A Three-Dimensional Adaptive Mesh Generation Approach Using Geometric Modeling With Multi-Regions and Parametric Surfaces

Abstract

This work presents a methodology for adaptive generation of 3D finite element meshes using geometric modeling with multiregions and parametric surfaces, considering a geometric model described by curves, surfaces, and volumes. This methodology is applied in the simulation of stress analysis of solid structures using a displacement-based finite element method and may be extended to other types of 3D finite element simulation. The adaptive strategy is based on an independent and hierarchical refinement of curves, surfaces, and volumes. From an initial model, new sizes of elements obtained from a discretization error analysis and from geometric restrictions are stored in a global background structure, a recursive spatial composition represented by an octree. Based on this background structure, the model's curves are initially refined using a binary partition algorithm. Curve discretization is then used as input for the refinement of adjacent surfaces. Surface discretization also employs the background octree-based refinement, which is coupled to an advancing front technique in the surface's parametric space to generate an unstructured triangulated mesh. Surface meshes are finally used as input for the refinement of adjacent volumetric domains, which also uses an advancing front technique but in 3D space. In all stages of the adaptive strategy, the refinement of curves, surface meshes, and solid meshes is based on estimated discretization errors associated with the mesh of the previous step in the adaptive process. In addition, curve and surface refinement takes curvature information into account. Numerical examples of simulation of engineering problems are presented in order to validate the methodology proposed in this work.

Optimized smoothing of discrete models of the implicitly defined geometrical objects' surfaces

“…The advantage of the proposed approach is that (unlike the results of [6][7][8][9][10]) it can be applied to both triangles and quadrangles, and also does not require the insertion of additional nodes and elements.…”

“…In [9], it has been proposed to use hierarchical structures (octrees) to increase the number of nodes in regions with the greatest surface curvature. The use of hierarchical structures for mesh improvement in the adaptive finite element analysis has been shown in [10]. In [11], features of implementation of hierarchical structures to improve models using a graphic processor have been considered.…”

“…One of the most widely used and at the same time simple methods of mesh improvement is local Laplacian smoothing [10]. It moves each node to the geometric center of the polygon formed by adjacent nodes (Fig.…”

A new approach to automatic and a priori mesh adaptation around circular holes for finite element analysis

“…Geometry can be taken into account from several considerations such as curvature, form features and geometric proximity. Several research approaches [18,30,33,34], as well as implementations in commercial FEA systems consider curvature as a key criterion to a priori adaptation. In these approaches, either curvature along edges and/or curvature components on faces of the geometric solid model are calculated to derive a size map that is intended to control the geometric discretization error (usually referred to as ε).…”

“…a). Note that using an octree based background mesh could also have been considered like in the work of Tchon et al and others [33,34]. Another option is using an unstructured mesh.…”