Modified Finite Element Method to Consider the Singularity of the Electric Field Using a Singularity Function

In the insulation design of an electric power apparatus, the triple junction which is a joining point of conductor, insulator, and gas should be considered carefully. At this point, three different materials are connected and the electric field intensity is not smooth. Local concentration of the electric field at this point can result in the surface flashover. Therefore, the accurate analysis of the electric field is necessary to design the apparatus with a triple junction. The conventional electric field analysis method such as the FEM (finite element method) can not take into account the triple junction problem accurately. In this paper, the singularity function is introduced and combined with the FEM to solve the triple junction problem. A discrete stress intensity factor is employed to prove the convergence of the proposed method. Several numerical tests show that the method can give an accurate solution around the triple junction and is very promising in solving the problem with the geometric singularity.