Buckling of Laminated Elliptical and Super-Elliptical Thin Plates

Year 2022, Volume: 33 Issue: 5, 12525 - 12552, 01.09.2022

Erkin Altunsaray İsmail Bayer

https://doi.org/10.18400/tekderg.839435

Abstract

In this computational study the buckling analysis of symmetrically laminated elliptical and super-elliptical thin plates was carried out. The plates were considered as clamped or simply supported at the boundary. The minimum buckling load was determined using the Rayleigh-Ritz method and the Galerkin Method based on the Classical Laminated Plate Theory (CLPT). The influence of the solution methods, shape functions, boundary conditions, super-elliptical power, lamination type, aspect ratio, and thickness on the critical buckling load were investigated using a parametric study. The verification of the isotropic case was performed comparing some results in the open literature, and reliable agreement was obtained. Convergence studies of the composite case with increasing terms (up to 10 terms) were achieved and sufficient accuracy was provided. During the preliminary design stage of composite structures, many design parameters such as panel sizes, panel thickness, stacking sequences, boundary conditions and loading conditions are taken into consideration. It is possible to evaluate these parameters quickly by using appropriate shape function with the Rayleigh-Ritz method.

Keywords

Super-elliptical composite thin plates, buckling, Classic Laminated Plate Theory (CLPT), Rayleigh-Ritz method

References

• [1] Shenoi, R.A. and Wellicome, J.F.), Composite Materials in Maritime Structures, (Fundamental Aspects) Volume-I. Cambridge University Press, NY., 1993a.
• [2] Shenoi, R.A. and Wellicome, J.F, Composite Materials in Maritime Structures, (Practical Considerations) Volume-II. Cambridge University Press, NY., 1993b.
• [3] Mouritz, A.P., Gellert, E., Burchill, P. and Challis, K., Review of advanced composite structures for naval ships and submarines, Compos. Struct. 53(1):21–41, 2001.
• [4] Altekin, M., Free transverse vibration of shear deformable super-elliptical plates, Wind and Struct. 24(4),307-331, 2017.
• [5] Kumar, Y., The Rayleigh–Ritz method for linear dynamic, static and buckling behavior of beams, shells and plates: A literature review,. J. Vibr. and Cont. 24(7): 1205-1227, 2018.
• [6] Timoshenko, S.P. and Gere, J.M., Theory of Elastic Stability, 2nd Edition. McGraw-Hill Book Company, USA, 1961.
• [7] Szilard, R., Theories and Applications of Plate Analysis: Classical Numerical and Engineering Methods, John Wiley & Sons, Inc., Hoboken, NJ, USA, 2004.
• [8] Dawe, D.J. and Craig, T.J., The vibration and stability of symmetrically-laminated composite rectangular plates subjected to in-plane stresses, Compos. Struct.5(4): 281-307, 1986.
• [9] Leissa, A.W., A review of laminated composite plate buckling, App. Mech. Rev. 40(5), 1987.
• [10] Aiello, M.A. and Ombres, L., Buckling and vibrations of unsymmetric laminates resting on elastic foundations under in-plane and shear forces, Compos. Struct. 44: 31-41, 1999.
• [11] Darvizeh, M., Darvizeh A., Ansari, R. and Sharma, C.B., Buckling analysis of generally laminated composite plates (generalized differential quadrature rules versus Rayleigh–Ritz method, Compos. Struct. 63:69–74, 2004.
• [12] Reddy, J.N., Mechanics of laminated composite plates and shells: Theory and Analysis, 2nd ed., Boca Raton, FL, CRC Press, 2004.
• [13] Shufrin, I., Rabinovitch, O. and Eisenberger, M., Buckling of symmetrically laminated rectangular plates with general boundary conditions – A semi analytical approach, Compos. Struct. 82: 521–531, 2008.
• [14] Seifi, R., Khoda-Yari, N. and Hosseini, H., Study of critical buckling loads and modes of cross-ply laminated annular plates, Compos. Part B Eng. 43(2): 422-430, 2012.
• [15] Altunsaray, E. and Bayer, İ., Buckling of symmetrically laminated quasi-isotropic thin rectangular plates, Steel and Compos. Struct. 17(3): 305-320, 2014.
• [16] Afsharmanesh, B., Ghaheri, A. and Taheri-Behrooz, F., Buckling and vibration of laminated composite circular plate on winkler-type foundation, Steel and Compos. Struct. 17(1): 1-19, 2014.
• [17] Ghaheri, A., Keshmiri, A. and Taheri-Behrooz, F., Buckling and vibration of symmetrically laminated composite elliptical plates on an elastic foundation subjected to uniform in-plane force, J. Eng. Mech. 140(7): 04014049-1-10, 2014.
• [18] Liew, K.M, Kitipornchai, S. and Lim, C.W., Free vibration analysis of thick superelliptical plates, J. Eng. Mech. 124 (2): 137-145, 1998.
• [19] Wang, C.M., Wang, L. and Liew, K.M., Vibration and buckling of super elliptical plates, J. Sound Vib. 171(3): 301-31, 1994.
• [20] Altekin, M., Free linear vibration and buckling of super-elliptical plates resting on symmetrically distributed point-supports on the diagonals, Thin Wall. Struct. 46:1066-1086, 2008.
• [21] Hasheminejad, S.M., Keshvari, M.M. and Ashory, M.R., Dynamic stability of super-elliptical plates resting on elastic foundations under periodic in-plane loads, J. Eng. Mech. 140(1):172-181, 2014.
• [22] Jazi, S.R. and Farhatnia, F., Buckling analysis of functionally graded super elliptical plate using pb-2 Ritz Method, Adv. Mat. Res. Vols.383-390: 5387-5391, 2012.
• [23] Sayyad, A.S. and Ghugal, Y.M., On the buckling of isotropic, transversely isotropic and laminated composite rectangular plates, Int. J. Struct. Stab. Dyn. 14(7): 1450020, 2014.
• [24] Ghaheri, A., Nosier, A. and Keshmiri. A., Parametric stability of symmetrically laminated composite super‐elliptical plates, J. Compos. Mat. 50(28): 3935‐3951, 2016.
• [25] Zhang, D.G., Nonlinear bending and thermal post-buckling analysis of FGM super elliptical thin plates, Res.& Rev.: J. Mat. Sci. 5(6): 64-73, 2017.
• [26] Altekin, M., Bending of super-elliptical Mindlin plates by finite element method, Teknik Dergi, 29, No:4, 8469-8496, 2018.
• [27] Mirzaei, M., Thermal buckling of temperature-dependent composite super elliptical plates reinforced with carbon nanotubes, J. Therm. Str. 41(7): 920-935, 2018.
• [28] Altunsaray, E. and Bayer, İ., Deflection and free vibration of symmetrically laminated quasi-isotropic thin rectangular plates for different boundary conditions, Ocean Eng. 57:197-222, 2013.
• [29] Altunsaray, E., Free vibration of symmetrically laminated quasi-isotropic super-elliptical thin plates" Steel and Compos. Struct. 29(4): 493-508, 2018.
• [30] Altunsaray, E. and Bayer, İ., Buckling Analysis of Symmetrically Laminated Rectangular Thin Plates under Biaxial Compression" Teknik Dergi, 29, No:4, 2021.
• [31] Sato, K., Free flexural vibrations of a simply supported elliptical plate subjected to an in-plane force, Theo. App. Mech. Jap. 50: 165–181, 2001.
• [32] Sato, K., Vibration and buckling of a clamped elliptical plate on elastic foundation and under uniform in-plane force, Theo. App. Mech. Jap. 51:49–62, 2002.
• [33] Tsai, S.W., Composites design. (4th Edition), Think Composites, 1988.