Numerical solutions for functionally graded solids under thermal and mechanical loads using a high-order control volume finite element method

In this article, a high-order control volume finite element method (CVFEM) is proposed to explore thermal stress analysis for functionally graded materials (FGMs) at steady state with the unstructured mesh capability for arbitrary-shaped domain. This formulation, also known as cell-vertex finite volume formulation, is useful for material engineers and scientists in determining the thermal response and thermo-deformations in FGM that subjected to thermal and mechanical loads such as thermal barrier plates, pressure vessels, heat exchanger tubes, etc. The heat conduction is considered for thermal analysis whereas the plane elasticity is considered for stress analysis. The quadratic interpolation for unknown variables and their derivatives are obtained from the shape functions of six-node triangular element given by the finite element theory. In addition, the material properties in functionally graded structure are also modeled by using the high-order shape functions. To verify and illustrate the accuracy of the proposed method, the results from our computer program are compared with those obtained analytically and numerically by a conventional Finite Element Method. The effect of grading parameter is also discussed.