'FE-Meshfree' QUAD4 element for free-vibration analysis

Computer Methods in Applied Mechanics and Engineering

Volumn 197, Issue 45-48, 2008, Pages 3595-3604

  Zhang, B R ^a   Rajendran, S ^a  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

FE LSPIM; FE meshfree; FE meshless; Finite element; Mesh distortion; QUAD4; Quadrilateral element

Indexed keywords

FUNCTION EVALUATION; LATTICE VIBRATIONS; STATIC ANALYSIS; TWO DIMENSIONAL; VIBRATION ANALYSIS; VIBRATIONS (MECHANICAL);

BENCH-MARK PROBLEMS; FE-LSPIM; FE-MESHFREE; FE-MESHLESS; FINITE ELEMENT; FINITE ELEMENT SHAPE FUNCTIONS; FINITE-ELEMENT METHODS; FREE-VIBRATION ANALYSIS; MESH DISTORTION; MESH-FREE; QUAD4; QUADRILATERAL ELEMENT; SHAPE FUNCTIONS;

FINITE ELEMENT METHOD;

EID: 50049108950     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2008.02.012     Document Type: Article

References (32)

1. Nayroles B., Touzot G., and Villon P. Generalizing the finite element method: diffuse approximation and diffuse elements. Comput. Mech. 10 (1992) 307-318
2. Belytschko T., Lu Y.Y., and Gu L. Element free Galerkin methods. Int. J. Numer. Methods Engrg. 37 (1994) 229-256
3. Belytschko T., Lu Y.Y., Gu L., and Tabbara M. Element-free Galerkin methods for static and dynamic fracture. Int. J. Solids Struct. 32 (1995) 2547-2570
4. Belytschko T., Krongauz Y., Fleming M., Organ D., and Liu W.K. Smoothing and accelerated computations in the element free Galerkin method. J. Comput. Appl. Math. 74 (1996) 111-126
5. Liu W.K., Jun S., and Zhang Y.F. Reproducing kernel particle methods. Int. J. Numer. Methods Engrg. 20 (1995) 1081-1106
6. Liu G.R., and Gu Y.T. A point interpolation method for two dimensional solids. Int. J. Numer. Methods Engrg. 50 (2001) 937-951
7. Atluri S.N., and Zhu T. A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Comput. Mech. 22 (1998) 117-127
8. Atluri S.N., Cho J.Y., and Kim H.G. Analysis of thin beams, using the meshless local Petrov-Galerkin (MLPG) method with generalized moving least squares interpolation. Comput. Mech. 24 (1999) 334-347
9. Atluri S.N., and Zhu T. New concepts in meshless methods. Int. J. Numer. Methods Engrg. 47 (2000) 537-556
10. Atluri S.N., and Zhu T. The meshless local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics. Comput. Mech. 25 (2000) 169-179
11. Zhu T., Zhang J.D., and Atluri S.N. A local boundary integral equation (LBIE) method in computational mechanics, and a meshless discretization approach. Comput. Mech. 21 (1998) 223-235
12. Liu G.R., and Gu Y.T. A local point interpolation method for stress analysis of two-dimensional solids. Int. J. Struct. Engrg. Mech. 11 (2001) 221-236
13. Lam K.Y., Wang Q.X., and Li H. A novel meshless approach-local Kriging (LoKriging) method with two-dimensional structural analysis. Comput. Mech. 33 (2004) 235-244
14. Cai Y.C., and Zhu H.H. A meshless local natural neighbour interpolation method for stress analysis of solids. Engrg. Anal. Bound. Elem. 28 (2004) 607-613
15. Ouatouati A.E., and Johnson D.A. A new approach for numerical modal analysis using the element-free method. Int. J. Numer. Methods Engrg. 46 (1999) 1-27
16. Liu G.R., and Chen X.L. A meshfree method for static and free vibration analysis of thin plates of complicated shape. J. Sound Vibr. 241 (2001) 839-855
17. Liu G.R., and Gu Y.T. A local radial point interpolation method (LRPIM) for free vibration analyses of 2-D solids. J. Sound Vibr. 246 (2001) 29-46
18. Zhou J.X., Zhang H.Y., and Zhang L. Reproducing kernel particle method for free and forced vibration analysis. J. Sound Vibr. 279 (2005) 389-402
19. Liew K.M., Ng T.Y., Zhao X., and Reddy J.N. Harmonic reproducing kernel particle method for free vibration analysis of rotating cylindrical shells. Comput. Methods Appl. Mech. Engrg. 191 (2002) 4141-4157
20. Li H., Wang Q.X., and Lam K.Y. Development of a novel meshless local Kriging (LoKriging) method for structural dynamic analysis. Comput. Methods Appl. Mech. Engrg. 193 (2004) 2599-2619
21. De Bel E., Villon Ph., and Bouillard P.H. Forced vibrations in the medium frequency range solved by a partition of unity method with local information. Int. J. Numer. Methods Engrg. 62 (2004) 1105-1126
22. Hao S., Park H.S., and Liu W.K. Moving particle finite element method. Int. J. Numer. Methods Engrg. 53 (2001) 1937-1958
23. Hao S., Liu W.K., and Belytschko T. Moving particle finite element method with global smoothness. Int. J. Numer. Methods Engrg. 59 (2004) 1007-1020
24. Tian R., and Yagawa G. Generalized nodes and high-performance elements. Int. J. Numer. Methods Engrg. 64 (2005) 2039-2071
25. Rajendran S., and Zhang B.R. A "FE-Meshfree" QUAD4 element based on partition of unity. Comput. Methods Appl. Mech. Engrg. 197 (2007) 128-147
26. Ooi E.T., Rajendran S., Yeo J.H., and Zhang B.R. A mesh distortion tolerant 8-node solid element based on the partition of unity method with inter-element compatibility and completeness properties. Finite Elem. Anal. Des. 43 (2007) 771-787
27. B.R. Zhang, Development of FE-meshfree hybrid methods and their application to static and free vibration problems in 2-D solid mechanics, Ph.D. Thesis, School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore, 2008.
28. Nagashima T. Node-by-node meshless approach and its application to structural analyses. Int. J. Numer. Methods Engrg. 46 (1999) 341-385
29. Taylor R.L., Beresford P.J., and Wilson E.L. A nonconforming element for stress analysis. Int. J. Numer. Methods Engrg. 10 (1976) 1211-1219
30. Brebbia C.A., Telles J.C.F., and Wrobel L.C. Boundary Element Techniques (1984), Springer-Verlag, Berlin
31. Lamb H. On waves in an elastic plate. Proc. Roy. Soc. London, Ser. A 93 (1917) 114-128
32. R. Mindlin, Waves and vibrations in isotropic elastic plates, in: Proceedings of the First Symposium on Naval Structural Mechanics, 1972, pp. 199-232.