Figure 23.3: Elements with sharp and flat angles ● Number of elements should be moderate related to efficiency of finite element analysis Topological consistency(homeomorphism)between the eract input domain and its mesh - related to robustness of finite element analysis 8, 9 Automation, adaptability, etc 23.1. 4 Finite Element Analysis in a CAD Environment See figure 23. 4 In Figure 23. 4, " input data preparation" includes the preparations of boundary conditions loads, and integration constants At etc. "post-processing of results" includes scientific visual- ization. etc 23.1.5 Background Information Delaunay Triangulation [4, 19 Given a set of points Pi, the Voronoi region, Vi is a set of points closer to a site Pi than any other site P,(See Figure 23.5). Delaunay triangulation is constructed by connecting those points whose Voronoi regions have a common edge(2D) or face(3D). Some properties of Delaunay triangulation are it maximizes the minimum angle(globally) circumcircle criterion: every circle passing through the 3 vertices of a triangle does not contain any other vertices . it covers the convex hull of all sites Mesh Conversion Performed if a mesh generator produces only one type of element and another type is required Quadrilaterals(Hexahedra)- Triangles(Tetrahedra)[12: easy and well-shaped mesh, ee Figure 23.6 Triangles(Tetrahedra)-Quadrilaterals(Hexahedra)Figure 23.3: Elements with sharp and flat angles • Number of elements – should be moderate. – related to efficiency of finite element analysis. • Topological consistency (homeomorphism) between the exact input domain and its mesh. – related to robustness of finite element analysis [8, 9]. • Automation, adaptability, etc. 23.1.4 Finite Element Analysis in a CAD Environment See Figure 23.4. In Figure 23.4, “input data preparation” includes the preparations of boundary conditions, loads, and integration constants ∆t etc.; “post-processing of results” includes scientific visual￾ization, etc. 23.1.5 Background Information Delaunay Triangulation [4, 19] Given a set of points Pi , the Voronoi region, Vi is a set of points closer to a site Pi than any other site Pj (See Figure 23.5). Delaunay triangulation is constructed by connecting those points whose Voronoi regions have a common edge (2D) or face (3D). Some properties of Delaunay triangulation are: • it maximizes the minimum angle (globally). • circumcircle criterion: every circle passing through the 3 vertices of a triangle does not contain any other vertices. • it covers the convex hull of all sites. Mesh Conversion Performed if a mesh generator produces only one type of element and another type is required. • Quadrilaterals (Hexahedra) → Triangles (Tetrahedra) [12]: easy and well-shaped mesh, see Figure 23.6. • Triangles (Tetrahedra) → Quadrilaterals (Hexahedra) 4