The influence of packing dimension on the effective thermal properties of doubly-periodic composites by using super hybrid finite body elements

Abstract

A super polygonal hybrid element is developed for investigating the effects of the packing dimension on effective thermal conductivities of composites containing a doubly periodic array of circular inclusions. In the analysis, a rectangular representative volume element (RVE) is employed to represent the packing dimension of the periodic microstructure and then is solved using a super hybrid finite element in which the fundamental solutions are taken as internal interpolation functions. The fundamental solutions used to satisfy both the heat transfer governing equation and the interfacial continuity between the inclusion and the surrounding matrix. The use of fundamental solutions makes the functional of stiffness matrix including boundary integrals only. As a result, significant efforts on mesh generation can be saved, and mesh reduction as well as high solution accuracy can be achieved. Finally, numerical examples are considered to investigate the role of the packing dimension of the RVE.