Generalized differential quadrature finite element method for cracked composite structures of arbitrary shape

Composite Structures

Volumn 106, Issue , 2013, Pages 815-834

  Viola, Erasmo ^a   Tornabene, Francesco ^a   Fantuzzi, Nicholas ^a  

^a UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

Arbitrary shape; Cracked flat plates; Free vibrations; Generalized differential quadrature; Generalized differential quadrature finite element method; Laminated composites

Indexed keywords

ARBITRARY SHAPE; FIRST-ORDER SHEAR DEFORMATION THEORY; FLAT PLATE; FREE VIBRATION; GENERALIZED DIFFERENTIAL QUADRATURE; GENERALIZED DIFFERENTIAL QUADRATURE METHODS; GEOMETRIC DISCONTINUITIES; NATURAL FREQUENCIES AND MODES;

CRACKS; EQUATIONS OF MOTION; LAMINATED COMPOSITES; VIBRATIONS (MECHANICAL);

FINITE ELEMENT METHOD;

EID: 84883087535     PISSN: 02638223     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruct.2013.07.034     Document Type: Article

References (78)

1. Soedel W. Vibrations of shells and plates 2004, Marcel Dekker.
2. Reddy J.N. Mechanics of laminated composite plates and shells 2003, CRC Press.
3. Carrera E., Brischetto S., Nali P. Plates and shells for smart structures: classical and advanced theories for modeling and analysis 2011, John Wiley & Sons.
4. Leissa AW. Vibration of plates. NASA SP-160, US Government Printing Office; 1969. Reprinted by The Acoustical Society of America; 1993.
5. Reddy J.N. Theory and analysis of elastic plates 1999, Taylor and Francis.
6. Huang C.S., Leissa A.W., Liao S.C. Vibration analysis of rectangular plates with edge V-notches. Int J Mech Sci 2008, 50:1255-1262.
7. Huang C.S., Leissa A.W. Vibration analysis of rectangular plates with side cracks via the Ritz method. J Sound Vib 2009, 323:974-988.
8. Huang C.S., Leissa A.W., Chan C.W. Vibrations of rectangular plates with internal cracks or slits. Int J Mech Sci 2011, 53:436-445.
9. Huang C.S., Leissa A.W., Li R.S. Accurate vibration analysis of thick, cracked rectangular plates. J Sound Vib 2011, 330:2079-2093.
10. Stahl B., Keer L.M. Vibration and stability of cracked rectangular plates. Int J Solids Struct 1972, 8:69-91.
11. Solecki R. Bending vibration of a simply supported rectangular plate with a crack parallel to one edge. Eng Fract Mech 1983, 18:1111-1118.
12. Khadem S.E., Rezaee M. Introduction of modified comparison functions for vibration analysis of a rectangular cracked plate. J Sound Vib 2000, 236:245-258.
13. Reissner E. The effect of transverse shear deformation on the bending of elastic plates. ASME J Appl Mech 1945, 12:A68-77.
14. Mindlin R.D. Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates. ASME J Appl Mech 1951, 18:31-38.
15. Qian G.L., Gu S.N., Jiang J.S. A finite element model of cracked plates and application to vibration problems. Comput Struct 1991, 39:483-487.
16. Yuan J., Dickinson S.M. The flexural vibration of rectangular plate systems approached by using artificial springs in the Rayleigh-Ritz method. J Sound Vib 1992, 159:39-55.
17. Liew K.M., Hung K.C., Lim M.K. A solution method for analysis of cracked plates under vibration. Eng Fract Mech 1994, 48:393-404.
18. Shu C. Differential quadrature and its application in engineering 2000, Springer.
19. Zong Z., Zhang Y. Advanced differential quadrature methods 2009, CRC Press.
20. Striz A.G., Chen W.L., Bert C.W. Static analysis of structures by the quadrature element method (QEM). Int J Solids Struct 1994, 31:2807-2818.
21. Bert C.W., Malik M. The differential quadrature method for irregular domains and application to plate vibration. Int J Mech Sci 1996, 38:589-606.
22. Chen C.N. The two-dimensional frame model of the differential quadrature element method. Comput Struct 1997, 62:555-571.
23. Shu C., Chew Y.T. Fourier expansion-based differential quadrature and its application to Helmholtz eigenvalue problems. Commun Numer Methods Eng 1997, 13:643-653.
24. Striz A.G., Chen W.L., Bert C.W. Free vibration of plates by the high accuracy quadrature element method. J Sound Vib 1997, 202:689-702.
25. Wang X.W., Gu H.Z. Static analysis of frame structures by the differential quadrature element method. Int J Numer Methods Eng 1997, 40:759-772.
26. Ghazi S.S.A., Barki F.A., Safwat H.M. Free vibration analysis of penta, hepta-gonal shaped plates. Comput Struct 1997, 62:395-407.
27. Zhong H.Z., He Y.H. Solution of Poisson and laplace equations by quadrilateral quadrature element. Int J Solids Struct 1998, 35:2805-2819.
28. Chen C.N. Solution of beam on elastic foundation by DQEM. J Eng Mech 1998, 124:1381-1384.
29. Chen C.N. The warping torsion bar model of the differential quadrature element method. Comput Struct 1998, 66:249-257.
30. Liu F.L., Liew K.M. Static analysis of Reissner-Mindlin plates by differential quadrature element method. J Appl Mech 1998, 65:705-710.
31. Wang X.W., Wang Y.L., Chen R.B. Static and free vibrational analysis of rectangular plates by the differential quadrature element method. Commun Numer Methods Eng 1998, 14:1133-1141.
32. Liu F.L., Liew K.M. Vibration analysis of discontinuous Mindlin plates by differential quadrature element method. J Vib Acoust 1999, 121:204-208.
33. Chen C.N. The development of irregular elements for differential quadrature element method: steady-state heat conduction analysis. Comput Methods Appl Mech Eng 1999, 170:1-14.
34. Chen C.N. The differential quadrature element method irregular element torsion analysis model. Appl Math Model 1999, 23:309-328.
35. Chen C.N. A generalized differential quadrature element method. Comput Methods Appl Mech Eng 2000, 188:553-566.
36. Wang C.M., Ang K.K., Yang L., Watanabe E. Vibration analysis of arbitrarily shaped sandwich plates via Ritz method. Mech Compos Mater Struct 2001, 8:101-118.
37. Chen C.N. Vibration of nonuniform shear deformable axisymmetric orthotropic circular plates solved by DQEM. Compos Struct 2001, 53:257-264.
38. Chen C.N. DQEM and DQFDM for the analysis of composite two-dimensional elasticity problems. Compos Struct 2003, 59:3-13.
39. Chen C.N. Dynamic response of shear-deformable axisymmetric orthotropic circular plate structures solved by the DQEM and EDQ based time integration schemes. Compos Struct 2004, 64:339-348.
40. Zong Z., Lam K.Y., Zhang Y.Y. A multidomain differential quadrature approach to plane elastic problems with material discontinuity. Math Comput Model 2005, 41:539-553.
41. Fantuzzi N. Generalized differential quadrature finite element method applied to advanced structural mechanics. PhD thesis, University of Bologna, DICAM Department; 2013.
42. Bert C.W., Malik M. Differential quadrature: a powerful new technique for analysis of composite structures. Compos Struct 1997, 39:179-189.
43. Karami G., Ali Shahpari S., Malekzadeh P. DQM analysis of skewed and trapezoidal laminated plates. Compos Struct 2003, 59:393-402.
44. Artioli E., Gould P.L., Viola E. A differential quadrature method for shear-deformable shells of revolution. Eng Struct 2005, 27:1879-1892.
45. Viola E., Tornabene F. Vibration analysis of damaged circular arches with varying cross-section. Struct Integr Durab (SID-SDHM) 2005, 1:155-169.
46. Lanhe W., Hua L., Daobin W. Vibration analysis of generally laminated composite plates by the moving least squares differential quadrature method. Compos Struct 2005, 68:319-330.
47. Viola E., Tornabene F. Vibration analysis of conical shell structures using GDQ method. Far East J Appl Math 2006, 25:23-39.
48. Tornabene F. Modellazione e Soluzione di Strutture a Guscio in Materiale Anisotropo. PhD thesis, University of Bologna, DISTART Department; 2007.
49. Tornabene F., Viola E. Vibration analysis of spherical structural elements using the GDQ method. Comput Math Appl 2007, 53:1538-1560.
50. Viola E., Dilena M., Tornabene F. Analytical and numerical results for vibration analysis of multi-stepped and multi-damaged circular arches. J Sound Vib 2007, 299:143-163.
51. Haftchenari H., Darvizeh M., Darvizeh A., Ansari R., Sharma C.B. Dynamic analysis of composite cylindrical shells using differential quadrature method (DQM). Compos Struct 2007, 78:292-298.
52. Marzani A., Tornabene F., Viola E. Nonconservative stability problems via generalized differential quadrature method. J Sound Vib 2008, 315:176-196.
53. Tornabene F., Viola E. 2-D solution for free vibrations of parabolic shells using generalized differential quadrature method. Eur J Mech A/Solids 2008, 27:1001-1102.
54. Malekzadeh P. Differential quadrature large amplitude free vibration analysis of laminated skew plates based on FSDT. Compos Struct 2008, 83:189-200.
55. Tornabene F. Vibration analysis of functionally graded conical, cylindrical and annular shell structures with a four-parameter power-law distribution. Comput Methods Appl Mech Eng 2009, 198:2911-2935.
56. Tornabene F., Viola E. Free vibrations of four-parameter functionally graded parabolic panels and shells of revolution. Eur J Mech A/Solids 2009, 28:991-1013.
57. Tornabene F., Viola E. Free vibration analysis of functionally graded panels and shells of revolution. Meccanica 2009, 44:255-281.
58. Tornabene F., Viola E., Inman D.J. 2-D differential quadrature solution for vibration analysis of functionally graded conical, cylindrical and annular shell structures. J Sound Vib 2009, 328:259-290.
59. Viola E., Tornabene F. Free vibrations of three parameter functionally graded parabolic panels of revolution. Mech Res Commun 2009, 36:587-594.
60. Hsu M.H. Vibration analysis of orthotropic rectangular plates on elastic foundations. Compos Struct 2010, 92:844-852.
61. Tornabene F., Marzani A., Viola E., Elishakoff I. Critical flow speeds of pipes conveying fluid by the generalized differential quadrature method. Adv Theor Appl Mech 2010, 3:121-138.
62. Andakhshideh A., Maleki S., Aghdam M.M. Non-linear bending analysis of laminated sector plates using generalized differential quadrature. Compos Struct 2010, 92:2258-2264.
63. Tornabene F. Free vibrations of laminated composite doubly-curved shells and panels of revolution via the GDQ method. Comput Methods Appl Mech Eng 2011, 200:931-952.
64. Tornabene F. 2-D GDQ solution for free vibrations of anisotropic doubly-curved shells and panels of revolution. Compos Struct 2011, 93:1854-1876.
65. Tornabene F. Free vibrations of anisotropic doubly-curved shells and panels of revolution with a free-form meridian resting on Winkler-Pasternak elastic foundations. Compos Struct 2011, 94:186-206.
66. Tornabene F., Liverani A., Caligiana G. FGM and laminated doubly-curved shells and panels of revolution with a free-form meridian: a 2-D GDQ solution for free vibrations. Int J Mech Sci 2011, 53:446-470.
67. Viola E., Rossetti L., Fantuzzi N. Numerical investigation of functionally graded cylindrical shells and panels using the generalized unconstrained third order theory coupled with the stress recovery. Compos Struct 2012, 94:3736-3758.
68. Tornabene F., Liverani A., Caligiana G. Laminated composite rectangular and annular plates: a GDQ solution for static analysis with a posteriori shear and normal stress recovery. Compos Part B: Eng 2012, 43:1847-1872.
69. Tornabene F., Liverani A., Caligiana G. Static analysis of laminated composite curved shells and panels of revolution with a posteriori shear and normal stress recovery using generalized differential quadrature method. Int J Mech Sci 2012, 61:71-87.
70. Tornabene F., Liverani A., Caligiana G. General anisotropic doubly-curved shell theory: a differential quadrature solution for free vibrations of shells and panels of revolution with a free-form meridian. J Sound Vib 2012, 331:4848-4869.
71. Tornabene F. Meccanica delle Strutture a Guscio in Materiale Composito. Il Metodo Generalizzato di Quadratura Differenziale, Esculapio; 2012.
72. Viola E., Tornabene F., Fantuzzi N. General higher-order shear deformation theories for the free vibration analysis of completely doubly-curved laminated shells and panels. Compos Struct 2013, 95:639-666.
73. Viola E., Tornabene F., Fantuzzi N. Static analysis of completely doubly-curved laminated shells and panels using general higher-order shear deformation theories. Compos Struct 2013, 101:59-93.
74. Tornabene F., Viola E. Static analysis of functionally graded doubly-curved shells and panels of revolution. Meccanica 2013, 48:901-930.
75. Tornabene F., Ceruti A. Free-form laminated doubly-curved shells and panels of revolution resting on Winkler-Pasternak elastic foundations: a 2-D GDQ solution for static and free vibration analysis. World J Mech 2013, 3:1-25.
76. Tornabene F., Viola E., Fantuzzi N. General higher-order equivalent single layer theory for free vibrations of doubly-curved laminated composite shells and panels. Compos Struct 2013, 104:94-117.
77. Tornabene F., Ceruti A. Mixed static and dynamic optimization of four-parameter functionally graded completely doubly-curved and degenerate shells and panels using GDQ method. Math Probl Eng 2013, 2013:1-33. Article ID 867079, http://dx.doi.org/10.1155/2013/867079.
78. Viola E, Tornabene F, Fantuzzi N. DiQuMASPAB Software, DICAM Department, Alma Mater Studiorum - University of Bologna. http://software.dicam.unibo.it/diqumaspab-project.