Adaptive triangular element generation and optimization-based smoothing: Part 2. On the surface

Abstract

A general and systematic approach to adaptive triangular element generation and optimization-based smoothing on the surface is presented in this paper. The approach starts from a rough triangular mesh that needs to be remeshed in order to meet the desired mesh density. Various local transformation processes including edge and face splitting, edge collapsing and edge swapping are employed for enhancement of mesh quality as well as for generation of new triangular elements from the rough triangular elements. An edge swapping scheme is proposed, which satisfy both of the Delaunay criterion and topological consistency. To reduce the geometrical error that is inevitable in remeshing, curvature of the surface is not only considered in determining the mesh density distribution but the characteristic edges and the triangular elements are also interpolated by the third-order chord-length spline curves and the bi-cubic Bezier patches, respectively. The nodal points of the generated mesh are smoothed by the physically-based smoothing scheme and then optimally placed by the optimization-based smoothing scheme. Through various application examples, the characteristics and effects of the presented approaches are quantitatively investigated.

Research and Implementation of 3D Surface Finite Element Mesh Generation Based on STEP

“…There are two steps for 3D model finite element mesh generation, i.e., surface element mesh generation and inner element mesh generation. Triangulation of the surface is implemented by applying parametric surface mapping method [5][6][7][8][9][10]. Geometrical and topological information of each surface is mapped and extracted to 2D parametric space after the model is imported and reconstructed according to STEP files.…”

Boundary Condition Related Mixed Boundary Element and its Application in FMBEM for 3D Elastostatic Problem

“…Therefore, this element generation algorithm can be directly integrated into any CAD software with ACIS kernel. The linear triangular elements are used because they can accurately represent the geometries [Cayol and Cornet (1997)] and automatically be generated for geometries [Lee and Joun (2008)]. In order to solve large scale problems, the mixed element method is applied to the fast multipole BEM (FMBEM) ; Chen and Xiao (2009); Wang et al (2013Wang et al ( , 2015] which can reduce the BEM's complexities of both time and space from O(N 2 ) to O(N ).…”