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

Acta Mechanica Solida Sinica 2018年第4期31卷 433-444页

作者： Changzheng Cheng Dong Pan zhiun han Meng Wu Zhongrong Niu School of Civil Engineering Hefei University of Technology Hefei 230009 China Department of Civil Environmental and Geo-Engineering University of Minnesota Minneapolis MN 55455 USA School of Mathematics Hefei University of Technology Hefei 230009 China

A new method named the state space boundary element method （SSBEM） is estab- lished, 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 synthe- sizes 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 intro- duced 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.

关键词： Boundary element method State space method Nearly singular integral Analytical formulation

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