Graded element method for the heat conduction analysis of gradient composites

Graded finite elements were proposed for the heat conduction analysis of gradient composites whose thermal properties were described by micromechanics. The spatially varying stiffness matrices of four-node and eight-node graded elements were calculated through linear and high-order interpolations of temperature fields. Several exact steady-state temperature and flux fields of graded composite plates under temperature gradient and thermal flux loads were presented. With reference to the exact solutions, the heat conduction finite element results of continuous gradient models and conventional, step-wise models were compared to validate the graded elements. The effects of some parameters on the graded elements were also discussed. It shows that the temperature fields resulting from graded and homogeneous elements are nearly the same; the graded elements can give more accurate local flux fields than homogeneous elements do when thermal loads are perpendicular to the material gradation; when they are parallel, the eight-node quadrilateral and homogeneous elements are both excellent, nevertheless, the four-node quadrilateral elements are worse.