DOI QR코드

DOI QR Code

Accurate buckling analysis of rectangular thin plates by double finite sine integral transform method

  • Ullah, Salamat (Faculty of Infrastructure Engineering, Dalian University of Technology) ;
  • Zhang, Jinghui (Faculty of Infrastructure Engineering, Dalian University of Technology) ;
  • Zhong, Yang (Faculty of Infrastructure Engineering, Dalian University of Technology)
  • 투고 : 2019.04.10
  • 심사 : 2019.06.12
  • 발행 : 2019.11.25

초록

This paper explores the analytical buckling solution of rectangular thin plates by the finite integral transform method. Although several analytical and numerical developments have been made, a benchmark analytical solution is still very few due to the mathematical complexity of solving high order partial differential equations. In solution procedure, the governing high order partial differential equation with specified boundary conditions is converted into a system of linear algebraic equations and the analytical solution is obtained classically. The primary advantage of the present method is its simplicity and generality and does not need to pre-determine the deflection function which makes the solving procedure much reasonable. Another advantage of the method is that the analytical solutions obtained converge rapidly due to utilization of the sum functions. The application of the method is extensive and can also handle moderately thick and thick elastic plates as well as bending and vibration problems. The present results are validated by extensive numerical comparison with the FEA using (ABAQUS) software and the existing analytical solutions which show satisfactory agreement.

키워드

참고문헌

  1. Adany, S., Visy, D. and Nagy, R. (2018), "Constrained shell Finite Element Method, Part 2: application to linear buckling analysis of thin-walled members", Thin-Walled Struct, 128, 56-70. https://doi.org/10.1016/j.tws.2017.01.022.
  2. Bui, T.Q. (2011), "Buckling analysis of simply supported composite laminates subjected to an in-plane compression load by a novel mesh-free method", Vietnam J. Mech., 33(2), 65-78. https://doi.org/10.15625/0866-7136/33/2/39.
  3. Bui, T.Q. and Nguyen, M.N. (2011), "A novel meshfree model for buckling and vibration analysis of rectangular orthotropic plates", Struct. Eng. Mech., 39(4), 579-598. https://doi.org/10.12989/sem.2011.39.4.579.
  4. Bui, T.Q., Nguyen, M.N. and Zhang, C. (2011), "Buckling analysis of Reissner-Mindlin plates subjected to in-plane edge loads using a shear-locking-free and meshfree method", Eng. Anal. Bound Elem., 35(9), 1038-1053. https://doi.org/10.1016/j.enganabound.2011.04.001.
  5. Civalek, O., Korkmaz, A. and Demir, C. (2010), "Discrete singular convolution approach for buckling analysis of rectangular Kirchhoff plates subjected to compressive loads on twoopposite edges", Adv. Eng. Softw., 41(4), 557-560. https://doi.org/10.1016/j.advengsoft.2009.11.002.
  6. Civalek, O. and Yavas, A. (2008), "Discrete singular convolution for buckling analyses of plates and columns", Struct. Eng. Mech., 29(3), 279-288. https://doi.org/10.12989/sem.2008.29.3.279.
  7. Ghannadpour, S.A.M. and Ovesy, H.R. (2009), "The application of an exact finite strip to the buckling of symmetrically laminated composite rectangular plates and prismatic plate structures", Compos. Struct., 89(1), 151-158. https://doi.org/10.1016/j.compstruct.2008.07.014.
  8. Huang, C.S., Lee, H.T., Li, P.Y., Hu, K.C., Lan, C.W. and Chang, M.J. (2019), "Three-dimensional buckling analyses of cracked functionally graded material plates via the MLS-Ritz method", Thin-Walled Struct, 134, 189-202. https://doi.org/10.1016/j.tws.2018.10.005.
  9. Jeyaraj, P. (2013), "Buckling and free vibration behavior of an isotropic plate under nonuniform thermal load", Int. J. Struct. Stab. Dyn., 13(03), https://doi.org/10.1142/S021945541250071X.
  10. Jiang, L., Wang, Y. and Wang, X. (2008), "Buckling analysis of stiffened circular cylindrical panels using differential quadrature element method", Thin-Walled Struct., 46(4), 390-398. https://doi.org/10.1016/j.tws.2007.09.004.
  11. Karamooz Ravari, M.R. and Shahidi, A.R. (2013), "Axisymmetric buckling of the circular annular nanoplates using finite difference method", Meccanica, 48(1), 135-144. https://doi.org/10.1007/s11012-012-9589-3.
  12. Karamooz Ravari, M.R., Talebi, S. and Shahidi, A.R. (2014), "Analysis of the buckling of rectangular nanoplates by use of finite-difference method", Meccanica, 49(6), 1443-1455. https://doi.org/10.1007/s11012-014-9917-x.
  13. Komur, M.A. and Sonmez, M. (2015), "Elastic buckling behavior of rectangular plates with holes subjected to partial edge loading", J. Constr. Steel Res., 112, 54-60. https://doi.org/10.1016/j.jcsr.2015.04.020.
  14. Lau, S. and Hancock, G. (1986), "Buckling of thin flat-walled structures by a spline finite strip method", Thin-Walled Struct., 4(4), 269-294. https://doi.org/10.1016/0263-8231(86)90034-0.
  15. Li, R., Tian, Y., Wang, P., Shi, Y. and Wang, B. (2016), "New analytic free vibration solutions of rectangular thin plates resting on multiple point supports", Int J. Mech. Sci., 110, 53-61. https://doi.org/10.1016/j.ijmecsci.2016.03.002.
  16. Li, R., Wang, B., Li, G., Du, J. and An, X. (2015), "Analytic free vibration solutions of rectangular thin plates point-supported at a corner", Int. J. Mech. Sci., 96, 199-205. https://doi.org/10.1016/j.ijmecsci.2015.04.004.
  17. Li, R., Wang, B. and Li, P. (2014), "Hamiltonian system-based benchmark bending solutions of rectangular thin plates with a corner point-supported", Int J. Mech. Sci., 85, 212-218. https://doi.org/10.1016/j.ijmecsci.2014.05.004.
  18. Li, R., Zheng, X., Wang, H., Xiong, S., Yan, K. and Li, P. (2018), "New analytic buckling solutions of rectangular thin plates with all edges free", Int. J. Mech. Sci., 144, 67-73. https://doi.org/10.1016/j.ijmecsci.2018.05.041.
  19. Li, R., Zhong, Y., Tian, B. and Liu, Y. (2009), "On the finite integral transform method for exact bending solutions of fully clamped orthotropic rectangular thin plates", Appl. Math. Lett., 22(12), 1821-1827. https://doi.org/10.1016/j.aml.2009.07.003.
  20. Lim, C.W., Cui, S. and Yao, W.A. (2007), "On new symplectic elasticity approach for exact bending solutions of rectangular thin plates with two opposite sides simply supported", Int. J. Solids. Struct., 44(16), 5396-5411. https://doi.org/10.1016/j.ijsolstr.2007.01.007.
  21. Lim, C. W., Lu, C. F., Xiang, Y. and Yao, W. (2009), "On new symplectic elasticity approach for exact free vibration solutions of rectangular Kirchhoff plates", Int. J. Eng. Sci., 47(1), 131-140. https://doi.org/10.1016/j.ijengsci.2008.08.003.
  22. Lim, C. W. and Xu, X. S. (2010), "Symplectic elasticity: theory and applications", Appl. Mech. Rev., 63(5), 050802. https://doi.org/10.1115/1.4003700.
  23. Liu, B. and Xing, Y. (2011), "Exact solutions for free vibrations of orthotropic rectangular Mindlin plates", Compos. Struct., 93(7), 1664-1672. https://doi.org/ 10.1016/j.compstruct.2011.01.014.
  24. Liu, B., Xing, Y. F. and Reddy, J. N. (2014), "Exact compact characteristic equations and new results for free vibrations of orthotropic rectangular Mindlin plates", Compos. Struct., 118, 316-321. https://doi.org/10.1016/j.compstruct.2014.07.051.
  25. Liu, Y. and Li, R. (2010), "Accurate bending analysis of rectangular plates with two adjacent edges free and the others clamped or simply supported based on new symplectic approach", Appl. Math. Model., 34(4), 856-865. https://doi.org/10.1016/j.apm.2009.07.003.
  26. Mahendran, M. and Murray, N. (1986), "Elastic buckling analysis of ideal thin-walled structures under combined loading using a finite strip method", Thin-Walled Struct., 4(5), 329-362. https://doi.org/10.1016/0263-8231(86)90029-7.
  27. Mijuskovic, O., Coric, B. and Scepanovic, B. (2015), "Accurate buckling loads of plates with different boundary conditions under arbitrary edge compression", Int. J. Mech. Sci., 101, 309-323. https://doi.org/10.1016/j.ijmecsci.2015.07.017.
  28. Ovesy, H. R., Ghannadpour, S. A. M. and Zia-Dehkordi, E. (2013), "Buckling analysis of moderately thick composite plates and plate structures using an exact finite strip", Compos. Struct., 95, 697-704. https://doi.org/10.1016/j.compstruct.2012.08.009.
  29. Simulia, D. S. (2013). "Abaqus 6.13 Analysis User's Guide." Dassault Systems, Providence, RI, USA.
  30. Singhatanadgid, P. and Taranajetsada, P. (2016), "Vibration analysis of stepped rectangular plates using the extended Kantorovich method", Mech. Adv. Mater. Struct., 23(2), 201-215. https://doi.org/10.1080/15376494.2014.949922.
  31. Tian, B., Li, R. and Zhong, Y. (2015), "Integral transform solutions to the bending problems of moderately thick rectangular plates with all edges free resting on elastic foundations", Appl. Math. Model., 39(1), 128-136. https://doi.org/10.1016/j.apm.2014.05.012.
  32. Tian, B., Zhong, Y. and Li, R. (2011), "Analytic bending solutions of rectangular cantilever thin plates", Arch. Civ. Mech. Eng., 11(4), 1043-1052. https://doi.org/10.1016/S1644-9665(12)60094-6.
  33. Timoshenko, S.P. (1961). Theory of Elastic Stability Second Edition. McGraw-Hill Book Company, Inc., New York, USA.
  34. Ullah, S., Zhong, Y. and Zhang, J. (2019), "Analytical buckling solutions of rectangular thin plates by straightforward generalized integral transform method", Int. J. Mech. Sci., 152, 535-544. https://doi.org/10.1016/j.ijmecsci.2019.01.025.
  35. Wang, B., Li, P. and Li, R. (2016), "Symplectic superposition method for new analytic buckling solutions of rectangular thin plates", Int. J. Mech. Sci., 119, 432-441. https://doi.org/10.1016/j.ijmecsci.2016.11.006.
  36. Wang, J., Liew, K. M., Tan, M. J. and Rajendran, S. (2002), "Analysis of rectangular laminated composite plates via FSDT meshless method", Int. J. Mech. Sci., 44(7), 1275-1293. https://doi.org/ 10.1016/S0020-7403(02)00057-7.
  37. Wang, X. and Huang, J. (2009), "Elastoplastic buckling analyses of rectangular plates under biaxial loadings by the differential qudrature method", Thin-Walled Struct., 47(1), 14-20. https://doi.org/10.1016/j.tws.2008.04.006.
  38. Wang, X., Tan, M. and Zhou, Y. (2003), "Buckling analyses of anisotropic plates and isotropic skew plates by the new version differential quadrature method", Thin-Walled Struct., 41(1), 15-29. https://doi.org/10.1016/S0263-8231(02)00100-3.
  39. Wu, C.P. and Lin, H.R. (2015), "Three-dimensional dynamic responses of carbon nanotube-reinforced composite plates with surface-bonded piezoelectric layers using Reissner's mixed variational theorem-based finite layer methods", J. Intell. Mater. Syst. Struct., 26(3), 260-279. https://doi.org/10.1177/1045389X14523859.
  40. Xiang, Y., Wang, C.M. and Kitipornchai, S. (2003), "Exact buckling solutions for rectangular plates under intermediate and end uniaxial loads", J. Eng. Mech., 129(7), 835-838. https://doi.org/10.1061/(ASCE)0733-9399(2003)129:7(835).
  41. Xing, Y.F. and Liu, B. (2009), "New exact solutions for free vibrations of thin orthotropic rectangular plates", Compos. Struct., 89(4), 567-574. https://doi.org/10.1016/j.compstruct.2008.11.010.
  42. Yufeng, X. and Wang, Z. (2017), "Closed form solutions for thermal buckling of functionally graded rectangular thin plates", Appl. Sci., 7(12), 1256. https://doi.org/10.3390/app7121256.
  43. Zhang, J., Zhou, C., Ullah, S., Zhong, Y. and Li, R. (2018), "Two-dimensional generalized finite integral transform method for new analytic bending solutions of orthotropic rectangular thin foundation plates", Appl. Math. Lett., 92, 8-14. https://doi.org/10.1016/j.aml.2018.12.019.
  44. Zhang, S. and Xu, L. (2018), "Analytical solutions for flexure of rectangular orthotropic plates with opposite rotationally restrained and free edges", Arch. Civ. Mech. Eng., 18(3), 965-972. https://doi.org/10.1016/j.acme.2018.02.005.
  45. Zhang, S. and Xu, L. (2017), "Bending of rectangular orthotropic thin plates with rotationally restrained edges: A finite integral transform solution", Appl. Math. Model., 46, 48-62. https://doi.org/10.1016/j.apm.2017.01.053.
  46. Zhang, Y. and Zhang, S. (2018), "Free transverse vibration of rectangular orthotropic plates with two opposite edges rotationally restrained and remaining others free", Appl. Sci., 9(1), 22. https://doi.org/10.3390/app9010022.
  47. Zhong, Y. and Yin, J.H. (2008), "Free vibration analysis of a plate on foundation with completely free boundary by finite integral transform method", Mech. Res. Commun., 35(4), 268-275. https://doi.org/10.1016/j.mechrescom.2008.01.004.
  48. Zhong, Y., Zhao, X. and Liu, H. (2014), "Vibration of plate on foundation with four edges free by finite cosine integral transform method", Lat. Am. J. Solids Struct., 11(5), 854-863. https://doi.org/10.1590/S1679-78252014000500008.
  49. Zhou, D., Cheung, Y.K. and Kong, J. (2000), "Free vibration of thick, layered rectangular plates with point supports by finite layer method", Int. J. Solids Struct., 37(10), 1483-1499. https://doi.org/10.1016/S0020-7683(98)00316-3.