Automatic mesh generation of heterogeneous objects for finite element analysis

Abstract

Adaptive meshing of 2D planar regions, curved surfaces as well as 3D volumes has been extensively studied in Finite Element Analysis (FEA) in the past few decades. Despite the maturity of these adaptive meshing approaches, most of the existing schemes assume the domain or sub-domain of interest is homogeneous. In the context of FEA of heterogeneous objects, traditional adaptive mesh generation strategies become inadequate as they fail to take into account the material heterogeneities. This thesis is motivated to tackle these problems and propose an adaptive mesh generation scheme for FEA of versatile heterogeneous materials. In order to tackle the material heterogeneities and the geometric complexities, the proposed adaptive meshing strategy embraces three steps: initial mesh generation, material-oriented refinement, and geometry-oriented refinement. Specifically, in the material-oriented refinement, a centroidal Voronoi tessellation (CVT)-based method is designed to control the mesh adaptation in terms of the material distribution. Based on a specific density function of material variations, the CVT-based method distributes the material composition variation over elements as equally as possible and thus minimizes the number of elements regarding a given material threshold. Experiments show that the proposed approach guarantees desirable mesh adaptation as well as high mesh quality.

By coupling the idea of adaptive meshing and a heterogeneous solid modeler, we further propose an automatic mesh generation strategy for heterogeneous objects. The automatic mesh generation method consists of two stages: preprocessing and adaptive mesh generation; the role of the former is to convert heterogeneous CAD models into meshing-suitable models while the latter aims to generate adaptive meshes with respect to the material and geometric information. In the adaptive mesh algorithm, we introduced a direct refinement algorithm rather than the previous step-wise approach to refine the targeted mesh according to the material threshold and the minimum angle simultaneously. In addition, an optimal Delaunay triangulation (ODT)-based method was utilized to improve the mesh quality and control the mesh density instead of the previous CVT-based method. Experiments show that the proposed automatic mesh generation method has the capacities to generate efficient meshes on both 2D and 3D heterogeneous object models with complex material distributions such as bidirectional and tri-directional.

As a natural progression of the preceding automatic mesh generation method, we develop an integrated CAD-FEA system for heterogeneous object design and analysis with the automatic mesh generator being an integral part. The integrated system includes three parts: heterogeneous solid modeler, automatic mesh generator, and FEA module. The main role of the automatic mesh generator here is to convert heterogeneous solid models into finite element models automatically so that FEA can be conducted. Experiments demonstrate that this integrated system releases FE analysts from a tedious task to manually construct finite element models and guarantees accurate FEA results.

The underlying idea of the adaptive meshing algorithm can be applied into a lot of applications. We show how to implement it into FEA of heterogeneous objects involving mesh refinements and construction of irregular porous structures which are regarded as special heterogeneous objects.