describes an algorithm that generates such a triangular mesh from a wire-frame model in the following two steps: (1) construct a triangulated surface by minimizing the strain energy of the thin- plate-bending model, and (2) generate a mesh by the bubble meshing method on the projected plane and project it back onto the triangulated surface. Since the mesh elements are distorted by the projection, the algorithm generates an anisotropic mesh on the projected plane so that an isotropic mesh results from the final projection back onto the surface. Extensions of the technique to anisotropic meshing and quadrilateral meshing are also discussed. The algorithm can generate a well-shaped, well-graded mesh on a smooth curved surface.