Hybrid Trefftz polygonal finite elements are proposed for the thermal analysis
of composites reinforced by dispersed fibers. In addition to a homogenous matrix, three
types of heterogeneities are considered in each polygon-shaped element: a circular
inclusion, an elliptical inclusion or a coated inclusion. Based on T-complete functions
satisfying the heat conduction governing equation, an interior temperature field is
assumed in inclusion, matrix as well as interphase if any. Whereas an auxiliary frame
temperature field is independently defined along the element outer-boundary. The
piecewise T-complete functions satisfy not only the governing equations but also
guarantees the temperature continuity on the interfaces by means of conformal mapping
technology. By using the divergence theorem, all the integrals involved in the single
hybrid functional are finally performed along the element outer-boundary only. This
facilitates the finite element modelling of heterogeneous materials. Several examples are
presented to demonstrate the accuracy and efficiency of the proposed method. It is also
concluded that there exists a linear relationship between the maximum number of Tcomplete
functions and the number of Gauss points sampled on each element side.
Keywords: Circular inclusion, Coating, Elliptical inclusion, Fiber-reinforced
composite, Heat conduction, Piecewise T-complete function, Polygonal element,
Single hybrid functional.