Browse > Article
http://dx.doi.org/10.12989/scs.2014.17.4.453

Stability of EG cylindrical shells with shear stresses on a Pasternak foundation  

Najafov, A.M. (Institute for Machine Elements and Lifting-and-Shifting Machines of Azerbaijan Technical University)
Sofiyev, A.H. (Department of Civil Engineering, Engineering Faculty, Suleyman Demirel University)
Hui, D. (Department of Mechanical Engineering, University of New Orleans)
Karaca, Z. (Department of Civil Engineering, Ondokuz Mayis University)
Kalpakci, V. (Department of Civil Engineering, Hasan Kalyoncu University)
Ozcelik, M. (Department of Geological Engineering, Suleyman Demirel University)
Publication Information
Steel and Composite Structures / v.17, no.4, 2014 , pp. 453-470 More about this Journal
Abstract
This article is the result of an investigation on the influence of a Pasternak elastic foundation on the stability of exponentially graded (EG) cylindrical shells under hydrostatic pressure, based on the first-order shear deformation theory (FOSDT) considering the shear stresses. The shear stresses shape function is distributed parabolic manner through the shell thickness. The governing equations of EG orthotropic cylindrical shells resting on the Pasternak elastic foundation on the basis of FOSDT are derived in the framework of Donnell-type shell theory. The novelty of present work is to achieve closed-form solutions for critical hydrostatic pressures of EG orthotropic cylindrical shells resting on Pasternak elastic foundation based on FOSDT. The expressions for critical hydrostatic pressures of EG orthotropic cylindrical shells with and without an elastic foundation based on CST are obtained, in special cases. Finally, the effects of Pasternak foundation, shear stresses, orthotropy and heterogeneity on critical hydrostatic pressures, based on FOSDT are investigated.
Keywords
buckling; composite structures; functionally graded; instability/stability; material properties;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 Gorbunov-Possadov, M.I., Malikova, T.A. and Solomin, V.I. (1984), Design of Structures on Elastic Foundation, Strojizdat, Moscow, Russia.
2 Grigorenko, Y.M. and Grigorenko, A.Y. (2013), "Static and dynamic problems for anisotropic inhomogeneous shells with variable parameters and their numerical solution (review)", Int. Appl. Mech., 49(2), 123-193.   DOI
3 Han, B. and Simitses, G.J. (1991), "Analysis of anisotropic laminated cylindrical shells subjected to destabilizing loads. Part II: Numerical results", Compos. Struct., 19(2), 183-205.   DOI   ScienceOn
4 Hui, D. (1986), "Imperfection-sensitivity of elastically supported beams and its relation to the double-cusp instability model", Proc. Roy. Soc. Lond. Math. Phys. Sci., 405(1828), 143-158.   DOI
5 Hui, D. and Hansen, J.S. (1980), "Two-mode buckling of an elastically supported plate and its relation to catastrophe-theory", J. Appl. Mech., 47(3), 607-612.   DOI
6 Jung, W.Y. and Han, S.C. (2014) "Shear buckling responses of laminated composite shells using a modified 8-node ANS shell element", Compos. Struct., 109, 119-129.   DOI
7 Kar, A. and Kanoria, M. (2009), "Generalized thermoelastic functionally graded orthotropic hollow sphere under thermal shock with three-phase-lag effect", Europe J. Mech. A-Solids, 28(4), 757-767.   DOI
8 Li, Z.M. and Lin, Z.Q. (2010), "Non-linear buckling and postbuckling of shear deformable anisotropic laminated cylindrical shell subjected to varying external pressure loads", Compos. Struct. 92(2), 553-567.   DOI
9 Kardomateas, G.A. (1997), "Koiter-based solution for the initial postbuckling behavior of moderately thick orthotropic and shear deformable cylindrical shells under external pressure", J. Appl. Mech., 64(4), 885-896.   DOI
10 Kasagi, A. and Sridharan, S. (1993), "Buckling and post-buckling analysis of thick composite cylindrical shells under hydrostatic pressure" Compos. Eng., 3(5), 467-487.   DOI
11 Kumar, Y. and Lal, R. (2012), "Vibrations of non-homogeneous orthotropic rectangular plates with bilinear thickness variation resting on Winkler foundation", Meccanica, 47(4), 893-915.   DOI
12 Lomakin, V.A. (1976), The Elasticity Theory of Non-homogeneous Materials, Nauka, Moscow, Russia.
13 Mantari, J.L. and Soares, C.G. (2014), "Optimized sinusoidal higher order shear deformation theory for the analysis of functionally graded plates and shells", Compos. B Eng., 56(1), 126-136.   DOI
14 Morimoto, T. and Tanigawa, Y. (2007), "Elastic stability of inhomogeneous thin plates on an elastic foundation", Arch. Appl. Mech., 77(9), 653-674.   DOI
15 Naili, S. and Oddou, C. (2000), "Buckling of short cylindrical shell surrounded by an elastic medium", J. Appl. Mech., 67(1), 212-214.   DOI
16 Najafov, A.M., Sofiyev, A.H. and Kuruoglu, N. (2013), "Torsional vibration and stability of functionally graded orthotropic cylindrical shells on elastic foundations", Meccanica, 48(4), 829-840.   DOI
17 Ng, T.Y. and Lam, K.Y. (1999), "Effects of elastic foundation on the dynamic stability of cylindrical shells", Struct. Eng. Mech., Int. J., 8(2), 193-205.   DOI
18 Pan, E. (2003), "Exact solution for functionally graded anisotropic elastic composite laminates", J. Compos. Mater., 37(21), 1903-1920.   DOI
19 Ootao, Y. and Tanigawa, Y. (2007), "Three-dimensional solution for transient thermal stresses of an orthotropic functionally graded rectangular plate", Compos. Struct., 80(1), 10-20.   DOI   ScienceOn
20 Palazotto, A.N. and Linnemann, P.E. (1991), "Vibration and buckling characteristics of composite cylindrical panels incorporating the effects of a higher-order shear theory", Int. J. Solid. Struct., 28(3), 341-361.   DOI
21 Paliwal, D.N. and Pandey, R.K. (2001), "Free vibrations of an orthotropic thin cylindrical shell on a Pasternak foundation", AIAA J., 39(11), 2188-2191.   DOI
22 Pelletier, J.L. and Vel, S.S. (2006), "An exact solution for the steady-state thermoelastic response of functionally graded orthotropic cylindrical shells", Int. J. Solid. Struct., 43(5), 1131-1158.   DOI   ScienceOn
23 Peng, X.L. and Li, X.F. (2012), "Elastic analysis of rotating functionally graded polar orthotropic disks", Int. J. Mech. Sci., 60(1), 84-91.   DOI
24 Ramirez, F., Heyliger, P.R. and Pan, E. (2006), "Static analysis of functionally graded elastic anisotropic plates using a discrete layer approach", Compos. B Eng., 37(1), 10-20.   DOI
25 Reddy, J.N. (2004), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, New York, USA.
26 Shariyat, M. and Asemi, K. (2014), "Three-dimensional non-linear elasticity-based 3D cubic B-spline finite element shear buckling analysis of rectangular orthotropic FGM plates surrounded by elastic foundations", Compos. B Eng., 56, 934-947.   DOI
27 Shen, H.S. and Wang, H. (2013), "Thermal postbuckling of functionally graded fiber reinforced composite cylindrical shells surrounded by an elastic medium", Compos. Struct., 102, 250-260.   DOI
28 Shen, H.S. (2008), "Boundary layer theory for the buckling and postbuckling of an anisotropic laminated cylindrical shell. Part II: Prediction under external pressure", Compos. Struct., 82(3), 362-370.   DOI
29 Shen, H.S. and Noda, N. (2007), "Post-buckling of pressure-loaded FGM hybrid cylindrical shells in thermal environments", Compos. Struct., 77(4), 546-560.   DOI   ScienceOn
30 Shen, H.S. (2013), "Postbuckling of axially-loaded laminated cylindrical shells surrounded by an elastic medium", Mech. Adv. Mater. Struct., 20(2), 130-150.   DOI
31 Shirakawa, K. (1983), "Effects of shear deformation and rotatory inertia on vibration and buckling of cylindrical shells", J. Sound Vib., 91(3), 425-437.   DOI
32 Sofiyev, A.H. (2011), "Thermal buckling of FGM shells resting on a two parameter elastic foundation", Thin-Wall. Struct., 49(10), 1304-1311.   DOI
33 Sofiyev, A.H. and Kuruoglu, N. (2014), "Buckling and vibration of shear deformable functionally graded orthotropic cylindrical shells under external pressures", Thin-Wall. Struct., 78, 121-130.   DOI
34 Sofiyev, A.H. and Marandi, B. (1996), "Dynamic stability problem of non-homogeneous cylindrical shells on elastic foundations", Proc. Inst. Math. Mech. Academy Sci. Azerbaijan, 5(8), 128-131. [In Russian]
35 Sofiyev, A.H., Omurtag, M.H. and Schnack, E. (2009), "The vibration and stability of orthotropic conical shells with non-homogeneous material properties under a hydrostatic pressure", J. Sound Vib., 319(3-5), 963-983.   DOI   ScienceOn
36 Thai, H.T. and Choi, D.H. (2012), "A refined shear deformation theory for free vibration of functionally graded plates on elastic foundation", Compos. B Eng., 43(5), 2335-2347.   DOI
37 Sofiyev, A.H., Schnack, E., Haciyev, V.C. and Kuruoglu, N. (2012), "Effect of the two-parameter elastic foundation on the critical parameters of non-homogeneous orthotropic shells", Int. J. Struct. Stabil. Dynam., 12(5), 24 p.
38 Tornabene, F. (2011), "Free vibrations of anisotropic doubly-curved shells and panels of revolution with a free-form meridian resting on Winkler-Pasternak elastic foundations", Compos. Struct., 94(1), 186-206.   DOI
39 Sofiyev, A.H., Deniz, A., Ozyigit, P. and Pinarlik, M. (2014), "Stability analysis of clamped nonhomogeneous shells on the elastic foundation", Acta Phys. Pol., 125(2), 459-461.   DOI
40 Soldatos, K.P. and Timarci, T. (1993), "A unified formulation of laminated composite, shear deformable, five-degrees-of-freedom cylindrical shell theories", Compos. Struct., 25(1-4), 165-171.   DOI
41 Tornabene, F., Fantuzzi, N., Viola, E. and Reddy, J.N. (2014), "Winkler-Pasternak foundation effect on the static and dynamic analyses of laminated doubly-curved and degenerate shells and panels", Compos. B Eng., 57, 269-296.   DOI
42 Wosu, S.N., Hui, D. and Daniel, L. (2012), "Hygrothermal effects on the dynamic compressive properties of graphite/epoxy composite material", Compos. B Eng., 43(3), 841-855.   DOI
43 Zenkour, A.M., Alam, M.N.M. and Radwan, A.F. (2013), "Bending of cross-ply laminated plates resting on elastic foundations under thermo-mechanical loading", Int. J. Mech. Mater. Des., 9(3), 239-251.   DOI
44 Atmane, H.A., Tounsi, A., Mechab, I. and Bedia, E.A.A. (2010), "Free vibration analysis of functionally graded plates resting on Winkler-Pasternak elastic foundations using a new shear deformation theory", Int. J. Mech. Mater. Des., 6(2), 113-121.   DOI
45 Akoz, A.Y. and Ergun, H. (2012), "Analysis of partially embedded beams in two-parameter foundation", Struct. Eng. Mech., Int. J., 42(1), 1-12.   DOI
46 Adany, S. (2014), "Flexural buckling of simply-supported thin-walled columns with consideration of membrane shear deformations: Analytical solutions based on shell model", Thin-Wall. Struct., 74, 36-48.   DOI
47 Alipour, M.M., Shariyat, M. and Shaban, M. (2010), "A semi-analytical solution for free vibration of variable thickness two-directional-functionally graded plates on elastic foundations", Int. J. Mech. Mater. Des., 6(4), 293-304.   DOI
48 Ambartsumian, S.A. (1964), Theory of Anisotropic Plates; Strength, Stability, Vibration, Technomic, Stamford, USA.
49 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.   DOI
50 Bagherizadeh, E., Kiani, Y. and Eslami, M.R. (2011), "Mechanical buckling of functionally graded material cylindrical shells surrounded by Pasternak elastic foundation", Compos. Struct., 93(11), 3063-3071.   DOI
51 Civalek, O. (2008), "Vibration analysis of conical panels using the method of discrete singular convolution", Comm. Numer. Meth. Eng., 24(3), 169-181.
52 Chen, J., Soh, A.K., Liu, J. and Liu, Z. (2004a), "Thermal fracture analysis of a functionally graded orthotropic strip with a crack", Int. J. Mech. Mater. Des., 1(2), 131-141.   DOI
53 Baron, C. (2011), "Propagation of elastic waves in an anisotropic functionally graded hollow cylinder in vacuum", Ultrasonics, 51(2), 123-130.   DOI
54 Batra, R.C. and Jin, J. (2005), "Natural frequencies of a functionally graded anisotropic rectangular plate", J. Sound Vib., 282(1), 509-516.   DOI   ScienceOn
55 Bouderba, B., Houari, M.S.A. and Tounsi, A. (2013), "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Compos. Struct., Int. J., 14(1), 85-104.   DOI   ScienceOn
56 Chen, W.Q., Bian, Z.G. and Ding, H.J. (2004b), "Three-dimensional vibration analysis of fluid-filled orthotropic FGM cylindrical shells", Int. J. Mech. Sci., 46(1), 159-171.   DOI   ScienceOn
57 Croll, J.G.A. (2001), "Buckling of cylindrical tunnel liners", J. Eng. Mech., 127(4), 333-341.   DOI
58 Eslami, M.R. and Shariyat, M. (1999), "A higher-order theory for dynamic buckling and postbuckling analysis of laminated cylindrical shells", J. Press. Vess. T.-ASME, 121(1), 94-102.   DOI
59 Ferreira, A.J.M., Roque, C.M.C., Neves, A.M.A., Jorge, R.M.N., Soares, C.M.M. and Reddy, J.N. (2011), "Buckling analysis of isotropic and laminated plates by radial basis functions according to a higher-order shear deformation theory", Thin-Wall. Struct., 49(7), 804-811.   DOI
60 Firouz-Abadi, R.D., Torkaman-Asadi, M.A. and Rahmanian, M. (2013), "Whirling frequencies of thin spinning cylindrical shells surrounded by an elastic foundation", Acta Mech., 224(4), 881-892.   DOI
61 Grigorenko, Y.M. and Vasilenko, A.T. (1992), Static Problems for Anisotropic Inhomogeneous Shells, Nauka, Moscow, Russia.
62 Fok, S.L. (2002), "Analysis of the buckling of long cylindrical shells embedded in an elastic medium using the energy method", J. Strain Anal. Eng. Design, 37(5), 375-383.   DOI