Analysis of heat flux singularity at 2D notch tip by singularity analysis method combined with boundary element technique

Abstract

It is known that the heat flux becomes infinite near the notch tip due to material or geometric discontinuities. Numerical methods such as boundary element method and finite element method cannot adequately analyze the accurate singular heat flux field since they traditionally employ piecewise polynomials. In this paper, the singularity analysis method coupled with the boundary element technique is proposed for the accurate analysis of two-dimensional singular heat flux field near the notch tip. The V-notched structure is departed into two parts, which are the near tip singular sector and far tip non-singular section. The singularity analysis is executed on the near notch tip sector for searching singularity orders and corresponding characteristic angular functions by introducing the heat flux asymptotic expansions into heat conduction governing equations. The conventional boundary element method is applied to modeling the far notch tip region because there is no heat flux singularity. The asymptotic expansions of the near tip physical field and the boundary integral equations established on the far notch tip region are combined together for solving the expansion coefficients in heat flux asymptotic expansions. Thus, the complete heat flux field near the notch vertex can be accurately determined.