`Mathematical Problems in EngineeringVolume 2012, Article ID 298903, 16 pageshttp://dx.doi.org/10.1155/2012/298903`
Research Article

## Numerical Solution of Solid Mechanics Problems Using a Boundary-Only and Truly Meshless Method

College of Mathematics Science, Chongqing Normal University, Chongqing 400047, China

Received 9 February 2012; Accepted 2 April 2012

Copyright © 2012 Xiaolin Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. J. Zhu and Z. Yuan, Boundary Element Analysis, Science Press, Beijing, China, 2009.
2. G. R. Liu, Meshfree Methods: Moving beyond the Finite Element Method, CRC Press, Boca Raton, Fla, USA, 2nd edition, 2010.
3. S. Li and W. K. Liu, Meshfree Particle Methods, Springer, Berlin, Germany, 2004.
4. Y. Xie Mukherjee and S. Mukherjee, “The boundary node method for potential problems,” International Journal for Numerical Methods in Engineering, vol. 40, no. 5, pp. 797–815, 1997.
5. Y. X. Mukherjee and S. Mukherjee, Boundary Methods: Elements, Contours, and Nodes, vol. 187, CRC Press, Boca Raton, Fla, USA, 2005.
6. S. N. Atluri, J. Sladek, V. Sladek, and T. Zhu, “Local boundary integral equation (LBIE) and it's meshless implementation for linear elasticity,” Computational Mechanics, vol. 25, no. 2, pp. 180–198, 2000.
7. J. Zhang, M. Tanaka, and T. Matsumoto, “Meshless analysis of potential problems in three dimensions with the hybrid boundary node method,” International Journal for Numerical Methods in Engineering, vol. 59, no. 9, pp. 1147–1166, 2004.
8. K. M. Liew, Y. Cheng, and S. Kitipornchai, “Boundary element-free method (BEFM) and its application to two-dimensional elasticity problems,” International Journal for Numerical Methods in Engineering, vol. 65, no. 8, pp. 1310–1332, 2006.
9. Y. Cheng and M. Peng, “Boundary element-free method for elastodynamics,” Science in China G, vol. 48, no. 6, pp. 641–657, 2005.
10. M. Peng and Y. Cheng, “A boundary element-free method (BEFM) for two-dimensional potential problems,” Engineering Analysis with Boundary Elements, vol. 33, no. 1, pp. 77–82, 2009.
11. X. Li, “Meshless Galerkin algorithms for boundary integral equations with moving least square approximations,” Applied Numerical Mathematics. An IMACS Journal, vol. 61, no. 12, pp. 1237–1256, 2011.
12. X. Li, “The meshless Galerkin boundary node method for Stokes problems in three dimensions,” International Journal for Numerical Methods in Engineering, vol. 88, no. 5, pp. 442–472, 2011.
13. J. G. Wang and G. R. Liu, “A point interpolation meshless method based on radial basis functions,” International Journal for Numerical Methods in Engineering, vol. 54, no. 11, pp. 1623–1648, 2002.
14. G. R. Liu and Y. T. Gu, “A local radial point interpolation method (LRPIM) for free vibration analyses of 2-D solids,” Journal of Sound and Vibration, vol. 246, no. 1, pp. 29–46, 2001.
15. B. D. Dai and Y. M. Cheng, “Local boundary integral equation method based on radial basis functions for potential problems,” Acta Physica Sinica, vol. 56, no. 2, pp. 597–603, 2007.
16. G. R. Liu and Y. T. Gu, “Boundary meshfree methods based on the boundary point interpolation methods,” Engineering Analysis with Boundary Elements, vol. 28, no. 5, pp. 475–487, 2004.
17. Y. T. Gu and G. R. Liu, “Hybrid boundary point interpolation methods and their coupling with the element free Galerkin method,” Engineering Analysis with Boundary Elements, vol. 27, no. 9, pp. 905–917, 2003.
18. X. Li, J. Zhu, and S. Zhang, “A hybrid radial boundary node method based on radial basis point interpolation,” Engineering Analysis with Boundary Elements, vol. 33, no. 11, pp. 1273–1283, 2009.
19. T. G. B. De Fiigueiredo, A New Boundary Element Formulation in Engineering, Springer, Berlin, Germany, 1991.
20. M. A. Golberg, C. S. Chen, and H. Bowman, “Some recent results and proposals for the use of radial basis functions in the BEM,” Engineering Analysis with Boundary Elements, vol. 23, no. 4, pp. 285–296, 1999.
21. S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, McGraw-Hill, New York, NY, USA, 3rd edition, 1970.