Generation of quadrilateral meshes on free-form surfaces
Meshing is one of the main steps of the finite element method. Free-form surfaces are widely used but their meshing process is still not straightforward. Moreover, quadrilateral elements are less used because quadrilateral meshes are generated with more difficulty than triangular ones. Here, a new method is introduced to mesh free-form surfaces with quadrilateral elements. At first, a triangular mesh is used to generate each quadrilateral element by merging two adjacent triangles. For this purpose, a frontal method is used. Then the remaining triangles are eliminated by moving one of them towards another one in order to create a quadrilateral element. Next, the mesh is optimized by topologic operators which eliminate mesh singularities. A specific node repositioning scheme is used to further improve the shape of the elements. Ultimately, the goal is to obtain a mesh with the largest number of nodes belonging to four adjacent elements. Various topological operators are described. Some of them are complex and effectively move singularities across the quadrilateral mesh to improve it. Finally, examples illustrate the behaviour and the efficiency of the approach described.
quadrilateral mesh free-form surfaces topologic operators mesh optimization