Free vibration and buckling analyses of composite plates with straight-sided quadrilateral domain based on DSC approach

Finite Elements in Analysis and Design

Volumn 43, Issue 13, 2007, Pages 1013-1022

  Civalek, Ömer ^a  

^a Faculty of Engineering   (Turkey)

Author keywords

Buckling; Composite; Discrete singular convolution; Free vibration; Skew plate; Trapezoidal plate

Indexed keywords

ALGORITHMS; BUCKLING; COMPUTATIONAL MECHANICS; MATHEMATICAL TRANSFORMATIONS; NUMERICAL METHODS; VIBRATION ANALYSIS;

DISCRETE SINGULAR CONVOLUTION; FREE VIBRATION; SKEW PLATE; TRAPEZOIDAL PLATE;

COMPOSITE MATERIALS;

EID: 34548609642     PISSN: 0168874X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.finel.2007.06.014     Document Type: Article

References (49)

1. Wei G.W. Discrete singular convolution for the solution of the Fokker-Planck equations. J. Chem. Phys. 110 (1999) 8930-8942
2. Wei G.W. Solving quantum eigenvalue problems by discrete singular convolution. J. Phys. B: At. Mol. Opt. Phys. 33 (2000) 343-352
3. Wei G.W. Discrete singular convolution for the sine-Gordon equation. Physica D 137 (2000) 247-259
4. Wei G.W. Wavelets generated by using discrete singular convolution kernels. J. Phys. A: Math. Gen. 33 (2000) 8577-8596
5. Wei G.W., Kouri D.J., and Hoffman D.K. Wavelets and distributed approximating functionals. Comput. Phys. Commun. 112 (1998) 1-6
6. Zhao S., Wei G.W., and Xiang Y. DSC analysis of free-edged beams by an iteratively matched boundary method. J. Sound Vib. 284 (2005) 487-493
7. Wei G.W. A new algorithm for solving some mechanical problems. Comput. Methods Appl. Mech. Eng. 190 (2001) 2017-2030
8. Wei G.W. Vibration analysis by discrete singular convolution. J. Sound Vib. 244 (2001) 535-553
9. Wei G.W. Discrete singular convolution for beam analysis. Eng. Struct. 23 (2001) 1045-1053
10. Wei G.W., Zhao Y.B., and Xiang Y. Discrete singular convolution and its application to the analysis of plates with internal supports. Part 1: theory and algorithm. Int. J. Numer. Methods Eng. 55 (2002) 913-946
11. Wei G.W., Zhao Y.B., and Xiang Y. A novel approach for the analysis of high-frequency vibrations. J. Sound Vib. 257 2 (2002) 207-246
12. Zhao Y.B., Wei G.W., and Xiang Y. Discrete singular convolution for the prediction of high frequency vibration of plates. Int. J. Solids Struct. 39 (2002) 65-88
13. Wei G.W., Zhao Y.B., and Xiang Y. The determination of natural frequencies of rectangular plates with mixed boundary conditions by discrete singular convolution. Int. J. Mech. Sci. 43 (2001) 1731-1746
14. Lim C.W., Li Z.R., Xiang Y., Wei G.W., and Wang C.M. On the missing modes when using the exact frequency relationship between Kirchhoff and Mindlin plates. Adv. Vib. Eng. 4 (2005) 221-248
15. Lim C.W., Li Z.R., and Wei G.W. DSC-Ritz method for high-mode frequency analysis of thick shallow shells. Int. J. Numer. Methods Eng. 62 (2005) 205-232
16. Bert C.W., and Francis P.H. Composite material mechanics: structural mechanics. AIAA J. 12 9 (1974) 1173-1186
17. Reddy J.N. A simple higher-order theory for laminated composite plates. ASME J. Appl. Mech. 51 (1984) 745-752
18. Noor A.K. Free vibrations of multilayered composite plates. AIAA J. 11 (1973) 1038-1039
19. Whitney J.M. The effect of boundary conditions on the response of laminated composites. J. Compos. Mater. 4 (1970) 192-203
20. Bert C.W., Wang X., and Striz A. Differential quadrature for static and free vibration analyses of anisotropic plates. Int. J. Solids Struct. 30 13 (1993) 1737-1744
21. Whitney J.M. Structural Analysis of Laminated Plates (1987), Technomic Publishing, Lancaster, PA
22. Li W.Y., Cheung Y.K., and Tham L.G. Spline finite strip analysis of general plates. J. Eng. Mech. ASCE 112 1 (1986) 43-54
23. Cheung Y.K., Tham L.G., and Li W.Y. Free vibration and static analysis of general plates by spline finite strip method. Comput. Mech. 3 (1988) 187-197
24. 3-spline functions. Int. J. Solids Struct. 31 (1994) 657-667
25. Liew K.M., and Han J.-B. A four-note differential quadrature method for straight-sided quadrilateral Reissner/Mindlin plates. Commun. Numer. Methods Eng. 13 (1997) 73-81
26. Liew K.M., and Lim C.W. A global continuum Ritz formulation for flexural vibration of pretwisted trapezoidal plates with one edge built in. Comput. Methods Appl. Mech. Eng. 114 3-4 (1994) 233-247
27. Lim C.W., and Liew K.M. Vibration of pretwisted cantilever trapezoidal symmetric laminates. Acta Mech. 111 3-4 (1995) 193-208
28. Lim C.W., Liew K.M., and Kitipornchai S. Vibration of arbitrarily laminated plates of general trapezoidal planform. J. Acoust. Soc. Am. 100 6 (1996) 3674-3685
29. Kitipornchai S., Xiang Y., Wang C.M., and Liew K.M. Buckling analysis of thick skew plates. Int. J. Numer. Methods Eng. 36 8 (1993) 1299-1310
30. Liew K.M., and Han J.-B. Bending analysis of simply supported shear deformable skew plates. J. Eng. Mech. ASCE 123 3 (1995) 214-221
31. Wang C.M., Liew K.M., and Alwis W.A.M. Buckling of skew plates and corner condition for simply supported edges. J. Eng. Mech. ASCE 118 4 (1992) 651-662
32. Liew K.M., Xiang Y., Kitipornchai S., and Wang C.M. Vibration of thick skew plates based on Mindlin shear deformation plate theory. J. Sound Vib. 168 (1993) 39-69
33. Liew K.M., Hung K.C., and Lim M.K. Vibration characteristic of simply supported thick skew plates in three-dimensional setting. J. Appl. Mech. ASME 62 (1995) 880-886
34. Chen C.C., Kitipornchai S., Lim C.W., and Liew K.M. Free vibration of symmetrically laminated thick-trapezoidal plates. Int. J. Mech. Sci. 41 (1999) 685-702
35. Lim C.W. Three-dimensional vibration analysis of a cantilevered parallelepiped: exact and approximate solutions. J. Acoust. Soc. Am. 106 6 (1999) 3375-3383
36. Liew K.M., Lim C.W., and Lim M.K. Transverse vibration of trapezoidal of variable thickness: unsymmetric trapezoids. J. Sound Vib. 177 4 (1994) 479-501
37. Chen C.C., Kitipornchai S., Lim C.W., and Liew K.M. Free vibration of symmetrically laminated thick-perforated plates. J. Sound Vib. 230 1 (2000) 111-132
38. Lim C.W., Liew K.M., and Kitipornchai S. Numerical aspects for free vibration of thick plates part I: formulation and verification. Comput. Methods Appl. Mech. Eng. 156 1-4 (1998) 15-29
39. Liew K.M., and Lim C.W. Vibratory characteristics of general laminates, I: symmetric trapezoids. J. Sound Vib. 183 4 (1995) 615-642
40. Karami G., Shahpari S.A., and Malekzadeh P. DQM analysis of skewed and trapezoidal laminated plates. Compos. Struct. 59 (2003) 393-402
41. Singh B., and Chakraverty S. Flexural vibration of skew plates using boundary characteristic orthogonal polynomials in two variables. J. Sound Vib. 173 (1994) 157-178
42. Wang S. Vibration of thin skew fibre reinforced composite laminates. J. Sound Vib. 201 (1997) 335-352
43. Jaunky N., Knight N.F., and Ambur D.R. Buckling of arbitrary quadrilateral anisotropic plates. Int. J. Solids Struct. 33 (1995) 938-944
44. Civalek O. An efficient method for free vibration analysis of rotating truncated conical shells. Int. J. Pressure Vessels Piping 83 (2006) 1-12
45. Civalek O. Three-dimensional vibration, buckling and bending analyses of thick rectangular plates based on discrete singular convolution method. Int. J. Mech. Sci. 49 (2007) 752-765
46. Civalek O. Nonlinear analysis of thin rectangular plates on Winkler-Pasternak elastic foundations by DSC-HDQ methods. Appl. Math. Modeling 31 (2007) 606-624
47. Liew K.M., and Lam K.Y. Application of two dimensional plate functions to flexural vibration of skew plates. J. Sound Vib. 139 2 (1990) 241-252
48. Ö. Civalek, Finite Element Analyses of Plates and Shells, Elazig, Firat University, 1998 (in Turkish).
49. Krishna Reddy A.R., and Palaninathan R. Free vibration of skew laminates. Comput. Struct. 70 (1999) 415-423