RI-IGABEM based on PIM in transient heat conduction problems of FGMs

Abstract

The isogeometric analysis boundary element method (IGABEM) has a broad application prospect due to its exact geometric representation and good approximation properties. In this paper, a novel radial integration IGABEM (RI-IGABEM) based on precise integration method (PIM) is proposed to solve transient heat conduction problems of functionally gradient materials (FGMs) with heat source Similar to traditional boundary element method (BEM), in which the fundamental solution for the Laplace equation is used to derive the boundary-domain integral equations, the domain integrals caused by the heat source and the thermal conductivity varying with coordinates and the initial temperature appear in the transient heat conduction problems. In order to preserve the advantage of IGABEM, i.e. only boundary is discretized, the radial integration method (RIM) is applied to transform the domain integral into an equivalent boundary integral. In addition, using a simple transformation method, the uniform potential method is successfully applied to solve the strongly singular integrals, and the Telles scheme and the element sub-division method are used to solve the weakly singular integrals in RI-IGABEM respectively. Furthermore, in order to improve the stability of numerical results, the PIM is adopted to solve the time domain problem. In order to validate the accuracy and convergence of the RI-IGABEM 2D and 3D numerical examples are used to discuss the influence of some factors, such as the number and the position of applied points, the order of basis functions, the number of model refinements and the length of time step.