Electric-thermal link finite element made of a FGM with spatial variation of material properties

Abstract

An effective 1D electric-thermal link finite element is presented in the paper, which is suitable for weak-coupled Joule heating analysis of the electric conductors and circuits made of a functionally graded material (FGM) with spatial continuous variation of material properties. Spatial continuous variation of material properties can be induced by spatial continuous variation of both the volume fractions and material properties of the FGM constituents. Finite element equations will be established for a new link finite element of constant cross-section and homogenized effective electric and thermal conductivity. Homogenization of the spatial varying material properties is done by extended mixture rules and laminate theory, where the real link element has been transformed to a multilayered sandwich link element. Numerical experiments will be done concerning calculation of the electric and thermal fields of the FGM conductors of circular and rectangular cross-sections with continuous spatial variation of material properties (with symmetric and asymmetric transversal variation, and polynomial longitudinal variation). The effect of division fineness of the link to layers in transversal direction on the solution results has been evaluated. The proposed link finite element can be used for thermal-electric analysis of sandwich and real multilayered conductors. The solution results will be discussed and compared with those obtained by using a very fine mesh of the 2D and 3D solid elements of a FEM commercial program.