A state space boundary element method with analytical nearly singular integral formulation

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 state space equation are combined together by the interfacial continuity condition to form the system equation of the SSBEM. The SSBEM synthesizes both advantages of the boundary element method and state space method, while it will get inaccurate result when it is used to evaluate the mechanical quantity of the point very close to the boundary element, because the Gaussian’s quadrature fails to calculate the nearly singular integral in the boundary integral equation. The analytical formulation developed by part of the authors before is introduced to deal with the nearly singular integral. Thus, the SSBEM can yield accurate physical quantities for the point very close to the boundary element. The SSBEM result can well agree with the one from the finite element method (FEM), while the discretized element is much less than the one in the FEM. Meanwhile, the SSBEM can analyze very thin coating while the FEM fails due to the limitation of Boolean operation tolerance.