Evaluation of heat flux intensity factor for a V-notched structure by the isogeometric boundary element method

Abstract

The conventional boundary element method using piecewise polynomial interpolation cannot accurately simulate the singular heat flux field around the vertex of the V-notch. Herein, the singularity eigen-analysis combined with the isogeometric boundary element method is proposed to calculate the singular heat flux field. The V-notched structure is divided into two parts, in which one is the heat flux singularity sector near the vertex and the other is the remained structure without heat flux singularity. In the singularity sector, the asymptotic expansion of the heat flux is introduced to transform the heat conduction governing equation into ordinary differential eigen equation, from which the singularity orders and eigen angular functions can be determined, except for the amplitude coefficients in the asymptotic expansion. The boundary integral equations for the heat conduction analysis established on the remained structure are discretized by the non-uniform rational B-spline (NURBS) elements. The amplitude coefficients, which are corresponding to the heat flux intensity factors, can be yielded by coupling the isogeometric boundary integral equations with the singularity asymptotic expansion analysis. A coordinate system transformation method is then proposed to transform the heat conduction governing equations of orthotropic and anisotropic material into the one of the isotropic material, and the heat flux intensity factors are approved to be invariable before and after coordinate transformation. Since the NURBS elements are used, fewer elements are required to evaluate the heat flux intensity factors compared with the conventional boundary element method.