Graded finite elements (GFEs) provide a promising way for simulating functionally graded materials. Nevertheless, the existing GFE method takes the conventional isoparametric transform functions as a unified representation for the material non-homogeneity in each element regardless of the practical global distribution forms of material properties. This inevitably leads to a certain difference between the local formulation of material property variation in the elements and the corresponding global gradation patterns. In order to eliminate this difference, an improved GFE algorithm is proposed in the present article. The property distribution in the element is formulated by substituting the isoparametric transform of the coordinates directly into the corresponding global gradation functions. Therefore, the local property distribution is always consistent with the global one. Both the improved six-node triangular elements (T6) and eight-node quadrilateral elements (Q8) are developed for non-homogeneous elastic, piezoelectric and magneto-electro-elastic materials, respectively. Exact solutions in three special cases are presented to make comparison with the numerical results, and the accuracy of the proposed algorithm is verified. It is demonstrated that the improved GFE is an effective method for the numerical simulation of functionally graded materials.
On the Finite Element Implementation of Functionally Graded Materials
