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THE MESHLESS VIRTUAL BOUNDARY METHOD AND ITS APPLICATIONS TO 2D ELASTICITY PROBLEMS |
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| Authors: | Sun Haitao Wang Yuanhan |
| Institution: | 1. Institut d'' Electronique et Télécommunications de Rennes (IETR), LUNAM Université, Université de Nantes, UMR CNRS, 6164, Rue Christian Pauc, BP 50609, Nantes 44306, France;2. Cerema (Centre for Expertise and Engineering on Risks, Environment, Mobility, Urban and Country Planning), 23 Avenue de l''Amiral Chauvin, BP 69, 49136 Les Ponts de Cé, France;3. Alyotech, 2 Rue Antoine Becquerel, 35700 Rennes, France;4. South China University of Technology, Guangzhou 510641, People''s Republic of China;1. Department of Civil and Environmental Engineering, Clarkson University, P.O. Box 5710, Potsdam, NY 13699-5710, USA;2. Department of Civil and Environmental Engineering and Construction and Director, Applied Geophysics Center, University of Nevada, Las Vegas, 4505 Maryland Parkway, Las Vegas, NV 89154-4015, USA;1. School of Civil Engineering, Central South University, Changsha, Hunan 410075, China;2. Key Laboratory of Heavy-haul Railway Engineering Structure, Ministry of Education, Central South University, Changsha, Hunan 410075, China;3. Key Laboratory of Transportation Tunnel Engineering, Ministry of Education, Southwest Jiaotong University, Chengdu 610031, China;4. Department of Geotechnical Engineering, School of Civil Engineering, Southwest Jiaotong University, Chengdu 610031, China;1. Industrial Chemistry Research Institute, 8 Rydygiera Street, 01-793 Warsaw, Poland;2. National Medicines Institute, 30/34 Chełmska Street, 00-725 Warsaw, Poland |
| Abstract: | A novel numerical method for eliminating the singular integral and boundary effect is processed. In the proposed method, the virtual boundaries corresponding to the numbers of the true boundary arguments are chosen to be as simple as possible. An indirect radial basis function network (IRBFN) constructed by functions resulting from the indeterminate integral is used to construct the approaching virtual source functions distributed along the virtual boundaries. By using the linear superposition method, the governing equations presented in the boundaries integral equations (BIE) can be established while the fundamental solutions to the problems are introduced. The singular value decomposition (SVD) method is used to solve the governing equations since an optimal solution in the least squares sense to the system equations is available. In addition, no elements are required, and the boundary conditions can be imposed easily because of the Kronecker delta function properties of the approaching functions. Three classical 2D elasticity problems have been examined to verify the performance of the method proposed. The results show that this method has faster convergence and higher accuracy than the conventional boundary type numerical methods. |
| Keywords: | numerical method singular integral boundary effect radial basis function networks integral equation virtual boundary source function singular value decomposition |
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