A moving Kriging interpolation-based meshless method for numerical simulation of Kirchhoff plate problems

International Journal for Numerical Methods in Engineering

Volumn 77, Issue 10, 2009, Pages 1371-1395

  Bui, Tinh Quoc ^a   Nguyen, Tan Nhat ^b   Nguyen Dang, Hung ^c  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

^b Hochiminh University of Polytechnics   (Viet Nam)

^c UNIVERSITY OF LIÈGE   (Belgium)

Author keywords

Element free Galerkin; Kirchhoff; Meshless; Moving Kriging interpolation; Thin plate

Indexed keywords

FUNCTION EVALUATION; GALERKIN METHODS; INTERPOLATION;

ELEMENT-FREE GALERKIN; KIRCHHOFF; MESHLESS; MOVING KRIGING INTERPOLATION; THIN PLATE;

COMPUTATIONAL MECHANICS;

EID: 60949102515     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2462     Document Type: Article

References (30)

1. Liu GR. Meshfree Methods, Moving beyond the Finite Element Method. CRC Press: U.S.A., 2003.
2. Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering 1999; 45:601-620.
3. Moës N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering 1999; 46:131-150.
4. Belytschko T, Lu YY, Gu L. Element free Galerkin method. International Journal for Numerical Methods in Engineering 1994; 37:229-256.
5. Lam KY, Wang QX, Hua Li. A novel meshless approach - local Kriging (LoKriging) method with two-dimensional structural analysis. Computational Mechanics 2004; 33:235-244.
6. Belyschko T, Organ D, Krongauz Y. A coupled finite element-element-free Galerkin method. Computational Mechanics 1995; 17:186-195.
7. Bui QT, Nguyen-Dang H. An equilibrium model in the element free Galerkin method. The Eighth International Conferences on Computational Structures Technology, Las Palmas de Gran Canaria, Spain, September 2006; 12-15.
8. Gu L. Moving Kriging interpolation and element free Galerkin method. International Journal for Numerical Methods in Engineering 2003; 56:1-11.
9. Dai KY, Liu GR, Lim KM, Gu YT. Comparison between the radial point interpolation and the Kriging interpolation used in meshfree method. Computational Mechanics 2003; 32:60-70.
10. Hua Li, Wang QX, Lam KY. Development of a novel meshless local Kriging (LoKriging) method for structural dynamic analysis. Computer Methods in Applied Mechanics and Engineering 2004; 193:2599-2619.
11. Tongsuk P, Kanok-Nukulchai W. On the parametric refinement of moving Kriging interpolations for element free Galerkin method. Computational Mechanics WCCM VI in Conjunction with APCOM'04, Beijing, China, September 2004; 5-10.
12. Tongsuk P, Kanok-Nukulchai W. Further investigation of element free Galerkin method using moving Kriging interpolation. International Journal of Computational Methods 2004; 1:1-21.
13. Liu Y, Hon YC, Liew KM. A meshfree Hermite-type radial point interpolation method for Kirchhoff plate problems. International Journal for Numerical Methods in Engineering 2006; 66:1153-1178.
14. Leitão VMA. A meshless method for Kirchhoff plate bending problems. International Journal for Numerical Methods in Engineering 2001; 52:1107-1130.
15. Liew KM. Response of plates of arbitrary shape subject to static loading. Journal of Engineering Mechanics 1992; 18:1783-1794.
16. Liew KM, Liu FL. Differential cubature method: a solution technique for Kirchhoff plates of arbitrary shape. Computer Methods in Applied Mechanics and Engineering 1997; 145:1-10.
17. Liu FL, Liew KM. Differential cubature method for static solutions of arbitrary shaped thick plates. International Journal of Solids and Structures 1998; 35:3655-3674.
18. Liew KM, Huang YQ, Reddy JN. Moving least squares differential quadrature method and its application to the analysis of shear deformable plates. International Journal for Numerical Methods in Engineering 2003; 56:2331-2351.
19. Liew KM, Huang YQ, Reddy JN. Analysis of general shaped thin plates by the moving least-squares differential quadrature method. Finite Elements in Analysis and Design 2004; 40:1453-1474.
20. n (n≥1) triangular hierarchy. Computer Methods in Applied Mechanics and Engineering 2004; 193:1013-1034.
21. n hierarchies. Computer Methods in Applied Mechanics and Engineering 2004; 193:954-987.
22. Liu WK, Han W, Lu H, Li S, Cao J. Reproducing kernel element method. Part I: theoretical formulation. Computer Methods in Applied Mechanics and Engineering 2004; 193:933-951.
23. Li S, Liu WK. Meshfree Particle Methods. Springer: Berlin, 2004.
24. Giunta AA, Watson LT. A comparison of approximation modeling techniques: polynomial versus interpolating models. AIAA-98-4758. Multidisciplinary Analysis and Design (MAD) Center for Advanced Vehicles, Virginia, 1998.
25. Nguyen NT. A meshless Kriging method for thin plate bending. European Master's Thesis, EMMC, University of Liege, Beligum, 2007.
26. Bui QT. Application of the element free Galerkin method for dual analysis. European Master's Thesis, EMMC, University of Liege, Beligum, 2005.
27. Timoshenko SP, Woinowsky-Kriger S. Theory of Plates and Shells (2nd edn). McGraw-Hill: New York, 1959.
28. MATLAB - The Language of Technical Computing. The MathWorks, Inc., 1999.
29. Sladek J, Sladek V, Mang HA. Meshless LBIE formulations for simply supported and clamped plates under dynamic load. Computers and Structures 2003; 81:1643-1651.
30. Staad Pro - Structural Analysis Program. Research Engineers, Inc., 1997.