Mesh generation on curved wire-frame models

Abstract In structural analysis, the wire-frame models are often employed to represent the shapes of curved faces. Finite element analysis of the curved faces requires that a well-shaped, well-sized mesh be smoothly generated on them. The algorithm described in this page generates such a mesh from a wire-frame model by the following three steps: (1) projection of the vertices of a given wire-frame model on a flat plane and generation of a 2D mesh on the plane, (2) generation of a triangulation-based surface by minimizing the strain energy of a thin-plate-bending model, and (3) fitting the mesh to the triangulation-based surface. This algorithm can generate well-shaped, well-sized triangular or quadrilateral meshes on the curved faces. Background In applications of structural analysis such as simulation of automobile crashes and sheet metal forming, automatic generation of a finite-element mesh is an essential process. If a surface or solid model has already been created, a mesh is generated in a parameter space of a trimmed surface function, such as trimmed NURBS, and mapped to a Euclidean space. There have been many papers on meshing of surface models. In practice, however, wire-frame models are often employed to represent the shapes of curved surfaces in structural analysis. One reason for this is that they are easier to construct than surface or solid models. Another is that, in the design of structural parts, exact surface data are not required, unlike in artistic design such as that of outer panels for cars which require good-looking surfaces. In the analysis of structural parts, the positions of holes and crack tips in the parts, the thicknesses of plates, the materials of the parts, and so on are more important than the exact shapes of the parts. Therefore, the characteristic lines of the parts are designed by using wire-frame models, and domains surrounded by the lines are interpolated smoothly. If a smooth mesh can be generated on a domain, structural analysis can be performed successfully. Mesh generation on curved wire-frame models The problem is to generate a triangular or quadrilateral mesh, that is well-shaped, well-sized and smooth on a surface, from input data of a wire-frame model and a node-spacing function (see the above figure). This algorithm consists of three steps described below. Step 1: Mesh generation on a plane by bubble mesh The vertices constructing a wire-frame model are projected on a plane and a triangular mesh is obtained on the plane by bubble meshing. The triangular mesh is converted into a quadrilateral mesh, if it is required. Step 2: Generation of a triangulation-based surface A wire-frame model does not define the inside of a face; therefore, a smooth surface obtained by minimizing the strain energy of the thin-plate-bending model can be generated from a wire-frame model by using FEM. Step 3: Fitting of the mesh to the triangulation-based surface The mesh generated in Step 1 is fitted to the triangulation-based surface generated in Step 2. Results of mesh generation on curved wire-frame models The above figures show two views of a given wire-frame model. The above figures show two views of a triangular mesh generated from the wire-frame model. The above figure shows a quadrilateral mesh converted from the triangular mesh. The above figures show two views of a triangular mesh generated from the wire-frame model, the position of a inside wire of which is modified from the previous wire-frame model. To the top page of meshing project

Last modified 30 June 1998