A combination of isogeometric technique and scaled boundary method for the solution of the steady-state heat transfer problems in arbitrary plane domain with Robin boundary

Abstract

The scaled boundary finite element method (SBFEM) has attracted considerable attention in recent years as a novel semi-analytical computational approach since only the boundary is discretized using finite element approach and the spatial dimension is reduced by one in this method. By introducing the radial and circumferential scaled boundary coordinates in this method, the reduction of spatial dimension is accomplished by using the conventional Lagrange functions to weaken the governing equations in the circumferential direction, while to work analytically in the radial direction. The NURBS-based isogeometric analysis (IGA) has remarkable advantages due to its integration of CAD/CAE, geometrical exact discretization for free-form shapes and numerical accuracy. Thus, an isogeometric analysis based on the framework of scaled boundary method (IGA-SBM) is proposed, which combines the concepts of IGA and SBFEM by employing NURBS to represent the unknown field variables in the circumferential direction. In this work, the IGA-SBM is extended to the solutions of the steady-state heat transfer problems in arbitrary plane domain enclosed by the complex boundary geometry. Four numerical examples are presented to illustrate that the excellent accuracy, computational efficiency and convergence performance of IGA-SBM. The numerical studies show that the heat transfer problems with complicated configuration can be more effectively handled by considering the combination of IGA and SBFEM.