Topology optimization of truncated cone insulator with graded permittivity using variable density method

Dielectrics with functionally graded material (d-FGM), which have spatially nonuniform dielectric properties, is effective to improve the insulation performance without complicating the structure. In the application of d-FGM, searching the optimal distribution of dielectric properties (permittivity or conductivity) is the most important goal, which however is difficult for conventional insulation design approaches. In this paper, the topology optimization technique is introduced to design a truncated cone insulator with permittivity FGM, which is to relieve local electric field (E-field) enhancement at the triple junctions. Firstly, a multi-objective topology optimization model is proposed using the variable density method. Secondly, the optimal values of several model parameters are determined based on the analysis of E-field uniformity. Finally, finite elements calculation demonstrates that the E-field uniformity is significantly improved for the topology-optimized permittivity FGM, and the E-field enhancement at triple junctions is strongly inhibited. It is thus expected that by applying the topology-optimized permittivity FGM insulator, the breakdown strength in gas or vacuum would be effectively improved.