HDQ-FD integrated methodology for nonlinear static and dynamic response of doubly curved shallow shells

Structural Engineering and Mechanics

Volumn 19, Issue 5, 2005, Pages 535-550

  Civalek, Ömer ^a   Ülker, Mehmet ^b  

^a AKDENIZ UNIVERSITY   (Turkey)

^b FIRAT UNIVERSITY   (Turkey)

Author keywords

Coupled methodology; Doubly curved shells; Harmonic differential quadrature; Non linear dynamic analysis

Indexed keywords

BOUNDARY CONDITIONS; DAMPING; DYNAMIC RESPONSE; FINITE DIFFERENCE METHOD; HARMONIC ANALYSIS; NONLINEAR SYSTEMS; PARTIAL DIFFERENTIAL EQUATIONS;

COUPLED METHODOLOGY; DOUBLE CURVED SHELLS; HARMONIC DIFFERENTIAL QUADRATURE; NON-LINEAR DYNAMIC ANALYSIS;

SHELLS (STRUCTURES);

EID: 18744399592     PISSN: 12254568     EISSN: None     Source Type: Journal    
DOI: 10.12989/sem.2005.19.5.535     Document Type: Article

References (51)

1. Bathe, K.J. (1982), Finite Element Procedures in Engineering Analysis, Englewood Cliffs. NJ: Prentice-Hall.
2. Bellman, R., Kashef, B.G. and Casti, J. (1972), "Differential quadrature: A technique for the rapid solution of nonlinear partial differential equation", J. of Computational Physics, 10, 40-52.
3. Bert, C.W. and Malik, M. (1996), "Differential quadrature method in computational mechanics: A review", Appl. Mech. Rev., 49(1), 1-28.
4. Bert, C.W. and Malik, M. (1996), "Free vibration analysis of thin cylindrical shells by the differential quadrature method", J. Press. Vessel Tech., 118, 1-12.
5. Celia, M.A. and Gray, W.G. (1992), Numerical Methods for Differential Equations, Fundamental Concepts for Scientific and Engineering Applications. NJ, Prentice Hall.
6. Chia, C.Y. (1980), Nonlinear Analysis of Plates, Mc-Graw Book Co., New York, N.Y.
7. Civalek, Ö. (2002), Differential Quadrature (DQ) for Static and Dynamic Analysis of Structures, (in Turkish), Firat University.
8. Civalek, Ö. (2004), "Application of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for buckling analysis of thin isotropic plates and elastic columns", Eng. Struct., An Int. J., 26(2), 171-186.
9. Civalek, Ö. and Ülker, M. (2004), "Harmonic differential quadrature (HDQ) for axisymmetric bending analysis of thin isotropic circular plates", Struct. Eng. Mech., Int. J., 17(1), 1-14.
10. Civalek, Ö. and Ülker, M. (2004), "Free vibration analysis of elastic beams using harmonic differential quadrature (HDQ)", Mathematical and Computational Applications, 9(2), 257-264.
11. Civalek, Ö. and Çatal, H.H. (2003), "Linear static and vibration analysis of circular and annular plates by the harmonic differential quadrature (HDQ) method", J. of Eng. and Arthitecture Faculty of Osmangazi University, 16(1), 45-76.
12. Civalek, Ö. and Çatal, H.H. (2002), "Dynamic analysis of one and two dimensional structures by the method of generalized differential quadrature", Turkish Bulletin of Engineering, 417, 39-46.
13. Civalek, Ö. (2003), "Linear and nonlinear dynamic response of multi- degree-of freedom-systems by the method of harmonic differential quadrature (HDQ)", PhD. Thesis, Dokuz Eylül University, I¡zmir, (in Turkish).
14. Civalek, Ö. (1998), Finite Element Analysis of Plates and Shells, Elaziĝ: Firat University, (in Turkish).
15. Civalek, Ö. (2004), "Geometrically non-linear static and dynamic analysis of plates and shells resting on elastic foundation by the method of polynomial differential quadrature (PDQ)", PhD. Thesis, Firat University, (in Turkish), Elaziĝ.
16. Civalek, Ö. (2004), "Geometrically nonlinear dynamic analysis of doubly curved isotropic shells resting on elastic foundation by a combination of HDQ- FD methods", Int. J. of Pressure Vessels and Piping, (in press).
17. Civalek, Ö. (2001), "Static, dynamic and buckling analysis of elastic bars using differential quadrature", XVI. National Technical Engineering Symposium, Paper No: 5, Ankara: METU.
18. Civalek, Ö. (2004), "Differential quadrature methods in vibration analysis", J. of Engineer and Machine, Turkish Chamber of Mechanical Eng., 45, 530, 27-36.
19. Hua, L. and Lam, K.Y. (2000), "The generalized differential quadrature method for frequency analysis of a rotating conical shell with initial pressure", Int. J. Numer. Meth. Engng, 48, 1703-1722.
20. Leissa, A.W., Lee, J.K. and Wang, A.J. (1983), "Vibration of cantilevered doubly curved shallow shells", Int. J. Solids Struct., 19, 411-424.
21. Leissa, A.W. and Kadi, A.S. (1971), "Curvature effects on shallow shell vibration", J. Sound Vib., 16, 173-187.
22. Leissa, A.W. and Nariata, Y. (1984), "Vibrations of completely free shallow shells of rectangular planform", J. Sound Vib., 96, 207-218.
23. Leissa, A.W. (1973), Vibration of Shells, NASA, SP-288.
24. Lim, C.W. and Liew, K.M. (1994), "A pb-2 Ritz formulation for flexural vibration of shallow cylindrical shells of rectangular planform", J. Sound Vib., 173(3), 343-375.
25. Liew, K.M. and Lim, C.W. (1995), "A Ritz vibration analysis of doubly curved rectangular shallow shells using a refined first-order theory", Comput. Meth. Appl. Mech. Eng., 127, 145-162.
26. Liew, K.M., Lim, C.M. and Kitipornchai, S. (1997), "Vibration of shallow shells: A review with bibliography", Trans. ASME Appl. Mech. Rev., 50(8), 431-444.
27. Liew, K.M. and Lim, C.M. (1996), "A higher order theory for vibration of doubly curved shallow shells", J. Appl. Mech., 63, 587-593.
28. Liew, K.M., Lim, M.K., Lim, C.W, Li, D.B. and Zhang, Y.R. (1995a), "Effects of initial twist and thickness variation on the vibration behaviour of shallow conical shells", J. Sound Vib., 180(2), 272-296.
29. Liew, K.M., Han, J-B, Xiao, Z.M. and Du, H. (1996), "Differential quadrature method for Mindlin plates on Winkler foundations", Int. J. Mech. Sci., 38(4), 405-421.
30. Liew, K.M., Teo, T.M. and Han, J.B. (1999), "Comparative accuracy of DQ and HDQ methods for three-dimensional vibration analysis of rectangular plates", Int. J. Numer. Meth. Eng., 45, 1831-1848.
31. Liew, K.M., Teo, T.M. and Han, J.-B. (2001), "Three-dimensional static solutions of rectangular plates by variant differential quadrature method", Int. J. Mech. Sci., 43, 1611-1628.
32. Liew, K.M. and Lim, C.W. (1995b), "Vibratory behavior of doubly curved shallow shells of curvilinear planform", J. Eng. Mech., ASCE, 121(2), 1277-1283.
33. Markus, S. (1988), The Mechanics of Vibrations of Cylindrical Shells, Elsevier, New York.
34. Matsunaga, H. (1999), "Vibration and stability of thick simply supported shallow shells subjected to in-plane stresses", J. Sound Vib., 225(1), 41-60.
35. Nath, Y., Mahrenholtz, O. and Varma, K.K. (1987), "Nonlinear dynamic response of a doubly curved shallow shell on an elastic foundation", J. Sound Vib., 112(1), 53-61.
36. Nath, Y. and Jain, R.K. (1983), "Nonlinear dynamic analysis of shallow spherical shells on elastic foundation", Int. J. Mech. Sci., 25(6), 409-419.
37. Nath, Y. and Kumar, S. (1995), "Chebyshev series solution to non-linear boundary value problems in rectangular domain", Comput. Meth. Appl. Mech. Eng., 125, 41-52.
38. Nath, Y. and Sandeep, K. (2000), "Nonlinear analysis of doubly curved shells: An analytical approach", Sadhana, 25(4), 343-352.
39. Nath, Y., Dumir, P.C. and Gandhi, M.L. (1983), "Choice of collocation points for axisymmertric nonlinear two point boundary value problems in statics of shallow shells", Engineering Transaction, 31(3), 331-340.
40. Shu, C. and Xue, H. (1997), "Explicit computations of weighting coefficients in the harmonic differential quadrature", J. Sound Vib., 204(3), 549-555.
41. Shu, C. (2000), Differential Quadrature and Its Application in Engineering, Springer, London.
42. Shu, C. (1996), "Free vibration analysis of composite laminated conical shells by generalized differential quadrature", J. Sound Vib., 194(4), 587-604.
43. Shu, C. and Richards, B.E. (1992), "Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations", Int. J. Numer. Meth. Fluids, 15, 791-798.
44. Soedel, W. (1996), Vibrations of Shells and Plates, Second Edition, Revised and Expanded, Marcal Dekker, Inc., New York.
45. Striz, A.G., Wang, X. and Bert, C.W. (1995), "Harmonic differential quadrature method and applications to analysis of structural components", Acta Mechanica, 111, 85-94.
46. Striz, A.G., Jang, S.K. and Bert, C.W. (1988), "Nonlinear bending analysis of thin circular plates by differential quadrature", Thin-Walled Structures, 6, 51-62.
47. Timoshenko, S. and Woinowski-Krieger, S. (1959), Theory of Plates and Shells, McGraw-Hill, NewYork.
48. Wu, T.Y. and Liu, G.R. (2000), "Axisymmetric bending solution of shells of revolution by the generalized differential quadrature rule", Int. J. Press. Vessel and Piping, 77, 149-157.
49. Wu, T.Y. and Liu, G.R. (2001), "Free vibration analysis of circular plates with variable thickness by the generalized differential quadrature rule", Int. J. Solids Struct., 38, 7967-7980.
50. Wu, T.Y., Wang, Y.Y. and Liu, G.R. (2002), "Free vibration analysis of circular plates using generalized differential quadrature rule", Comput. Meth. Appl. Mech. Eng., 191, 5365-5380.
51. Zienkiewicz, O.C. (1977), The Finite Element Method in Engineering Science. (3rd ed.). London, McGraw-Hill.