Abstract: In order to solve the problem of near singular integral calculation in the analysis of elastic statics of thin structures by boundary element method(BEM), a nonlinear sinh-sigmoidal combined transformation method was proposed,and it was integrated into the boundary element program to eliminate the near singularity of integration in radial and angular directions. Firstly, adaptive blocking technology was applied to the integration unit, and iterative sinh transform was used to eliminate the near singularity of the integration kernel function in the radial direction. Then, considering the feature that the sigmoid transform kernel function could gather a large number of Gaussian integral points to both ends of the integration interval, it could be used to eliminate the near singularity in the angle direction. Finally, the sinh-sigmoidal combined transformation method was integrated into the boundary element program. Taking the bolted thin gasket as the analysis object, the finite element method (FEM)and boundary element method(BEM) were respectively used to carry out numerical analysis of its elastic statics problems to verify the effectiveness of the method. The analysis results show that the method has good convergence when calculating the average error of the isotropic force of the gasket under ideal working conditions. When analyzing the displacement change of the surface node of the thin gasket under the preload under the actual working condition, the calculation error of the finite element method and the boundary element method is less than 1%, but the boundary element method has obvious advantages in calculation scale and efficiency. The research results show that the sinhsigmoidal combined transformation method can effectively eliminate the near singularity of the integral in the radial and angular directions, and the boundary element program integrating the method has both efficiency and accuracy in analyzing the elastic statics of thin gaskets.
Key words: sealing property; nonlinear transformation method;elastic and static properties analysis; near singular integral calculation; boundary element method(BEM); finite element method(FEM); calculation efficiency; calculation accuracy