A high-order control volume finite element method for thermoelastic analysis of functionally graded solids with mixed grids

In this article, a new two-dimensional control volume finite element method has been developed for thermoelastic analysis in functionally graded materials. A nine-node quadrilateral element and a six-node triangular element are employed to deal with the mixed-grid problem. The unknown variables and material properties are defined at the node. The high-order shape functions of six-node triangular and nine-node quadrilateral element are employed to obtain the unknown variables and their derivatives. In addition, the material properties in functionally graded structure are also modeled by applying the high-order shape functions. The capabilities of the presented method to heat conduction problem, elastic problem, and thermoelastic problem have been validated. First, the defined location of material properties is found to be important for the accuracy of the numerical results. Second, the presented method is proven to be efficient and reliable for the elastic analysis in multi-phase materials. Third, the presented method is capable of high-order mixed grids. The memory and computational costs of the presented method are also compared with other numerical methods.