Adaptive Mesh Generation for Finite Element Analysis of Functionally Graded Materials

Abstract

Finite Element Analysis (FEA) is an important step for the design of structures or components formed by heterogeneous objects such as multi-material objects, Functionally Graded Materials (FGMs), etc. The main objective of the FEA-based design of heterogeneous objects is to simultaneously optimize both geometric shapes and material distributions over the design domain (e.g., Homogenization Design Method). However, the accuracy of the FEA-based design wholly depends on the quality of the finite element models generated. Therefore, there exists an increasing need for developing a new mesh generation algorithm adaptive to both geometric complexity and material distributions. In this paper, a two-dimensional adaptive mesh generation algorithm is proposed based on the discretization by which continuous material variation inside an object is converted into step-wise variation. The proposed algorithm first creates nodes on the iso-material contours of the discretized solid models. Triangular meshes are then generated inside each iso-material region formed by iso-material contours. Current implementation considers two-dimensional problems and thus needs to be extended to include three-dimensional problems in the near future.