Abstract
Using Reddy’s third-order shear deformation plate theory (TSDT) with von Kármán geometrical nonlinearity, this work presents an analytical solution on the buckling and postbuckling behaviors of eccentrically stiffened functionally graded material (ES-FGM) plates on elastic foundations subjected to in-plane compressive loads or thermal loads or thermo-mechanical loads. Plates are reinforced by closely spaced FGM stiffeners. The material properties of the plate and stiffeners are assumed to be temperature-dependent. Theoretical formulations based on the smeared stiffeners technique and TSDT are derived. The expressions of thermal parameters are found in the analytical form. Applying Galerkin method, the expressions to determine the critical buckling load and analyze the postbuckling mechanical and thermal load–deflection curves are obtained. Two iterative algorithms are presented for the case of temperature-dependent plate material properties. The effects of thermal element, FGM stiffeners, geometrical and material parameters, initial imperfection, and foundation are considered and discussed. By comparing the present results with those in references, the accuracy of the present study is affirmed.
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Ferreira, A.J.M., Roque, C.M.C., Neves, A.M.A., Jorge, R.M.N., Soares, C.M.M., Reddy, J.N.: Buckling analysis of isotropic and laminated plates by radial basis functions according to a higher-order shear deformation theory. Thin Walled Struct. 49, 804–811 (2011)
Samsam Shariat, B.A., Eslami, M.R.: Buckling of thick functionally graded plates under mechanical and thermal loads. Compos. Struct. 78, 433–439 (2007)
Khabbaz, R.S., Manshadi, B.D., Abedian, A.: Nonlinear analysis of FGM plates under pressure loads using the higher-order shear deformation theories. Compos. Struct. 89, 333–344 (2009)
Duc, N.D., Tung, H.V.: Mechanical and thermal postbuckling of higher order shear deformable functionally graded plates on elastic foundations. Compos. Struct. 93, 2874–2881 (2011)
Javaheri, R., Eslami, M.R.: Buckling of functionally graded plates under in-plane compressive loading. J. Appl. Math. Mech. 82, 277–283 (2002)
Javaheri, R., Eslami, M.R.: Thermal buckling of functionally graded plates. AIAA J. 40, 162–169 (2002)
Javaheri, R., Eslami, M.R.: Thermal buckling of functionally graded plates based on the higher order theory. J. Therm. Stress 25(1), 603–25 (2002)
Na, K.S., Kim, J.H.: Three-dimensional thermo–mechanical buckling analysis for functionally graded composite plates. Compos. Struct. 73, 413–422 (2006)
Lanhe, W.: Thermal buckling of a simply supported moderately thick rectangular FGM plate. Compos. Struct. 64, 211–218 (2004)
Kiani, Y., Eslami, M.R.: An exact solution for thermal buckling of annular FGM plates on an elastic medium. Compos. B Eng. 45, 101–110 (2013)
Hui, D., Du, I.H.Y.: Initial postbuckling behavior of imperfect antisymmetric crossply cylindrical shells under torsion. J. Appl. Mech. ASME 54, 174–180 (1987)
Zhang, X., Han, Q.: Buckling and postbuckling behaviors of imperfect cylindrical shells subjected to torsion. Thin Wall. Struct. 45, 1035–1043 (2007)
Jiang, Q., Wang, X., Zhu, Y., Hui, D., Qiu, Y.: Mechanical, electrical and thermal properties of aligned carbon nanotube/polyimide composites. Compos. B Eng. 56, 408–412 (2014)
Bagherizadeh, E., Kiani, Y., Eslami, M.R.: Mechanical buckling of functionally graded material cylindrical shells surrounded by Pasternak elastic foundation. Compos. Struct. 93, 3063–3071 (2011)
Najafov, A.M., Sofiyev, A.H., Kuruoglu, N.: Torsional vibration and stability of functionally graded orthotropic cylindrical shells on elastic foundations. Meccanica 48, 829–840 (2013)
Sofiyev, A.H., Avcar, M.: The stability of cylindrical shells containing a FGM layer subjected to axial load on the Pasternak foundation. Engineering 2, 228–236 (2010)
Sofiyev, A.H., Kuruoglu, N.: Torsional vibration and buckling of the cylindrical shell with functionally graded coatings surrounded by an elastic medium. Compos. B Eng. 45, 1133–1142 (2013)
Sofiyev, A.H.: The buckling of FGM truncated conical shells subjected to axial compressive load and resting on Winkler-Pasternak foundations. Int. J. Press. Vessels Pip. 87, 753–761 (2010)
Sofiyev, A.H.: Non-linear buckling behavior of FGM truncated conical shells subjected to axial load. Int. J. Nonlinear Mech. 46, 711–719 (2011)
Sofiyev, A.H.: Non-linear buckling of an FGM truncated conical shell surrounded by an elastic medium. Int. J. Press. Vessels Pip. 107, 38–49 (2013)
Shen, H.S.: Thermal postbuckling behavior of functionally graded cylindrical shells with temperature-dependent properties. Int. J. Solids Struct. 41, 1961–1974 (2004)
Shen, H.S.: Thermal postbuckling behavior of shear deformable FGM plates with temperature-dependent properties. Int. J. Mech. Sci. 49, 466–478 (2007)
Shen, H.S., Wang, Z.X.: Nonlinear bending of FGM plates subjected to combined loading and resting on elastic foundations. Compos. Struct. 92, 2517–2524 (2010)
Lal, A., Jagtap, K.R., Singh, B.N.: Postbuckling response of functionally graded materials plate subjected to mechanical and thermal loadings with random material properties. Appl. Math. Model. 37, 2900–2920 (2013)
Akbari, M., Kiani, Y., Eslami, M.R.: Thermal buckling of temperature-dependent FGM conical shells with arbitrary edge supports. Acta Mech. 226, 897–915 (2015)
Mirzavand, B., Eslami, M.R.: A closed-form solution for thermal buckling of piezoelectric FGM rectangular plates with temperature-dependent properties. Acta Mech. 218, 87–101 (2011)
Timoshenko, S.P., Gere, J.M.: Theory of Elastic Stability. McGraw-Hill, New York (1961)
Steen, E.: Elastic buckling and postbuckling of eccentrically stiffened plates. Int. J. Solids Struct. 25, 751–768 (1989)
Bedair, O.K.: Influence of stiffener location on the stability of stiffened plates under compression and in-plane bending. Int. J. Mech. Sci. 39, 33–49 (1997)
Bich, D.H., Dung, D.V., Nam, V.H.: Nonlinear dynamical analysis of eccentrically stiffened functionally graded cylindrical panels. Compos. Struct. 94, 2465–2473 (2012)
Najafizadeh, M.M., Hasani, A., Khazaeinejad, P.: Mechanical stability of functionally graded stiffened cylindrical shells. Appl. Math. Model. 33, 1151–1157 (2009)
Dung, D.V., Nam, V.H.: Nonlinear dynamic analysis of eccentrically stiffened functionally graded circular cylindrical thin shells under external pressure and surrounded by an elastic medium. Eur. J. Mech. A/Solids 46, 42–53 (2014)
Dung, D.V., Hoa, L.K., Nga, N.T.: On the stability of functionally graded truncated conical shells reinforced by functionally graded stiffeners and surrounded by an elastic medium. Compos. Struct. 108, 77–90 (2014)
Dung, D.V., Hoa, L.K.: Nonlinear torsional buckling and postbuckling of eccentrically stiffened FGM cylindrical shells in thermal environment. Compos. B Eng. 69, 378–388 (2015)
Reddy, J.N.: A simple higher-order theory for laminated composite plates. J. Appl. Mech. 51, 745–752 (1984)
Reddy, J.N.: Analysis of functionally graded plates. Int. J. Numer. Methods Eng. 47, 663–684 (2000)
Reddy, J.N.: Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. CRC Press LLC, Boca Raton (2004)
Shen, H.S.: Functionally Graded Materials; Nonlinear Analysis of Plates and Shells. CRC Press LLC, Boca Raton (2009)
Brush, D.O., Almroth, B.O.: Buckling of Bars, Plates and Shells. McGraw-Hill, New York (1975)
Birman, V., Bert, C.W.: Dynamic stability of reinforced composite cylindrical shells in thermal fields. J. Sound Vib. 142, 183–190 (1990)
Thai, H.-T., Choi, D.-H.: Analytical solutions of refined plate theory for bending buckling and vibration analyses of thick plates. Appl. Math. Model. 37, 8310–8323 (2013)
Reddy, J.N., Chin, C.D.: Thermo–mechanical analysis of functionally graded cylinders and plates. J. Therm. Stress 21, 593–626 (1998)
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Van Dung, D., Nga, N.T. Buckling and postbuckling nonlinear analysis of imperfect FGM plates reinforced by FGM stiffeners with temperature-dependent properties based on TSDT. Acta Mech 227, 2377–2401 (2016). https://doi.org/10.1007/s00707-016-1637-y
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DOI: https://doi.org/10.1007/s00707-016-1637-y