Thermal Analysis of Composites with Trefftz Finite Element Methods

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.