Finite Element Analysis (FEA) is an important step for the design of structures or components formed by heterogeneous objects such as multi-materials, Functionally Graded Materials (FGMs), etc. The main objective of the FEA-based design of heterogeneous objects is to simultaneously optimize both geometry and material distribution 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. Therefore, there exists an increasing need for generating finite element models adaptive to both geometric complexity and material distribution. This paper introduces a method for FEA-based design of heterogeneous objects. At the design stage, a heterogeneous solid model is first created by referring to the libraries of primary materials and composition functions that are already available in the field of material science. The heterogeneous solid model is then discretized into an object model onto which appropriate material properties are mapped. Discretization converts continuous material variations inside an object into stepwise variations. Next, the object model is adaptively meshed and converted into a finite element model. The meshing algorithm first creates nodes on the iso-material curves (or surfaces) of heterogeneous solid models. Triangular (or tetrahedral) meshes are then generated inside each iso-material region formed by iso-material curves (or surfaces). FEA using commercial software is finally performed to estimate stress levels. This FEA-based design cycle is repeated until a satisfactory solution is obtained. If the design objective is satisfactory, the object model is fed to the fabrication system where a process planning is performed to create instructions for LM machines. An example (FGM pressure vessel) is shown to illustrate the entire FEA-based design cycle.

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