Automatic three-dimensional finite element mesh generation via modified ray casting

Three-dimensional (3-D) finite element mesh generation has been the target of automation due to the complexities associated with generating and visualizing the mesh. A fully automatic 3-D mesh generation method is developed. The method is capable of meshing CSG solid models. It is based on modifying the classical ray-casting technique to meet the requirements of mesh generation. The modifications include the utilization of the element size in the casting process, the utilization of 3-D space box enclosures, and the casting of ray segments (rays with finite length). The method begins by casting ray segments into the solid. Based on the intersections between the segments and the solid boundary, the solid is discretized into cells arranged in a structure. The cell structure stores neighbourhood relations between its cells. Each cell is meshed with valid finite elements. Mesh continuity between cells is achieved via the neighbourhood relations. The last step is to process the boundary elements to represent closely the boundary. The method has been tested and applied to a number of solid models. Sample examples are presented.     

有限元网格的拓扑分析

有限元网格生成及节点编号优化是有限元分析的关键技术之一。在有限元计算过程中,可通过优化节点编号来减少整体刚度矩阵的带宽,从而节约存储空间,减少有限元分析的计算时间。通过分析有限元网格的拓扑关系,依据单元节点相关性,提出了构造单元节点拓扑阵和组装有限元网格整体节点拓扑阵的有效方法,为优化有限元网格节点编号,减小有限元方程组中总体刚度矩阵的带宽奠定了基础。     

THREE-DIMENSIONAL FINITE ELEMENT MESHING BY INCREMENTAL NODE INSERTION

This paper describes an efficient algorithm for fully automated three-dimensional finite element meshing which is applicable to non-convex geometry and non-manifold topology. This algorithm starts with sparsely placed nodes on the boundaries of a geometric model and a corresponding 3-D Delaunay triangulation. Nodes are then inserted incrementally by checking the tetrahedral mesh geometry and topological compatibility between Delaunay triangulation and the geometric model. Topological compatibility is checked in a robust manner by a method which relies more on a mesh's topology than its geometry. The node placement strategy is tightly coupled to an incremental Delaunay triangulation algorithm, and results in a low growth rate of computational time.     

On the fracture toughness anisotropy of mechanically poled ferroelectric ceramics

In this paper an incremental constitutive theory for the deformation due to switching in ferroelectrics is applied to predict the fracture toughness anisotropy in these materials after mechanical poling. Mechanical poling of an initially unpoled specimen differs from electrical poling in that only mechanical stresses are applied to the material. Therefore, no electrical polarization can develop. After mechanical poling, for example by a uniaxial applied stress, the fracture toughness of a ferroelectric ceramic for cracks running parallel or orthogonal to the poling direction will differ. Finite element computations of the steady crack growth process have been carried out to quantify these differences. Results are generated for a range of constitutive properties for three crack growth directions with respect to the initial mechanical poling direction. The results are discussed in relation to available experimental data and to the toughness anisotropy due to electrical poling.