Three-dimensional transient heat conduction problems in FGMs via IG-DRBEM

In this paper, the isogeometric dual reciprocity boundary element method (IG-DRBEM) is firstly applied to solve three-dimensional (3D) transient heat conduction problems in functionally graded materials (FGMs) with heat sources. Using the fundamental solution of the 3D potential problem, the integral equation of boundary-domain is established by the weighted residual method. The normalized temperature is introduced, and the domain integral is transformed into the boundary integral by the dual reciprocity method (DRM). Finally, the theoretical framework of the isogeometric BEM for FGMs problems is established. Furthermore, the effects of different approximation functions, time steps, element refinements and the distance from the inner point to the boundary on the results are discussed in detail via several examples, which verify the validity of the presented method. In order to promote the development of IGBEM, the program code of this article can be obtained by sending email to yubochina@hfut.edu.cn.