Generation of quadrilateral meshes on free-form surfaces

Meshing is one of the main steps of the finite element method. Free-form su rfaces are widely used bur their meshing process is still not straightforwa rd. Moreover, quadrilateral elements are less used because quadrilateral me shes are generated with more difficulty than triangular ones. Here, a new m ethod 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 u sed. Then the remaining triangles are eliminated tay moving one of them tow ards 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 num ber of nodes belonging to four adjacent elements. Various topological opera tors are described. Some of them are complex and effectively move singulari ties across the quadrilateral mesh to improve it. Finally, examples illustr ate the behaviour and the efficiency of the approach described. (C) 1999 El sevier Science Ltd. All rights reserved.