Steady heat conduction analyses using an interpolating element-free Galerkin scaled boundary method

Abstract

Through use of the improved interpolating moving least-squares (IIMLS) shape functions in the circumferential direction of the scaled boundary method based on the Galerkin approach, an interpolating element-free Galerkin scaled boundary method (IEFG–SBM) is developed in this paper for analyzing steady heat conduction problems, which weakens the governing differential equations in the circumferential direction and seeks analytical solutions in the radial direction. The IIMLS method exhibits some advantages over the moving least-squares approximation and the interpolating moving least-squares method because its shape functions possess the delta function property and the involved weight function is nonsingular. In the IEFG–SBM, only a nodal data structure on the boundary is required and the primary unknown quantities are real solutions of nodal variables. Higher accuracy and faster convergence are obtained due to the increased smoothness and continuity of shape functions. Based on the IEFG–SBM, the steady heat conduction problems with thermal singularities and unbounded domains can be ideally modeled. Some numerical examples are presented to validate the availability and accuracy of the present method for steady heat conduction analysis.