EFFICIENT REFORMULATION OF THE THERMOELASTIC HIGHER-ORDER THEORY FOR FUNCTIONALLY GRADED MATERIALS

摘要

The majority of techniques employed in the analysis of functionally graded materials (FGMs) use the so-called uncoupled approach, based on homogenized material property variations, which ignores the effect of local microstructural interaction. The higher-order theory for FGMs (HOTFGM) is a coupled approach that explicitly takes the effect of microstructural gradation and, thus, the local interaction of the spatially variable inclusion phase(s), into account. Despite its demonstrated utility, however, the original formulation of HOTFGM is computationally intensive. Herein, an efficient reformulation of HOTFGM is presented based on the local/global conductivity and stiffness matrix formulations. In this approach, surface-averaged quantities are the primary variables which replace volume-averaged quantities employed in the original formulation. The reformulation eliminates redundant continuity equations and, therefore, decreases the size of the overall systems of equations for the thermal and mechanical problem by approximately 60%, facilitating modeling of realistic microstructures. Explicit expressions for the elements of the local conductivity and stiffness matrices, which relate the surface average heat flux/traction quantities to the corresponding surface average temperatures/displacements facilitate the theory's implementation, as well as comparison with the finite-element approach. The presented results illustrate the efficiency of the reformulation and its advantages in analyzing FGMs.