Abstract
In the present work, an innovative approach is developed and employed to investigate the buckling load of composite laminated plates using polar representation of the fourth-order flexural stiffness tensor. Based on the Rayleigh–Ritz method for calculating the buckling load of orthotropic uncoupled laminates, a new approach is proposed for calculating the critical buckling load as a function of fiber orientation and the number of layers. A new formula is also represented for measuring the possible numbers of buckling modes based on the length-to-width ratio of the plate. Moreover, the new methods make it easy to handle buckling problems, optimization and design of laminated plates subjected to in-plane loads. The efficiency and precision of this method are proved by numerical examples. The anisotropic parts of the buckling load are calculated, and their polar variations are investigated.
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Turvey, G.J., Marshall, I.H.: Buckling and Post-buckling of Composite Plates’. Chapman and Hall, UK (1995)
Shanmugam, N.E., Wang, C.M.: Analysis and Design of Plated Structures, Volume 2: Stability. Elsevier, England (2007)
Euler, L.: Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes sive solutio problematis isoperimetrici latissimo sensu accepti: Vol. 1. Springer Science & Business Media, (1952)
Potier-Ferry, M.: Foundations of elastic postbuckling theory. In: Buckling and Post-buckling, pp. 1–82. Springer, Berlin (1987)
Budiansky, B.: Theory of buckling and post-buckling behavior of elastic structures. J. Adv. Appl. Mech. 14, 1–65 (1974)
Golubitsky, M., Schaeffer, D.G.: A theory for imperfect bifurcation via singularity theory. J. Appl. Math. 1, 21–98, Springer, Berlin (1988)
Bloom, F., Douglas, C.: Handbook of Thin Plate Buckling and Postbuckling. Chapman and Hall/CRC, USA (2000)
March, H.: Buckling of flat plywood plates in compression: shear or combined compression and shear. Forest products, Lab Report, No. 1316 (1942)
Wittrick, W.H.: Correlation between some stability problems for orthotropic and isotropic plates under biaxial and uniaxial direct stress. Aeronaut. Q. 4(1), 83–95 (1952)
Chamis, C.C.: Buckling of anisotropic composite plates. J. Struct. Div 95(2), 2119–39 (1969)
Prabhakara, M.K., Chia, C.Y.: Post-buckling behaviour of rectangular orthotropic plates. J. Mech. Eng. Sci. 15, 25–33 (1973)
Ramesh, C., Basava, R.B.: Post-Buckling analysis of rectangular orthotropic plates. Int. J. Mech. Sci. 15, 81–97 (1973)
Manuel, S.: Post-buckling of orthotropic composite plates loaded in compression. AIAA J. 21(12), 1729–1735 (1983)
Reddy, J.N.: Mechanics of Laminated Composite Plates and Shells, 2nd edn. CRC Press, Boca Raton (2004)
Jones, R.M.: Mechanics of Composite Materials. McGraw-Hill, New York (1975)
Berthelot, J.M.: Matériaux Composites Comportement mécanique et analyse des Structures. MSSON, Paris (1992)
Akbarov, S.D.: Stability Loss and Buckling Delamination. Springer, Berlin (2012)
Shanmugam, N.E., Wang, C.M.: (Eds.) Analysis and Design of Plated Structures: Dynamics (Vol. 1). Elsevier, (2007)
Padmanav, D., Singh, B.N.: Buckling and post-buckling of laminated composite plates. Mech. Res. Commun. 46, 1–7 (2012)
Rosalin, S., Singh, B.N.: A new trigonometric zigzag theory for buckling and free vibration analysis of laminated composite and sandwich plates. Compos. Struct. 117, 316–332 (2014)
Khalili, S.M.R., Abbaspour, P., Malekzadeh Fard, K.: Buckling of non-ideal simply supported laminated plate on Pasternak foundation. Appl. Math. Comput. 219(12), 6420–6430 (2013)
Assaee, H., Hajikazemi, M., Ovesy, H.R.: The effect of anisotropy on post-buckling behavior of laminated plates using semi-energy finite strip method. Compos. Struct. 94(5), 1880–1885 (2012)
Seifi, R., Khoda-yari, N., Hosseini, H.: Study of critical buckling loads and modes of cross-ply laminated annular plates. Compos. Eng. Part B 43(2), 422–430 (2012)
Shadmehri, F., Hoa, S.V., Hojjati, M.: Buckling of conical composite shells. Compos. Struct. 94(2), 787–792 (2012)
Ovesy, H.R., Fazilati, J.: Parametric instability analysis of laminated composite curved shells subjected to non-uniform in-plane load. Compos. Struct. 108, 449–455 (2014)
Ni, Z., Yuan, J., Chen, B.: Buckling of the SS-C-SS-C symmetrical composite rectangular plate under linear-varying in-plane load. Compos. Struct. 107, 528–536 (2014)
Vannucci, P., Verchery, G.: Designing with Anisotropy. Part 2: Laminates Without Membrane-flexure Coupling. Comptes rendus de ICCM 12 (12th International, Conference on Composite Materials), Article N\(^{\circ }\). 572 Paris, (1999)
Vannucci, P., Verchery, G.: Designing with anisotropy. Part 3: Quasi-homogeneous laminates: Comptes rendus de ICCM 12 (Twelfth International Conference on Composite Materials), Article N\(^{\circ }\).573. Paris, France (1999)
Vannucci, P., Verchery, G.: A special class of uncoupled and quasi-homogeneous laminates. Compos. Sci. Tech. 61(10), 1465–1473 (2001)
Kazemi, M.: Contribution to the study of the behavior in buckling of the laminated plates by using the polar method. Ph.D Dissertation, Université de Bourgogne, Dijon. (2005)
Boresi, A.P., Chong, K., Lee, J.D.: Elasticity in Engineering Mechanics. Wiley, Hoboken, NJ (2010)
Verchery, G.: Les invariants des tenseurs d’ordre 4 du type de l’élasticité. In Mechanical Behavior of Anisotropic Solids/Comportment Méchanique des Solides Anisotropes, 93–104. Springer, Netherlands, (1982)
Vannucci, P.: Plane anisotropy by the polar method. Meccanica 40(4–6), 437–54 (2005)
Vannucci, P.: Influence of invariant material parameters on the flexural optimal design of thin anisotropic laminates. Int. J. Mech. Sci. 51, 192–203 (2009)
Vincenti, A.: Conception et optimisation de composites par méthode polaire et algorithmes génétiques. PhD Thesis, Université de Bourgogne, ISAT [in French] Nevers France (2002)
Vannucci, P., Verchery, G.: Stiffness design of laminates using the polar method. Int. J. Solid. Struct. 38(50–51), 9281–9294 (2001)
Vannucci, P., Riccardo, B., Bennati, S.: Exact optimal flexural design of laminates. Compos. Struct. 90(3), 337–345 (2009)
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Kazemi, M. A new exact semi-analytical solution for buckling analysis of laminated plates under biaxial compression. Arch Appl Mech 85, 1667–1677 (2015). https://doi.org/10.1007/s00419-015-1011-x
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DOI: https://doi.org/10.1007/s00419-015-1011-x