Chinese Journal of Theoretical and Applied Mechani ›› 2013, Vol. 45 ›› Issue (6): 908-918.DOI: 10.6052/0459-1879-13-057

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A GENERAL ALGORITHM FOR CALCULATING NEARLY SINGULAR INTEGRALS OVER HIGH-ORDER ELEMENTS IN 3D BEM

Zhang Yaoming1,2, Li Xiaochao1, Vladimir Sladek3, Jan Sladek3   

  1. 1. Institute of Applied Mathematics, School of Mathematics, Shandong University of Technology, Zibo 255049, China;
    2. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China;
    3. Institute of Construction and Architecture, Slovak Academy of Sciences, Bratislava 84503, Slovakia
  • Received:2013-03-05 Revised:2013-05-10 Online:2013-11-23 Published:2013-11-25
  • Supported by:

    The project was supported by the National Natural Science Foundation of Shandong Province of China(ZR2010AZ003) and the Opening Fund of the State Key Laboratory of Structural Analysis for Industrial Equipment(GZ1307).

Abstract:

This work presents a general methodology to compute nearly singular integrals arising in 3D BEM using the eight-node second-order quadrilateral and six-node second-order triangular surface elements. The proposed method constructs a new distance function. The exponential transformation, which was proposed by present authors and is accurate and easy to implement according to extensive applications of 2D BEM, will be extended to 3D BEM to remove the near singularities of integrands. Several numerical examples are given to verify the high efficiency and the stability of the proposed scheme.

Key words:

BEM|nearly singular integrals|high-order geometry elements|transformation|3D elasticity problem

CLC Number: