An interpolating local Petrov-Galerkin method for potential problems

International Journal of Applied Mechanics

Volumn 6, Issue 1, 2014, Pages

  Chen, L ^a,b   Liu, C ^a   Ma, H P ^a   Cheng, Y M ^a  

^a SHANGHAI UNIVERSITY   (China)

^b CHANG'AN UNIVERSITY   (China)

Author keywords

Heaviside step function; interpolating local Petrov Galerkin method; Meshless local Petrov Galerkin method; moving Kriging interpolation; potential problem

Indexed keywords

GALERKIN METHODS;

HEAVISIDE STEP FUNCTION; LOCAL PETROV-GALERKIN METHOD; MESHLESS LOCAL PETROV-GALERKIN METHODS; MOVING KRIGING INTERPOLATIONS; POTENTIAL PROBLEMS;

INTERPOLATION;

EID: 84899093360     PISSN: 17588251     EISSN: 1758826X     Source Type: Journal    
DOI: 10.1142/S1758825114500094     Document Type: Article

References (51)

1. Atluri, S. N. and Zhu, T. [1998] "A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics," Computational Mechanics 22(2), 117-127.
2. Atluri, S. N. and Zhu, T. [2000] "The meshless local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics," Computational Mechanics 25(2-3), 169-179.
3. Bai, F., Li, D., Wang, J. and Cheng, Y. [2012] "An improved complex variable element-free Galerkin (IVVEFG) method for two-dimensional elasticity problems," Chinese Physics B 21(2), 020204.
4. Beer, G. and Watson, J. O. [1989] "Infinite boundary elements," International Journal for Numerical Methods in Engineering 28(5), 1233-1247.
5. Belytschko, T., Lu, Y. Y. and Gu, L. [1994] "Element-free Galerkin methods," International Journal for Numerical Methods in Engineering 37(2), 229-256.
6. Belytschko, T., Krongauz, Y., Organ, D., Fleming, M. and Krysl, P. [1996] "Meshless method: An overview and recent developments," Computer Methods in Applied Mechanics and Engineering 139(1-4), 3-47.
7. Brebbia, C. A. and Wrobel, L. C. [1984] Boundary Element Techniques Theory and Applications in Engineering (Springer-Verlag, Berlin).
8. Chen, L. and Liew, K. M. [2011] "A local Petrov-Galerkin approach with moving Kriging interpolation for solving transient heat conduction problems," Computational Mechanics 47, 455-467.
9. Cheng, Y. and Peng, M. [2005a] "Boundary element-free method for elastodynamics," Science in China Series G: Physics, Mechanics and Astronomy 48(6), 641-657.
10. Cheng, Y., Peng, M. and Li, J. [2005b] "The complex variable moving least-square approximation and its application," Chinese Journal of Theoretical and Applied Mechanics 37(6), 719-723.
11. Cheng, Y. and Li, J. [2006] "A complex variable meshless method for fracture problems," Science in China Series G: Physics, Mechanics & Astronomy 49(1), 46-59.
12. Cheng, Y., Wang, J. and Li, R. [2012] "The complex variable element-free Galerkin (CVEFG) method for two-dimensional elastodynamics problems," International Journal of Applied Mechanics 4(4), 1250042.
13. Dai, B. and Cheng, Y. [2010] "An improved local boundary integral equation method for two-dimensional potential problems," International Journal of Applied Mechanics 2(2), 421-436.
14. Dai, K. Y., Liu, G. R., Lim, K. M. and Gu, Y. T. [2003] "Comparison between the radial point interpolation and the Kriging interpolation used in meshfree methods," Computational Mechanics 32(1-2), 60-70.
15. Gu, L. [2003] "Moving Kriging interpolation and element-free Galerkin method," International Journal for Numerical Methods in Engineering 56(1), 1-11.
16. Hong, W., Liu, Z. S. and Suo, Z. G. [2009] "Inhomogeneous swelling of a gel in equilibrium with a solvent and mechanical load," International Journal of Solids and Structures 46(17), 3282-3289.
17. Kitipornchai, S., Liew, K. M. and Cheng, Y. [2005] "A boundary element-free method (BEFM) for three-dimensional elasticity problems," Computational Mechanics 36(1), 13-20.
18. Lam, K. Y., Wang, Q. X. and Lam, K. Y. [2004] "A novel meshless approach - Local Kriging (LoKriging) method with two-dimensional structural analysis," Computational Mechanics 33(3), 235-244.
19. Lei, Z. X., Liew, K. M. and Yu, J. L. [2013a] "Buckling analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method," Composite Structures 98, 160-168.
20. Lei, Z. X., Liew, K. M. and Yu, J. L. [2013b] "Large deflection analysis of functionally graded carbon nanotube-reinforced composite plates by the element-free kp-Ritz method," Computer Methods in Applied Mechanics and Engineering 256, 189-199.
21. Li, S. and Liu, W. K. [2002] "Meshless and particles methods and their applications," Applied Mechanics Review 55, 1-34.
22. Li, D., Bai, F., Cheng, Y. and Liew, K. M. [2012] "A novel complex variable element-free Galerkin method for two-dimensional large deformation problems," Computer Methods in Applied Mechanics and Engineering 233-236, 1-10.
23. Liew, K. M., Ng, T. Y. and Wu, Y. C. [2002a] "Meshfree method for large deformation analysis-a reproducing kernel particle approach," Engineering Structures 24, 543-551.
24. Liew, K. M., Wu, Y. C., Zou, G. P. and Ng. T. Y. [2002b] "Elasto-plasticity revisited: Numerical analysis via reproducing kernel particle method and parametric quadratic programming," International Journal of Numerical Methods in Engineering 55, 669-683.
25. Liew, K. M., Wang J., Tan, M. J. and Rajendran, S. [2004] "Nonlinear analysis of laminated composite plates using the mesh-free kp-Ritz method based on FSDT," Computer Methods in Applied Mechanics and Engineering 193, 4763-4779.
26. Liew, K. M., Cheng, Y. and Kitipornchai, S. [2005] "Boundary element-free method (BEFM) for two-dimensional elastodynamic analysis using Laplace transform," International Journal of Numerical Methods in Engineering 64(12), 1610-1627.
27. Liew, K. M., Cheng, Y. and Kitipornchai, S. [2006] "Boundary element-free method (BEFM) and its application to two-dimensional elasticity problems," International Journal for Numerical Methods in Engineering 65(8), 1310-1332.
28. Liew, K. M., Cheng, Y. and Kitipornchai, S. [2007a] "Analyzing the 2D fracture problems via the enriched boundary element-free method," International Journal of Solids and Structures 44(11-12), 4220-4233.
29. Liew, K. M., Feng, C., Cheng, Y. and Kitipornchai, S. [2007b] "Complex variable moving least-squares method: A meshless approximation technique," International Journal of Numerical Methods in Engineering 70(1), 46-70.
30. Liew, K. M. and Cheng, Y. [2009] "Complex variable boundary element-free method for two-dimensional elastodynamic problems," Computer Methods in Applied Mechanics and Engineering 198(49-52), 3925-3933.
31. Liu, W. K., Jun, S. and Zhang, Y. F. [1995] "Reproducing kernel particle methods," International Journal for Numerical Methods in Fluids 20(8-9), 1081-1106.
32. Liu, Z. S., Harsono E. and Swaddiwudhipong S. [2009] "Material characterization based on instrumented and simulated indentation tests," International Journal of Applied Mechanics 1(1), 61-84.
33. Ochiai, Y., Sladek, V. and Sladek, J. [2006] "Transient heat conduction analysis by triplereciprocity boundary element method," Engineering Analysis with Boundary Elements 30(3), 194-204.
34. Peng, M. and Cheng, Y. [2009] "A boundary element-free method (BEFM) for twodimensional potential problems," Engineering Analysis with Boundary Elements 33(1), 77-82.
35. Peng, M., Liu, P. and Cheng, Y. [2009] "The complex variable element-free Galerkin (CVEFG) method for two-dimensional elasticity problems," International Journal of Applied Mechanics 1(2), 367-385.
36. Peng, M., Li, D. and Cheng, Y. [2011] "The complex variable element-free Galerkin (CVEFG) method for elasto-plasticity problems," Engineering Structures 33(1), 127-135.
37. Ren, H., Cheng, Y. and Zhang, W. [2009] "An improved boundary element-free method (IBEFM) for two-dimensional potential problems," Chinese Physics B 18(10), 4065-4073.
38. Ren, H., Cheng, Y. and Zhang, W. [2010] "An improved boundary element-free method (IBEFM) for two-dimensional elasticity problems," Science China Physics, Mechanics and Astronomy 53(4), 758-766.
39. Ren, H. and Cheng, Y. [2011] "The interpolating element-free Galerkin (IEFG) method for two-dimensional elasticity problems," International Journal of Applied Mechanics 3(4), 735-758.
40. Ren, H. and Cheng, Y. [2012] "A new element-free Galerkin method based on improved complex variable moving least-squares approximation for elasticity," International Journal of Computational Materials Science and Engineering 1(1), 1250011.
41. Selvadurai, A. P. S. [2000] Partial Differential Equations in Mechanics (Springer, Berlin).
42. Tinh, Q. B., Tan, N. N. and Hung, N. D. [2009] "A moving Kriging interpolation-based meshless method for numerical simulation of Kirchhoff plate problems," International Journal for Numerical Methods in Engineering 77(10), 1371-1395.
43. Tongsuk, P. and Kanok-Nukulchai, W. [2004] "Further investigation of element free Galerkin method using moving Kriging interpolation," International Journal of Computational Methods 1(2), 345-365.
44. Zhang, Z., Liew, K. M., Cheng, Y. and Li, Y. [2008] "Analyzing 2D fracture problems with the improved element-free Galerkin method," Engineering Analysis with Boundary Elements 32(3), 241-250.
45. Zhang, Z., Zhao, P. and Liew, K. M. [2009a] "Improved element-free Galerkin method for two-dimensional potential problems," Engineering Analysis with Boundary Elements 33(4), 547-554.
46. Zhang, Z., Zhao, P. and Liew, K. M. [2009b] "Analyzing three-dimensional potential problems with the improved element-free Galerkin method," Computational Mechanics 44(2), 273-284.
47. Zhang, Z., Li, D., Cheng, Y. and Liew, K. M. [2012] "The improved element-free Galerkin method for three-dimensional wave equation," Acta Mechanica Sinica 28(3), 808-818.
48. Zhao, X., Ng, T. Y. and Liew, K. M. [2004] "Free vibration of two-side simply-supported laminated cylindrical panels via the mesh-free kp-Ritz method," International Journal of Mechanical Sciences 46, 123-142.
49. Zhao, X., Yang, Y. and Liew, K. M. [2007] "Geometrically nonlinear analysis of cylindrical shells using the element-free kp-Ritz method," Engineering Analysis with Boundary Elements 31, 783-792.
50. Zhu, P. and Liew, K. M. [2011] "Free vibration analysis of moderately thick functionally graded plates by local Kriging meshless method," Composite Structures 93, 2925-2944.
51. Zhu, P. and Liew, K. M. [2012] "A local Kriging meshless method for free vibration analysis of functionally graded circular plates in thermal environments," Procedia Engineering 31, 1089-1094.