Thermal analysis of elliptical fiber-reinforced composites by the hybrid Trefftz finite element method

Abstract A hybrid Trefftz finite element method (HT-FEM) is developed for microstructural modeling of fiber-reinforced composites and porous materials. In this method, each polygon contains an elliptical inclusion (fiber) and serves as an element. A frame temperature field is assumed along the element outer-boundary, while intra-element temperature fields in the matrix as well as in the inclusion are independently assumed as a linear combination of T-complete functions. Using the complex functions and conformal mapping technology, systematic construction of T-complete functions which satisfy not only the governing equations but also the continuity of temperature on the inclusion-matrix interface is conducted. Unlike the studies in the literature, only one hybrid functional is required to link the two assumed fields in the inclusion and surrounding matrix. The resultant element stiffness equation involves the integrals along the element outer-boundary only. The proposed method is verified against ABAQUS solutions. Numerical results show that HT-FEM can capture the severe perturbation of otherwise regular distribution of temperature and heat flux due to the presence of inclusions or voids. The size and inclination of the elliptical inclusion have a significant influence on the effective thermal conductivity of the composite. It is also pointed out that the effective thermal conductivity is a cosine function in terms of two times the inclination angle.