A State Space Boundary Element Method with Analytical Formulas for Nearly Singular Integrals

Abstract

A new method named the state space boundary element method (SSBEM) is established, in which the problem domain is divided into two parts. One is the boundary element domain which includes the interested inner point, and the other is the state space domain. The boundary integral equation and the state space equation are combined together based on the interfacial continuity condition to form the system equation of the SSBEM. The SSBEM synthesizes both advantages of the boundary element method and the state space method. However, it can give inaccurate results when being used to evaluate the mechanical quantity of a point very close to the boundary element, because the Gaussian quadrature fails to calculate the nearly singular integrals. The analytical formulas were developed by part of the authors before introduced to deal with the nearly singular integrals. Thus, the SSBEM can yield accurate physical quantities for the points very close to the boundary element. The SSBEM results agree well with those of the finite element method (FEM), while the discretized elements are far fewer than those of the FEM. Meanwhile, the SSBEM can analyze very thin coating, while the FEM fails due to the limitation of tolerance for Boolean operations.