Structural Engineering and Mechanics

  • 제74권5호
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  • Pages.577-588
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  • 2020
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Buckling of laminated composite plates with elastically restrained boundary conditions

  • Kouchakzadeh, Mohammad Ali (Department of Aerospace Engineering, Sharif University of Technology) ;
  • Rahgozar, Meysam (Department of Aerospace Engineering, Sharif University of Technology) ;
  • Bohlooly, Mehdi (Department of Aerospace Engineering, Sharif University of Technology)
  • 투고 : 2018.09.23
  • 심사 : 2020.01.10
  • 발행 : 2020.06.10
⟨ 이전 논문 다음 논문 ⟩

초록

A unified solution is presented for the buckling analysis of rectangular laminated composite plates with elastically restrained edges. The plate is subjected to biaxial in-plane compression, and the boundary conditions are simulated by employing uniform distribution of linear and rotational springs at all edges. The critical values of buckling loads and corresponding modes are calculated based on classical lamination theory and using the Ritz method. The deflection function is defined based on simple polynomials without any auxiliary function. The verifications of the current study are carried out with available combinations of classic boundary conditions in the literature. Through parametric study with a wide range of spring factors with some classical as well as some not classical boundary conditions, competency of the present model of boundary conditions is proved.

키워드

참고문헌

  1. Akgoz, B. and Civalek, O. (2011), "Nonlinear vibration analysis of laminated plates resting on nonlinear two-parameters elastic foundations", Steel Compos. Struct., 11, 403-421. https://doi.org/10.12989/scs.2011.11.5.403.
  2. Aydogdu, M., Aksencer, T. (2018), "Buckling of cross-ply composite plates with linearly varying In-plane loads", Compos. Struct., 183, 221-231. https://doi.org/10.1016/j.compstruct.2017.02.085.
  3. Baucke, A., Mittelstedt, C. (2015), "Closed-form analysis of the buckling loads of composite laminates under uniaxial compressive load explicitly accounting for bending-twisting-coupling", Compos. Struct., 128, 437-454. https://doi.org/10.1016/j.compstruct.2014.12.054.
  4. Belkacem, A., Tahar, H.D., Abderrezak, R., Amine, B.M., Mohamed, Z., Boussad, A. (2018), "Mechanical buckling analysis of hybrid laminated composite plates under different boundary conditions", Struct. Eng. Mech., 66, 761-769. https://doi.org/10.12989/sem.2018.66.6.761.
  5. Bohlooly, M., Malekzadeh Fard, K. (2019), "Buckling and postbuckling of concentrically stiffened piezo-composite plates on elastic foundations", J. Appl. Comput. Mech., 5, 128-140. https://dx.doi.org/10.22055/jacm.2018.25539.1277.
  6. Bohlooly, M., Mirzavand, B. (2015), "Closed form solutions for buckling and postbuckling analysis of imperfect laminated composite plates with piezoelectric actuators", Compos. Part B Eng., 72, 21-29. https://doi.org/10.1016/j.compositesb.2014.10.049.
  7. Bohlooly, M., Mirzavand, B. (2016), "A closed-form solution for thermal buckling of cross-ply piezolaminated plates", J. Struct. Stability Dynam. 16, 1450112. https://doi.org/10.1142/S0219455414501120.
  8. Bohlooly, M., Mirzavand, B. (2017), "Thermomechanical buckling of hybrid cross-ply laminated rectangular plates", Adv. Compos. Mater., 26, 407-426. https://doi.org/10.1080/09243046.2016.1197492.
  9. Bohlooly, M., Mirzavand, B. (2018), "Postbuckling and deflection response of imperfect piezo-composite plates resting on elastic foundations under in-plane and lateral compression and electro-thermal loading", Mech. Adv. Mater. Struct., 25, 192-201. https://doi.org/10.1080/15376494.2016.1255818.
  10. Bohlooly, M., Mirzavand, B., Fard, K.M. (2018), "An analytical approach for postbuckling of eccentrically or concentrically stiffened composite double curved panel on nonlinear elastic foundation", Appl. Math. Modell., 62, 415-435. https://doi.org/10.1016/j.apm.2018.06.008.
  11. Brush, D.O., Almroth, B.O. and Hutchinson, J. (1975), "Buckling of bars, plates, and shells", J. Appl. Mech., 42, 911. https://doi.org/10.1115/1.3423754.
  12. Cetkovic, M. and Vuksanovic, D. (2011), "Large deflection analysis of laminated composite plates using layerwise displacement model", Struct. Eng. Mech., 40, 257-277. https://doi.org/10.12989/sem.2011.40.2.257.
  13. Civalek, O. and Acar, M.H. (2007), "Discrete singular convolution method for the analysis of Mindlin plates on elastic foundations", J. Pressure Vessels Piping, 84, 527-535. https://doi.org/10.1016/j.ijpvp.2007.07.001.
  14. Dietrich, L., Kawahara, W., Phillips, A. (1978), "An experimental study of plastic buckling of a simply supported plate under edge thrusts", Acta Mechanica, 29, 257-267. https://doi.org/10.1007/BF01176641.
  15. Fard, K.M., Bohlooly, M. (2017), "Postbuckling of piezolaminated cylindrical shells with eccentrically/concentrically stiffeners surrounded by nonlinear elastic foundations", Compos. Struct., 171, 360-369. https://doi.org/10.1016/j.compstruct.2017.03.058.
  16. Feng, K., Xu, J. (2016), "Buckling Analysis of Composite Cylindrical Shell Panels by Using Legendre Polynomials Hierarchical Finite-Strip Method", J. Eng. Mech., 143, 04016121. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001181.
  17. Ghasemabadian, M., Saidi, A. (2017), "Stability analysis of transversely isotropic laminated Mindlin plates with piezoelectric layers using a Levy-type solution", Struct. Eng. Mech., 62, 675-693. https://doi.org/10.12989/sem.2017.62.6.675.
  18. Golmakani, M. and Far, M.S. (2017), "Buckling analysis of biaxially compressed double-layered graphene sheets with various boundary conditions based on nonlocal elasticity theory", Microsyst. Technol., 23, 2145-2161. https://doi.org/10.1007/s00542-016-3053-6.
  19. Gunda, J.B. (2013), "Thermal post-buckling analysis of square plates resting on elastic foundation: A simple closed-form solutions", Appl. Math. Modell., 37, 5536-5548. https://doi.org/10.1016/j.apm.2012.09.031.
  20. Hosseini-Hashemi, S., Kermajani, M., Nazemnezhad, R. (2015), "An analytical study on the buckling and free vibration of rectangular nanoplates using nonlocal third-order shear deformation plate theory", Europ. J. Mech. A/Solids, 51, 29-43. https://doi.org/10.1016/j.euromechsol.2014.11.005.
  21. Iyengar, K.S.R. and Karasimhan, K. (1965), "Buckling of rectangular plates with clamped and simply-supported edges", Publications de l'Institut Mathematique, 19, 31-40.
  22. Jin, G., Su, Z., Shi, S., Ye, T., Gao, S. (2014), "Three-dimensional exact solution for the free vibration of arbitrarily thick functionally graded rectangular plates with general boundary conditions", Compos. Struct., 108, 565-577. https://doi.org/10.1016/j.compstruct.2013.09.051.
  23. Khov, H., Li, W.L., Gibson, R.F. (2009), "An accurate solution method for the static and dynamic deflections of orthotropic plates with general boundary conditions", Compos. Struct., 90, 474-481. https://doi.org/10.1016/j.compstruct.2009.04.020.
  24. Kiani, Y. (2017), "Buckling of FG-CNT-reinforced composite plates subjected to parabolic loading", Acta Mechanica, 228, 1303-1319. https://doi.org/10.1007/s00707-016-1781-4.
  25. Latifi, M., Farhatnia, F. and Kadkhodaei, M. (2013), "Buckling analysis of rectangular functionally graded plates under various edge conditions using Fourier series expansion", Europ. J. Mech. A/Solids, 41, 16-27. https://doi.org/10.1016/j.euromechsol.2013.01.008.
  26. Li, Q. and Pan Iu, V. (2010), "Three-Dimensional Buckling Analysis of Rectangular Plates with In-Plane Compressive Loads", AIP Conference Proceedings, 674-677. https://doi.org/10.1063/1.3452256.
  27. Li, W.L. (2000), "Free vibrations of beams with general boundary conditions", J. Sound Vib., 237, 709-725. https://doi.org/10.1006/jsvi.2000.3150.
  28. Li, W.L. (2004), "Vibration analysis of rectangular plates with general elastic boundary supports", J. Sound Vib., 273, 619-635. https://doi.org/10.1016/S0022-460X(03)00562-5.
  29. Liew, K., Xiang, Y., Kitipornchai, S. (1996), "Analytical buckling solutions for Mindlin plates involving free edges", J. Mech. Sci., 38, 1127-1138. https://doi.org/10.1016/0020-7403(95)00108-5.
  30. Liu, G., Chen, X., Reddy, J. (2002), "Buckling of symmetrically laminated composite plates using the element-free Galerkin method", J. Struct. Stability Dynam. 2, 281-294. https://doi.org/10.1142/S0219455402000634.
  31. Lopatin, A., Morozov, E. (2009), "Buckling of the SSFF rectangular orthotropic plate under in-plane pure bending", Compos. Struct., 90, 287-294. https://doi.org/10.1016/j.compstruct.2009.03.006.
  32. Matsunaga, H. (2005), "Thermal buckling of cross-ply laminated composite and sandwich plates according to a global higher-order deformation theory", Compos. Struct., 68, 439-454. https://doi.org/10.1016/j.compstruct.2004.04.010.
  33. Mijuskovic, O., Coric, B., Scepanovic, B. (2014), "Exact stress functions implementation in stability analysis of plates with different boundary conditions under uniaxial and biaxial compression", Thin-Walled Struct., 80, 192-206. https://doi.org/10.1016/j.tws.2014.03.006.
  34. Mijuskovic, O., Coric, B., Scepanovic, B. (2015), "Accurate buckling loads of plates with different boundary conditions under arbitrary edge compression", J. Mech. Sci.,101, 309-323. https://doi.org/10.1016/j.ijmecsci.2015.07.017.
  35. Mirzaei, M. and Kiani, Y. (2016), "Thermal buckling of temperature dependent FG-CNT reinforced composite plates", 51, 2185-2201. https://doi.org/10.1007/s11012-015-0348-0.
  36. Mirzavand, B. and Bohlooly, M. (2015), "Thermal buckling of piezolaminated plates subjected to different loading conditions", J. Thermal Stresses, 38, 1138-1162. https://doi.org/10.1080/01495739.2015.1073506.
  37. Mirzavand, B., Bohlooly, M. (2019), "Higher-Order Stability Analysis of Imperfect Laminated Piezo-Composite Plates on Elastic Foundations Under Electro-Thermo-Mechanical Loads", J. Solid Mech., 11, 550-569. https://doi.org/10.22034/JSM.2019.666689.
  38. Nosier, A., Kapania, R., Reddy, J. (1994), "Low-velocity impact of laminated composites using a layerwise theory", Comput. Mech., 13, 360-379. https://doi.org/10.1007/BF00512589.
  39. Panda, S.K., Ramachandra, L. (2010), "Buckling of rectangular plates with various boundary conditions loaded by non-uniform inplane loads", J. Mech. Sci.,52, 819-828. https://doi.org/10.1016/j.ijmecsci.2010.01.009.
  40. Qu, Y., Hua, H., Meng, G. (2013), "A domain decomposition approach for vibration analysis of isotropic and composite cylindrical shells with arbitrary boundaries", Compos. Struct., 95, 307-321. https://doi.org/10.1016/j.compstruct.2012.06.022.
  41. Raju, G., Wu, Z., Kim, B.C., Weaver, P.M. (2012), "Prebuckling and buckling analysis of variable angle tow plates with general boundary conditions", Compos. Struct., 94, 2961-2970. https://doi.org/10.1016/j.compstruct.2012.04.002.
  42. Reddy, J.N. (2004), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC press, Florida, U.S.A.
  43. Shufrin, I., Rabinovitch, O. and Eisenberger, M. (2008a), "Buckling of laminated plates with general boundary conditions under combined compression, tension, and shear-A semi-analytical solution", Thin-Walled Structures, 46, 925-938. https://doi.org/10.1016/j.tws.2008.01.040.
  44. Shufrin, I., Rabinovitch, O., Eisenberger, M. (2008b), "Buckling of symmetrically laminated rectangular plates with general boundary conditions-A semi analytical approach", Compos. Struct., 82, 521-531. https://doi.org/10.1016/j.compstruct.2007.02.003.
  45. Shukla, K., Nath, Y., Kreuzer, E., Kumar, K. (2005), "Buckling of laminated composite rectangular plates", J. Aerosp. Eng., 18, 215-223. https://doi.org/10.1061/(ASCE)0893-1321(2005)18:4(215).
  46. Singhatanadgid, P., Jommalai, P. (2016), "Buckling analysis of laminated plates using the extended Kantorovich method and a system of first-order differential equations", J. Mech. Sci. Technol., 30, 2121-2131. https://doi.org/10.1007/s12206-016-0419-8.
  47. Song, X., Cao, T., Gao, P., Han, Q. (2020), "Vibration and damping analysis of cylindrical shell treated with viscoelastic damping materials under elastic boundary conditions via a unified Rayleigh-Ritz method", J. Mech. Sci.,165, 105158. https://doi.org/10.1016/j.ijmecsci.2019.105158.
  48. Song, X., Han, Q., Zhai, J. (2015), "Vibration analyses of symmetrically laminated composite cylindrical shells with arbitrary boundaries conditions via Rayleigh-Ritz method", Compos. Struct., 134, 820-830. https://doi.org/10.1016/j.compstruct.2015.08.134.
  49. Swaminathan, K., Naveenkumar, D. (2014), "Higher order refined computational models for the stability analysis of FGM plates- Analytical solutions", Europ. J. Mech. A/Solids, 47, 349-361. https://doi.org/10.1016/j.euromechsol.2014.06.003.
  50. Tamijani, A.Y., Kapania, R.K. (2012), "Chebyshev-ritz approach to buckling and vibration of curvilinearly stiffened plate", AIAA J., 50, 1007-1018. https://doi.org/10.2514/1.J050042.
  51. Tang, Y., Wang, X. (2011), "Buckling of symmetrically laminated rectangular plates under parabolic edge compressions", Int. J. Mech. Sci., 53, 91-97. https://doi.org/10.1016/j.ijmecsci.2010.11.005.
  52. Thai, H.-T., Kim, S.-E. (2011), "Levy-type solution for buckling analysis of orthotropic plates based on two variable refined plate theory", Compos. Struct., 93, 1738-1746. https://doi.org/10.1016/j.compstruct.2011.01.012.
  53. Ungbhakorn, V., Singhatanadgid, P. (2006), "Buckling analysis of symmetrically laminated composite plates by the extended Kantorovich method", Compos. Struct., 73, 120-128. https://doi.org/10.1016/j.compstruct.2005.02.007.
  54. Uymaz, B., Aydogdu, M. (2013a), "Three dimensional mechanical buckling of FG plates with general boundary conditions", Compos. Struct., 96, 174-193. https://doi.org/10.1016/j.compstruct.2012.07.033.
  55. Uymaz, B., Aydogdu, M. (2013b), "Three dimensional shear buckling of FG plates with various boundary conditions", Compos. Struct., 96, 670-682. https://doi.org/10.1016/j.compstruct.2012.08.031
  56. Wang, C., Zhang, H., Challamel, N., Duan, W. (2017), "On boundary conditions for buckling and vibration of nonlocal beams", Europ. J. Mech. A/Solids, 61, 73-81. https://doi.org/10.1016/j.euromechsol.2016.08.014.
  57. Xiang, Y., Liew, K., Kitipornchai, S. (1996), "Exact buckling solutions for composite laminates: proper free edge conditions under in-plane loadings", Acta Mechanica, 117, 115-128. https://doi.org/10.1007/BF01181041
  58. Yu, L., Wang, C. (2008), "Buckling of rectangular plates on an elastic foundation using the Levy method", AIAA J., 46, 3163-3167. https://doi.org/10.2514/1.37166.
  59. Zhang, X., Li, W.L. (2009), "Vibrations of rectangular plates with arbitrary non-uniform elastic edge restraints", J. Sound Vib., 326, 221-234. https://doi.org/10.1016/j.jsv.2009.04.021.