Novel Regularized Boundary Element Method for 3D-Potential Problems
This presentation is mainly devoted to the research on the regularization of indirect boundary integral equations (IBIEs) for three dimensional problems and establishes the new theory and method of the regularized BEM. The two special tangential vectors, which are linearly independent and associated with the normal vectors, are constructed, and then a characteristics theorem for the contour integrations of the normal and tangential gradients of some quantities, related with the fundamental solutions for 3D elastic problems, is presented. A limit theorem for the transformation from domain integral equations into boundary integral equations (BIEs) is also proposed. Based on this, together with a novel decomposition technique to the fundamental solution, the regularized BIEs with indirect unknowns, which don’t involve the direct calculation of CPV and HFP integrals, are derived for 3D potential problems. Compared with the widely practiced direct regularized BEMs, the presented method has many advantages. First, the 1, C α continuity requirement for density function in the direct formulation can be relaxed to the piecewise 0, C α continuity in the presented formulation for the respective singular integral to exist. Second, it is more suitable for solving the structures of thin bodies, considering the solution process for boundary or field quantities doesn’t involve the HFP integrals and nearly HFP integrals so the Regularization algorithm to the considered singular or nearly singular integrals is more effective. Third, the proposed regularized BIEs can calculate the any displacement gradients and stresses on the boundary, but not limited to the tractions, and also independent of the displacement BIEs. A systematic approach for implementing numerical solutions is produced by adopting the 0 C continuous elements to depict the boundary surface and the discontinuous interpolation function to approximate the boundary quantities. Especially, for the boundary value problems with elliptic surfaces or piecewise plane surfaces boundary, an isogeometric exact element is developed to model its boundary with almost no error. The validity of the proposed scheme is demonstrated by several benchmark examples. Excellent agreement between the numerical results and exact solutions was obtained even with using small amounts of element.
BEM Regularized boundary integral equations(IBIEs) 3D-Potential problem
Zhang Yaoming Qu Wenzhen
Institute of Applied Mathematics, Shandong University of Technology, Zibo 255049,Shandong Province, Institute of Applied Mathematics, Shandong University of Technology, Zibo 255049,Shandong Province,
国际会议
长沙
英文
1-1
2012-05-18（万方平台首次上网日期，不代表论文的发表时间）