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Buckling of thick deep laminated composite shell of revolution under follower forces
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 Title & Authors
Buckling of thick deep laminated composite shell of revolution under follower forces
Khayat, Majid; Poorveis, Davood; Moradi, Shapour; Hemmati, Mona;
 Abstract
Laminated composite shells are commonly used in various engineering applications including aerospace and marine structures. In this paper, using semi-analytical finite strip method, the buckling behavior of laminated composite deep as well as thick shells of revolution under follower forces which remain normal to the shell is investigated. The stiffness caused by pressure is calculated for the follower forces subjected to external fibers in thick shells. The shell is divided into several closed strips with alignment of their nodal lines in the circumferential direction. The governing equations are derived based on first-order shear deformation theory which accounts for through thickness-shear flexibility. Displacements and rotations in the middle surface of shell are approximated by combining polynomial functions in the meridional direction as well as truncated Fourier series with an appropriate number of harmonic terms in the circumferential direction. The load stiffness matrix which accounts for variation of loads direction will be derived for each strip of the shell. Assembling of these matrices results in global load stiffness matrix which may be un-symmetric. Upon forming linear elastic stiffness matrix called constitutive stiffness matrix, geometric stiffness matrix and load stiffness matrix, the required elements for the second step analysis which is an eigenvalue problem are provided. In this study, different parameter effects are investigated including shell geometry, material properties, and different boundary conditions. Afterwards, the outcomes are compared with other researches. By considering the results of this article, it can be concluded that the deformation-dependent pressure assumption can entail to decrease the calculated buckling load in shells. This characteristic is studied for different examples.
 Keywords
thick deep shell;laminated composite;follower force;finite strip method;buckling;
 Language
English
 Cited by
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Nanotechnology, smartness and orthotropic nonhomogeneous elastic medium effects on buckling of piezoelectric pipes, Structural Engineering and Mechanics, 2016, 58, 5, 931  crossref(new windwow)
 References
1.
ABAQUS/standard user's manual (1998), Vols. I-III, Version 5.8, Pawtucket, RI: Hibbitt, Karlsson & Sorensen, Inc.

2.
Altman, W. and Oliveira, M.G.D. (1988), "Vibration and Stability cantilevered cylindrical shell panels under follower forces", J. Sound Vib., 122(2), 291-298. crossref(new window)

3.
Altman, W. and Oliveira, M.G.D. (1990), "Vibration and Stability shell panels with slight internal damping under follower forces", J. Sound Vib., 136(1), 45-50. crossref(new window)

4.
Argyris, J.H. and Symeonidis, S. (1981), "Nonlinear finite element analysis of elastic system under nonconservative loading-natural formulation, part 1, quasistatic problems", Comput. Meth. Appl. Mech. Eng., 26, 75-123. crossref(new window)

5.
Asadi, E. and Qatu, M.S. (2012), "Static analysis of thick laminated shells with different boundary conditions using GDQ", Thin Wall. Struct., 51, 76-81. crossref(new window)

6.
Asadi, E. and Qatu, M.S. (2013), "Free vibration of thick laminated cylindrical shells with different boundary conditions using general differential quadrature", J. Vib. Control, 19(3), 356-366. crossref(new window)

7.
Asadi, E., Wang, W. and Qatu, M.S. (2012), "Static and vibration analyses of thick deep laminated cylindrical shells using 3D and various shear deformation theories", Compos. Struct., 94(2), 494-500. crossref(new window)

8.
Bolotin, V.V. (1963), Nonconservative Problems Of The Theory Of Elastic Stability, Pergamon Press, New York, NY, USA.

9.
Cagdas, I.U. and Adali, S. (2011), "Buckling of cross-ply cylinders under hydrostatic pressure considering pressure stiffness", Ocean Eng., 38(4), 559-569. crossref(new window)

10.
Casimir, J.B., Nguyen, M.C. and Tawfiq, I. (2007), "Thick shells of revolution: Derivation of the dynamic stiffness matrix of continuous elements and application to a tested cylinder", Comput. Struct., 85(23-24), 1845-1857. crossref(new window)

11.
Chao, C.C., Tung, T.P. and Chern, Y.C. (1988), "Buckling of thick orthotropic spherical shells", Compos. Struct., 9(2), 113-137. crossref(new window)

12.
Chen, J., Dawe, D.J. and Wang, S. (2000), "Nonlinear transient analysis of rectangular composite laminated plates", Compos. Struct., 49(2), 129-139. crossref(new window)

13.
Chen, W. and Zhang, W. (1993), "Buckling analysis of ring-stiffened cylindrical shells by compound strip method", 12th International Conference Computational Mechanics, Stuttgart, Germany, August.

14.
Cohen, G.A. (1966), "Conservative of a normal pressure field acting on a shell", AIAA J., 4(10).

15.
Dooms, D., Degrande, G., De Roeck, G. and Reynders, E. (2004), "Wind induced vibration of thin-walled cylindrical structures", International Conference on Noise and Vibration Engineering, Leuven, Belgium, September.

16.
Fukuchi, N. and Tanaka, T. (2006), "Non-periodic motions and fractals of a circular arch under follower forces with small disturbances", Struct. Eng. Mech., 6(2), 87-101.

17.
Goyal, V.K. and Kapania, R.K. (2008), "Dynamic stability of laminated beams subjected to nonconservative loading", Thin Wall. Struct., 46(12), 1359-1369. crossref(new window)

18.
Heppler, G.R. and Hansen, J.S. (1986), "A mindlin element for thick and deep shells", Comput. Meth. Appl. Mech. Eng., 54(1), 21-47. crossref(new window)

19.
Hibbitt, H.D. (1979), "Some follower forces and load stiffness", Int. J. Numer. Meth. Eng., 14(6), 207-23.

20.
Iwata, K., Tsukimor, K. and Kubo, F. (1991), "A Symmetric Load-Stiffness Matrix for Buckling Analysis of Shell Structures under Pressure Loads", Int. J. Press. Ves. Pip., 45(1), 101-120. crossref(new window)

21.
Kang, J.H. (2012), "There-dimensional vibration analysis of joined thick conical-cylindrical shells of revolution with variable thickness", J. Sound Vib., 331(18), 4187-4198. crossref(new window)

22.
Kang, J.H. (2015), "Vibrations of truncated shallow and deep conical shells with non-uniform thickness", Struct. Eng. Mech., 55(1), 29-46. crossref(new window)

23.
Kang, J.H. and Leissa, A.W. (2005), "Three-dimensional vibration analysis of thick hyperboloidal shells of revolution", J. Sound Vib., 282(1-2), 277-296. crossref(new window)

24.
Kasagi, A. and Sridharan, S. (1993), "Buckling and postbuckling analysis of thick composite cylindrical shells under hydrostatic pressure", Compos. Eng., 3(5), 467-481. crossref(new window)

25.
Koiter, W.T. (1967), General Equations Of Elastic Stability For Thin Shells, Theory of Thin Shells, Univ. of Houston Press, USA.

26.
Lazzari, M., Vitaliani, R.V., Majowiecki, M. and Saett, A.V. (2003), "Dynamic behavior of a tensegrity system subjected to follower wind loading", Comput. Struct., 81(22-23), 2199-2217. crossref(new window)

27.
Lu, G. and Mao, R. (2001), "A study of the plastic buckling of axially compressed cylindrical shells with a thick-shell theory", Int. J. Mech. Sci., 43(10), 2319-2330. crossref(new window)

28.
Nali, P., Carrera, E. and Lecca, S. (2011), "Assessments of refined theories for buckling analysis of laminated plates", Compos. Struct., 93(2), 456-464. crossref(new window)

29.
Ovesy, H.R. and Fazilati, J. (2009), "Stability analysis of composite laminated plate and cylindrical shell structures using semi-analytical finite strip method", Compos. Struct., 89(3), 467-474. crossref(new window)

30.
Park, S.H. and Kim, J.H. (2002), "Dynamic stability of a stiff-edged cylindrical shell subjected to a follower force", Comput. Struct., 80(3-4), 227-233. crossref(new window)

31.
Poorveis, D. and Kabir, M.Z. (2006), "Buckling of discretely stringer-stiffened composite cylindrical shells under combined axial compression and external pressure", Scientia Iranica, 13(2), 113-123.

32.
Qatu, M.S. (1999), "Accurate equations for laminated composite deep thick shells", Int. J. Solid. Struct., 36(19), 2917-2941. crossref(new window)

33.
Romano, G. (1971), "Potential operators and conservative systems", Proceedings of the 14th Polish Solid Mechanics Conference, Kroscjenko, Poland, September.

34.
Ross, C.T.F. and Little, A.P.F. (2007), "Design charts for the general instability of ring-stiffened conical shells under external hydrostatic pressure", Thin Wall. Struct., 45(2), 199-208. crossref(new window)

35.
Ross, C.T.F., Sawkins, D. and Johns, T. (1999), "A Inelastic buckling of thick-walled circular conical shells under external hydrostatic pressure", Ocean Eng., 26(12), 1297-1310. crossref(new window)

36.
Sanders, J. and Lyell, J. (1959), "An improved first-approximation theory for thin shells", NASA Technical Report, NASA-TR-R24.

37.
Schweizerhof, K. and Ramm, E. (1984), "Displacement dependent pressure loads in nonlinear finite element analysis", Comput. Struct., 18(6), 1099-1114. crossref(new window)

38.
Sheinman, I. and Tene, Y. (1974), "Potential energy of a normal pressure field acting on an arbitrary shell", AIAA J., 11(8), 1216-1216.

39.
Spagnoli, A. (2001), "Different buckling modes in axially stiffened conical shells", Eng. Struct., 23(8), 957-965. crossref(new window)

40.
Teng, J.G. and Hong, T. (1998), "Nonlinear thin shell theories for numerical buckling predictions", Thin Wall. Struct., 31(1-3), 89-115. crossref(new window)

41.
Thangam Babu, P.V. and Reddy, D.V. (1973), "Frequency analysis of orthotropic circular cylindrical panels by the finite strip method", Build. Sci., 8(3), 229-241. crossref(new window)

42.
Tornabene, F. (2011), "2-D GDQ solution for free vibrations of anisotropic doubly-curved shells and panels of revolution", Compos. Sstruct., 93(7), 1854-1876. crossref(new window)

43.
Tornabene, F. and Viola, E. (2008), "2-D solution for free vibrations of parabolic shells using generalized differential quadrature method", Eur. J. Mech. A/Solid., 27(6), 1001-1025. crossref(new window)

44.
Tornabene, F., Brischetto, S., Fantuzzi, N. and Viola, E. (2015), "Numerical and exact models for free vibration analysis of cylindrical and spherical shell panels", Compos. Part B: Eng., 81, 231-250. crossref(new window)

45.
Tornabene, F., Fantuzzi, N. and Bacciocchi, M. (2014), "Free vibrations of free-form doubly-curved shells made of functionally graded materials using higher-order equivalent single layer theories", Compos. Part B: Eng., 67, 490-509. crossref(new window)

46.
Tornabene, F., Fantuzzi, N. and Bacciocchi, M. (2014), "The local GDQ method applied to general higherorder theories of doubly-curved laminated composite shells and panels: The free vibration analysis", Compos. Struct., 116, 637-660. crossref(new window)

47.
Tornabene, F., Fantuzzi, N., Bacciocchi, M. and Dimitri, R. (2015), "Free vibrations of composite oval and elliptic cylinders by the generalized differential quadrature method", Thin Wall. Struct., 97, 114-129. crossref(new window)

48.
Tornabene, F., Fantuzzi, N., Bacciocchi, M. and Dimitri, R. (2015), "Dynamic analysis of thick and thin elliptic shell structures made of laminated composite materials", Compos. Struct., 133, 278-299. crossref(new window)

49.
Tornabene, F., Fantuzzi, N., Bacciocchi, M. and Viola, E. (2015), "Higher-order theories for the free vibrations of doubly-curved laminated panels with curvilinear reinforcing fibers by means of a local version of the GDQ method", Compos. Part B: Eng., 81, 196-230. crossref(new window)

50.
Tornabene, F., Fantuzzi, N., Bacciocchi, M. and Viola, E. (2015), "A new approach for treating concentrated loads in doubly-curved composite deep shells with variable radii of curvature", Compos. Struct., 131, 433-452. crossref(new window)

51.
Wang, J. and Schweizerhof, K. (1996), "Study on free vibration of moderately thick orthotropic laminated shallow shells by boundary domain elements", Appl. Math. Model., 20(8), 579-584. crossref(new window)

52.
Wang, Q. (2003), "On complex flutter and buckling analysis of a beam structure subjected to static follower force", Struct. Eng. Mech., 16(5), 533-556. crossref(new window)

53.
Wang, S. Dawe, D.J. (1999), "Buckling of composite shell structures using the spline finite strip method", Compos. Part B, 30(4), 351-364. crossref(new window)

54.
Wang, X.H. and Redekop, D. (2011), "Free vibration analysis of moderately-thick and thick toroidal shells", Struct. Eng. Mech., 39(4), 449-463. crossref(new window)

55.
Yaghoubshahi, M., Asadi, E. and Fariborz, S.J. (2011), "A higher-order shell model applied to shell with mixed boundary condations", Proceeding of The Institution of Mechanical Engineering, Part C., 224.

56.
Zhong, W.X. and Cheung, Y.K. (1998), "The precise finite strip method", Compos. Struct., 69(6), 773-783. crossref(new window)