Adaptive meshing for finite element analysis of heterogeneous materials

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 paper is motivated to tackle such problems and propose an adaptive mesh generation scheme for FEA of versatile heterogeneous materials. The proposed approach takes full advantages of the material heterogeneity information, and the mesh density is formulated with a specific function of the material variations. Dual triangulation of centroidal Voronoi tessellation is then constructed and necessary mesh subdivision is applied with respect to a predefined material threshold. Experiments show that the proposed approach distributes the material composition variation over mesh elements as equally as possible and thus minimizes the number of elements in terms of the given material threshold. FEA results show that the proposed method can significantly decrease the mesh complexities as well as computational resources in FEA of heterogeneous objects and compared with existing approaches, significant mesh reduction can be achieved without sacrifice in FEA qualities.

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