A moving Kriging interpolation-based meshfree method for free vibration analysis of Kirchhoff plates

Computers and Structures

Volumn 89, Issue 3-4, 2011, Pages 380-394

  Bui, Tinh Quoc ^a   Nguyen, Minh Ngoc ^b  

^a UNIVERSITY OF SIEGEN   (Germany)

^b RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

Meshfree; Moving Kriging interpolation; Plate; Vibration

Indexed keywords

ESSENTIAL BOUNDARY CONDITIONS; FREE-VIBRATION ANALYSIS; FURTHER DEVELOPMENT; GEOMETRIC SHAPE; KIRCHHOFF; KIRCHHOFF PLATES; KRIGING INTERPOLATION; MESH-FREE METHOD; MESHFREE; NUMERICAL EXAMPLE; PLATE; SPECIAL TREATMENTS; VIBRATION; WEAK FORM;

BOUNDARY CONDITIONS; COMPUTATIONAL MECHANICS; INTERPOLATION; NUMERICAL METHODS;

VIBRATION ANALYSIS;

EID: 78650926513     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruc.2010.11.006     Document Type: Article

References (60)

1. R.A. Gingold, and J.J. Moraghan Smoothed particle hydrodynamics: theory and applications to non-spherical stars Mon Not R Astr Soc 181 1977 375 389
2. B. Nayroles, G. Touzot, and P. Villon Generalizing the FEM: diffuse approximation and diffuse elements Comput Mech 10 1992 307 318
3. T. Belytschko, Y.Y. Lu, and L. Gu Element free Galerkin method Int J Numer Methods Eng 37 1994 229 256
4. W.K. Liu, S. Jun, and Y.F. Zhang Reproducing kernel particle methods Int J Numer Methods Fluids 20 1995 1081 1106
5. T.J. Liszka, C.A.M. Duarte, and W.W. Tworzydlo hp-meshless cloud method Comput Methods Appl Mech Eng 139 1996 263 288
6. S.N. Arluri, and T.-L. Zhu A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics Comput Mech 22 1998 117 127
7. G.R. Liu, and Y.T. Gu A point interpolation method for two-dimensional solids Int J Numer Methods Eng 50 2001 937 951
8. G.R. Liu, and J.G. Wang A point interpolation meshless method based on radial basis functions Int J Numer Methods Eng 54 2002 1623 1648
9. T. Rabczuk, T. Belytschko, and S.P. Xiao Stable particle methods based on Lagrangian kernels Comput Methods Appl Mech Eng 193 2004 1035 1063
10. T. Belytschko, Y. Krongauz, D. Organ, M. Fleming, and P. Krysl Meshless methods: an overview and recent developments Comput Methods Appl Mech Eng 139 1996 3 47
11. V.P. Nguyen, T. Rabczuk, S. Bordas, and M. Duflot Meshless methods: a review and computer implementation aspects Math Comput Sim 79 2008 763 813
12. S. Li, and W.K. Liu Meshfree particle method 2004 Springer, Berlin, Heidelberg New York
13. G.R. Liu Meshfree methods, moving beyond the finite element method 2003 CRC Press USA
14. Y.X. Mukherjee, and S. Mukherjee On boundary conditions in the element free Galerkin methods Comput Mech 19 1997 267 270
15. T. Belytschko, and M. Tabbara Dynamic fracture using element-free Galerkin methods Int J Numer Methods Eng 39 1996 923 938
16. P. Krysl, and T. Belytschko Analysis of thin plates using element-free Galerkin methods Comput Mech 17 1995 26 35
17. J.Y. Cho, Y.M. Song, and Y.H. Choi Boundary locking induced by penalty enforcement of essential boundary conditions in mesh-free methods Comput Methods Appl Mech Eng 131 2008 1167 1183
18. X. Zhang, M.-W. Lu, and J.L. Wegner A meshless model for jointed rock structures Int J Numer Methods Eng 47 2000 1649 1661
19. T. Zhu, and S.N. Atluri Modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method Comput Mech 21 1998 211 222
20. Y.Y. Lu, T. Belytschko, and L. Gu A new implementation of the element free Galerkin method Comput Meth Appl Mech Eng 113 1994 397 414
21. T. Belyschko, D. Organ, and Y. Krongauz A coupled finite element-element free Galerkin method Comput Mech 17 1995 186 195
22. Y. Krongauz, and T. Belyschko Enforcement of essential boundary conditions in meshless approximations using finite elements Comput Methods Appl Mech Eng 131 1996 133 145
23. S. Fernandez-Mendez, and A. Huerta Imposing essential boundary conditions in mesh-free methods Comput Methods Appl Mech Eng 193 2004 1257 1275
24. D. Hegen Element-free Galerkin methods in combination with finite element approaches Comput Methods Appl Mech Eng 135 1996 143 166
25. T. Rabczuk, S.P. Ziao, and M. Sauer Coupling of mesh-free methods with finite elements: basic concepts and test results Commun Numer Methods Eng 22 2006 1031 1065
26. Y.T. Gu, and L.C. Zhang Coupling of the meshfree and finite element methods for determination of the crack tip fields Eng Fract Mech 75 2008 986 1004
27. F.C. Guenther, and W.K. Liu Implementation of boundary conditions for meshless methods Comput Methods Appl Mech Eng 163 1998 205 230
28. Y.Y. Lu, T. Belytschko, and M. Tabbara Element-free Galerkin method for wave propagation and dynamic fracture Comput Methods Appl Mech Eng 126 1995 131 153
29. J.S. Chen, C. Pan, C.T. Wu, and W.K. Liu Reproducing kernel particle methods for large deformation analysis of non-linear structures Comput Methods Appl Mech Eng 139 1996 195 227
30. M.K. Liew, J. Wang, T.Y. Ng, and M.J. Tan Free vibration and buckling analyses of shear-deformable plates based on FSDT meshfree method J Sound Vib 276 2004 997 1017
31. X. Zhang, X. Liu, M.-W. Lu, and Y. Chen Imposition of essential boundary conditions by displacement constraint equations in meshless methods Commun Numer Methods Eng 17 2001 165 178
32. L. Gu Moving Kriging interpolation and element free Galerkin method Int J Numer Methods Eng 56 2003 1 11
33. Y.K. Dai, G.R. Liu, K.M. Lim, and Y.T. Gu Comparison between the radial point interpolation and the Kriging interpolation used in meshfree method Comput Mech 32 2003 60 70
34. K.Y. Lam, Q.X. Wang, and H. Li A novel meshless approach - local Kriging (LoKriging) method with two-dimensional structural analysis Comput Mech 33 2004 235 244
35. H. Li, Q.X. Wang, and K.Y. Lam Development of a novel meshless local Kriging (LoKriging) method for structural dynamic analysis Comput Methods Appl Mech Eng 193 2004 2599 2619
36. Tongsuk P, Kanok-Nukulchai W. On the parametric refinement of moving Kriging interpolations for element free Galerkin method. In: Proceeding of computational mechanics WCCM VI in conjunction with APCOM'04, September 5-10, Beijing, China; 2004.
37. P. Tongsuk, and W. Kanok-Nukulchai Further investigation of element free Galerkin method using moving Kriging interpolation Int J Comput Methods 1 2004 1 21
38. V. Sayakoummane, and W. Kanok-Nukulchai A meshless analysis of shells based on moving Kriging interpolation Int J Comput Methods 4 2007 543 565
39. Q.T. Bui, N.T. Nguyen, and H. Nguyen-Dang A moving Kriging interpolation-based meshless method for numerical simulation of Kirchhoff plate problems Int J Numer Methods Eng 77 2009 1371 1395
40. Nguyen NT. A meshless Kriging method for thin plate bending. European Master's thesis, EMMC, University of Liege, Beligum; 2007.
41. M. Duflot, and H. Nguyen-Dang Dual analysis by a meshless method Commun Numer Methods Eng 18 2002 621 631
42. Bui QT, Nguyen-Dang H. An equilibrium model in the element free Galerkin method. In: Topping BHV, Montero G, Montenegro R. editors. Proceedings of the eighth international conferences on computational structures technology. Stirlingshire, UK: Civil-Comp Press, paper 177; 2006. doi:10.4203/ccp.83.177.
43. Bui QT. Application of the element free Galerkin method for dual analysis. European Master's thesis, EMMC, University of Liege, Beligum, 2005.
44. Y. Liu, Y.C. Hon, and K.M. Liew A meshfree Hermite-type radial point interpolation method for Kirchhoff plate problems Int J Numer Methods Eng 66 2006 1153 1178
45. A.V.M. Leitão A meshless method for Kirchhoff plate bending problems Int J Numer Methods Eng 52 2001 1107 1130
46. G.R. Liu, and X.L. Chen A mesh-free method for static and free vibration analyses of thin plates of complicated shape J Sound Vib 241 2001 839 855
47. K.M. Liew, and F.L. Liu Differential cubature method: a solution technique for Kirchhoff plates of arbitrary shape Comput Methods Appl Mech Eng 145 1997 1 10
48. P. Krysl, and T. Belytschko Analysis of thin shells by the element-free Galerkin method Int J Solids Struct 33 1996 3057 3078
49. K.M. Liew, Y.Q. Huang, and J.N. Reddy Analysis of general shaped thin plates by the moving least-squares differential quadrature method Finite Elem Anal Des 40 2004 1453 1474
50. J. Sladek, V. Sladek, and H.M. Mang Meshless LBIE formulations for simply supported and clamped plates under dynamic load Comput Struct 81 2003 1643 1651
51. n(n ≥ 1) triangular hierarchy Comput Methods Appl Mech Eng 193 2004 1013 1034
52. T. Rabczuk, and P.M.A. Areias A meshfree thin shell for arbitrary evolving cracks based on an external enrichment CMES 16 2006 115 130
53. T. Rabczuk, P.M.A. Areias, and T. Belyschko A meshfree thin shell method for non-linear dynamic fracture Int J Numer Methods Eng 72 2007 524 548
54. T. Rabczuk, R. Gracie, J.H. Song, and T. Belyschko Immersed particle method for fluid-structure interaction Int J Numer Methods Eng 81 2010 48 71
55. H. Nguyen-Xuan, T. Rabczuk, S. Bordas, and J.F. Debognie A smoothed finite element method for plate analysis Comput Methods Appl Mech Eng 197 2008 1184 1203
56. N. Nguyen-Thanh, T. Rabczuk, H. Nguyen-Xuan, and S. Bordas A smoothed finite element method for shell analysis Comput Methods Appl Mech Eng 198 2008 165 177
57. J.T. Chen, I.L. Chen, K.H. Chen, Y.T. Lee, and Y.T. Yeh A meshless method for free vibration analysis of circular and rectangular clamped plates using radial basis function Eng Anal Bound Elem 28 2004 535 545
58. J. Dolbow, and T. Belytschko An introduction to programming the meshless element-free Galerkin method Arch Comput Methods Eng 5 1998 207 241
59. X. Cui, G.R. Liu, and G. Li A smoothed Hermit radial point interpolation method for thin plate analysis Arch Appl Mech 2009 10.1007/s00419-009-0392-0
60. Abbassian F, Dawswell DJ, Knowles NC. Free vibration benchmarks. Atkins Eng Sci 1987.