Eigenvalue analysis of thin plate with complicated shapes by a novel mesh-free method

International Journal of Applied Mechanics

Volumn 3, Issue 1, 2011, Pages 21-46

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

^a UNIVERSITY OF SIEGEN   (Germany)

^b RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

frequency; Mesh free; moving Kriging interpolation; plate; vibration

Indexed keywords

COMPLICATED SHAPE; EIGENVALUE ANALYSIS; EIGENVALUE EQUATIONS; ESSENTIAL BOUNDARY CONDITIONS; FREQUENCY; FURTHER DEVELOPMENT; KIRCHHOFF; KRIGING INTERPOLATION; KRIGING INTERPOLATION TECHNIQUE; MESH-FREE METHOD; MESHFREE; NUMERICAL EXAMPLE; ORTHOGONAL TRANSFORMATION TECHNIQUE; PLATE; PLATE THEORIES; SHAPE FUNCTIONS; THIN PLATE; THIN PLATE STRUCTURE; VIBRATION PROBLEM; WEAK FORM;

BOUNDARY CONDITIONS; COMPUTATIONAL MECHANICS; DELTA FUNCTIONS; FINITE ELEMENT METHOD; INTERPOLATION; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; PLATES (STRUCTURAL COMPONENTS);

EIGENVALUES AND EIGENFUNCTIONS;

EID: 80051877845     PISSN: 17588251     EISSN: 1758826X     Source Type: Journal    
DOI: 10.1142/S1758825111000853     Document Type: Article

References (35)

1. Abbassian, F., Dawswell, D. J. and Knowles, N. C. [1987] Free Vibration Benchmarks (Atkins Engineering Sciences, Glasgow).
2. Atluri, S. N. [2004] The Meshless Local Petrov-Galerkin (MLPG) Method (Tech. Science Press).
3. Atluri, S. N. and Zhu, T. [1998] "A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics," Comput. Mech. 22, 117-127. (Pubitemid 128620889)
4. Belytschko, T., Lu, Y. Y. and Gu, L. [1994] "Element free Galerkin method," Int. J. Numer. Meth. Eng. 37, 229-256.
5. Belyschko, T., Organ, D. and Krongauz, Y. [1995] "A coupled finite element - element free Galerkin method," Comput. Mech. 17, 186-195.
6. Belytschko, T. and Black, T [1999] "Elastic crack growth in finite elements with minimal remeshing," Int. J. Numer. Meth. Eng. 45, 601-620.
7. Bui, Q. T. [2005] "Application of the element free Galerkin method for dual analysis," European Master's thesis, EMMC, University of Liege, Belgium.
8. Bui, Q. T. and Nguyen-Dang, H. [2006] "An equilibrium model in the element free Galerkin method," Proc. Eight Int. Conf. Computational Structures Technology, Las Palmas de Gran Canaria, Spain, pp. 12-15.
9. Bui, Q. T., Nguyen, N. T. and Nguyen-Dang, H. [2009] "A moving Kriging interpolationbased meshless method for numerical simulation of Kirchhoff plate problems," Int. J. Numer. Meth. Eng. 77, 1371-1395.
10. Chen, J. T., Chen, I. L., Chen, K. H., Lee, Y. T. and Yeh, Y. T. [2004] "A meshless method for free vibration analysis of circular and rectangular clamped plates using radial basis function," Eng. Anal. Bound. Elem. 28, 535-545.
11. Cui, X., Liu, G. R. and Li, G. [2009] "A smoothed Hermite radial point interpolation method for thin plate analysis," Arch. Appl. Mech., doi: 10.1007/s00419-009-0392-0.
12. Cui, X. Y., Liu, G. R., Li, G. Y. and Zhang, G. Y. [2010] "Thin plate formulation without rotation DOFs based on radial point interpolation method," Int. J. Numer. Meth. Eng., doi: 10.1002/nme.3000.
13. Dai, K. Y., Liu, G. R., Lim, M. K. and Gu, Y. T. [2003] "Comparison between the radial point interpolation and the Kriging interpolation used in mesh-free method," Comput. Mech. 32, 60-70.
14. Duflot, M. and Nguyen-Dang, H. [2002] "Dual analysis by a meshless method," Commun. Numer. Meth. Eng. 18, 621-631.
15. Giunta, A. A. and Watson, L. T. [1998] "A comparison of approximation modeling techniques: Polynomial versus interpolating models," Multidisciplinary Analysis and Design (MAD) Center for Advanced Vehicles, Virginia 2406. AIAA-4758.
16. Gu, L. [2003] "Moving Kriging interpolation and element free Galerkin method," Int. J. Numer. Meth. Eng. 56, 1-11. (Pubitemid 36080886)
17. Krysl, P. and Belytschko, T. [1995] "Analysis of thin plates by the element-free Galerkin method," Comput. Mech. 17, 26-35.
18. Lam, K. Y., Wang, Q. X. and Li, H. [2004] "A novel meshless approach - Local Kriging (LoKriging) method with two-dimensional structural analysis," Comput. Mech. 33, 235-244.
19. Leitão, A. V. M. [2001] "A meshless method for Kirchhoff plate bending problems," Int. J. Numer. Meth. Eng. 52, 1107-1130.
20. Li, H., Wang, Q. X. and Lam, K. Y. [2004] "Development of a novel meshless Local Kriging (LoKriging) method for structural dynamic analysis," Comput. Meth. Appl. Mech. Eng. 193, 2599-2619. (Pubitemid 38503369)
21. Li, S. and Liu, W. K. [2004] Mesh-free Particles Methods (Springer Berlin Heidelberg, New York, Germany).
22. Liew, K. M., Huang, Y. Q. and Reddy, J. N. [2004] "Analysis of general shaped thin plates by the moving least-squares differential quadrature method," Finit. Elem. Anal. Design 40, 1453-1474.
23. Liew, K. M. and Liu, F. L. [1997] "Differential cubature method: A solution technique for Kirchhoff plates of arbitrary shape," Comput. Meth. Appl. Mech. Eng. 145, 1-10. (Pubitemid 127411462)
24. Liu, G. R. [2003] Mesh-free Methods, Moving Beyond the Finite Element Method (CRC Press, USA).
25. Liu, G. R. and Chen, X. L. [2001] "A mesh-free method for static and free vibration analyses of thin plates of complicated shape," J. Sound Vibr. 241, 839-855. (Pubitemid 32370158)
26. Liu, Y., Hon, Y. C. and Liew, K. M. [2006] "A mesh-free Hermite-type radial point interpolation method for Kirchhoff plate problems," Int. J. Numer. Meth. Eng. 66, 1153-1178. (Pubitemid 43778363)
27. Melenk, J. M. and Babuska, I. [1996] "The partition of unity finite element method: Basic theory and applications," Comput. Meth. Appl. Mech. Eng. 139, 289-314. (Pubitemid 126382701)
28. Moes, N., Dolbow, J. and Belytschko, T. [1999] "A finite element method for crack growth without remeshing," Int. J. Numer. Meth. Eng. 46, 131-150. (Pubitemid 30508928)
29. Nguyen, N. T. [2007] "A meshless Kriging method for thin plate bending," European Master's thesis, EMMC, University of Liege, Belgium.
30. Sayakoummane, V. and Kanok-Nukulchai, W. [2007] "A meshless analysis of shells based on moving Kriging interpolation," Int. J. Comput. Meth. 4, 543-565. (Pubitemid 350238708)
31. Simkins, D. C. Jr., Li, S., Lu, H. and Liu, W. K. [2004] "Reproducing kernel element method. Part IV: Globally compatible Cn (n = 1) triangular hierarchy," Comput. Meth. Appl. Mech. Eng. 193, 1013-1034. (Pubitemid 38439204)
32. Sladek, J., Sladek, V. and Mang, H. M. [2003] "Meshless LBIE formulations for simply supported and clamped plates under dynamic load," Comput. Struct. 81, 1643-1651.
33. Tongsuk, P. and Kanok-Nukulchai, W. [2004a] "On the parametric refinement of moving Kriging interpolations for element free Galerkin method," Computational Mechanics WCCM VI in Conjunction with APCOM'04, Sept. 5-10, Beijing, China.
34. Tongsuk, P. and Kanok-Nukulchai, W. [2004b] "Further investigation of element free Galerkin method using moving Kriging interpolation," Int. J. Comput. Meth. 1, 1-21.
35. Zhou, D. and Ji, T. [2006] "Free vibration of rectangular plates with continuously distributed spring-mass," Int. J. Sol. Struct. 43, 6502-6520. (Pubitemid 44374520)