Smart Structures and Systems

  • 제13권1호
  • /
  • Pages.111-135
  • /
  • 2014
  • /
  • 1738-1584(pISSN)
  • /
  • 1738-1991(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

3D buckling analysis of FGM sandwich plates under bi-axial compressive loads

  • Wu, Chih-Ping (Department of Civil Engineering, National Cheng Kung University) ;
  • Liu, Wei-Lun (Department of Civil Engineering, National Cheng Kung University)
  • 투고 : 2012.11.13
  • 심사 : 2013.05.24
  • 발행 : 2014.01.25
⟨ 이전 논문 다음 논문 ⟩

초록

Based on the Reissner mixed variational theorem (RMVT), finite rectangular layer methods (FRLMs) are developed for the three-dimensional (3D) linear buckling analysis of simply-supported, fiber-reinforced composite material (FRCM) and functionally graded material (FGM) sandwich plates subjected to bi-axial compressive loads. In this work, the material properties of the FGM layers are assumed to obey the power-law distributions of the volume fractions of the constituents through the thickness, and the plate is divided into a number of finite rectangular layers, in which the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-plane variations of the field variables of each individual layer, respectively, and an h-refinement process is adopted to yield the convergent solutions. The accuracy and convergence of the RMVT-based FRLMs with various orders used for expansions of each field variables through the thickness are assessed by comparing their solutions with the exact 3D and accurate two-dimensional ones available in the literature.

키워드

참고문헌

  1. Akhras, G. and Li, W.C. (2007), "Three-dimensional static, vibration and stability analysis of piezoelectric composite plates using a finite layer method", Smart Mater. Struct., 16(3), 561-569. https://doi.org/10.1088/0964-1726/16/3/002
  2. Akhras, G. and Li, W.C. (2008), "Three-dimensional thermal buckling analysis of piezoelectric composite plates using the finite layer method", Smart Mater. Struct., 17(5), 1-8.
  3. Brischetto, S. and Carrera, E. (2010), "Advanced mixed theories for bending analysis of functionally graded plates", Comput. Struct., 88(23-24), 1474-1483. https://doi.org/10.1016/j.compstruc.2008.04.004
  4. Carrera, E. (2000a), "A priori vs. a posteriori evaluation of transverse stresses in multilayered orthotropic plates", Compos. Struct., 48(4), 245-260. https://doi.org/10.1016/S0263-8223(99)00112-9
  5. Carrera, E. (2000b), "An assessment of mixed and classical theories on global and local response of multilayered orthotropic plates", Compos. Struct., 50(2), 183-198. https://doi.org/10.1016/S0263-8223(00)00099-4
  6. Carrera E. (2001), "Developments, ideas, and evaluations based upon Reissner's Mixed Variational Theorem in the modeling of multilayered plates and shells", Appl. Mech. Rev., 54, 301-329. https://doi.org/10.1115/1.1385512
  7. Carrera, E. (2003a), "Historical review of zig-zag theories for multilayered plates and shells", Appl. Mech. Rev., 56, 287-308. https://doi.org/10.1115/1.1557614
  8. Carrera, E. (2003b), "Theories and finite elements for multilayered plates and shells: A unified compact formulation with numerical assessment and benchmarks", Arch. Comput. Method. E., 10(3), 215-296. https://doi.org/10.1007/BF02736224
  9. Carrera, E. and Brischetto, S. (2009), "A survey with numerical assessment of classical and refined theories for the analysis of sandwich plates", Appl. Mech. Rev., 62, 1-17.
  10. Carrera, E., Brischetto, S., Cinefra, M. and Soave, M. (2010), "Refined and advanced models for multilayered plates and shells embedding functionally graded material layers", Mech. Adv. Mater. Struct., 17(8), 603-621. https://doi.org/10.1080/15376494.2010.517730
  11. Carrera, E., Brischetto, S. and Robaldo, A. (2008), "A variable kinematic model for the analysis of functionally graded material plates", AIAA J., 46(1), 194-203. https://doi.org/10.2514/1.32490
  12. Carrera, E. and Ciuffreda, A. (2005a), "Bending of composites and sandwich plates subjected to localized lateral loadings: A comparison of various theories", Compos. Struct., 68(2), 185-202. https://doi.org/10.1016/j.compstruct.2004.03.013
  13. Carrera, E. and Ciuffreda, A. (2005b), "A unified formulation to assess theories of multilayered plates for various bending problems", Compos. Struct., 69(3), 271-293. https://doi.org/10.1016/j.compstruct.2004.07.003
  14. Cheung, Y.K., Jiang, C.P. (2001), "Finite layer method in analysis of piezoelectric composite laminates", Comput. Method. Appl. Mech. Eng., 191(8-10), 879-901. https://doi.org/10.1016/S0045-7825(01)00285-7
  15. Cheung, Y.K. and Kong, J. (1993), "Approximate three-dimensional analysis of rectangular thick laminated plates: bending, vibration and buckling", Comput. Struct., 47(2), 193-199. https://doi.org/10.1016/0045-7949(93)90367-M
  16. D'Ottavio, M. and Carrera, E. (2010), "Variable-kinematics approach for linearized buckling analysis of laminated plates and shells", AIAA J., 48(9), 1987-1996. https://doi.org/10.2514/1.J050203
  17. Fan, J. and Ye, J. (1993), "Exact solutions of buckling for simply supported thick laminates", Compos. Struct., 24(1), 23-28. https://doi.org/10.1016/0263-8223(93)90051-Q
  18. Gu, H. and Chattopadhyay, A. (2000), "Three-dimensional elasticity solution for buckling of composite laminates", Compos. Struct., 50(1), 29-35. https://doi.org/10.1016/S0263-8223(00)00066-0
  19. Kim, S.E., Thai, H.T. and Lee, J. (2009a), "Buckling analysis of plates using the two variable refined plate theory", Thin Wall. Struct., 47(4), 455-462. https://doi.org/10.1016/j.tws.2008.08.002
  20. Kim, S.E., Thai, H.T. and Lee, J. (2009b), "A two variable refined plate theory for laminated composite plates", Compos. Struct., 89(2), 197-205. https://doi.org/10.1016/j.compstruct.2008.07.017
  21. Na, K.S. and Kim, J.H. (2004), "Three-dimensional thermal buckling analysis of functionally graded materials", Compos. Part B - Eng., 35(5), 429-437. https://doi.org/10.1016/j.compositesb.2003.11.013
  22. Na, K.S. and Kim, J.H. (2006), "Three-dimensional thermomechanical buckling analysis for functionally graded composite plates", Compos. Struct., 73(4), 413-422. https://doi.org/10.1016/j.compstruct.2005.02.012
  23. Nali, P., Carrera, E. and Lecca, S. (2011), "Assessments of refined theories for buckling analysis of laminated plates", Compos. Struct., 93(2), 456-464. https://doi.org/10.1016/j.compstruct.2010.08.035
  24. Noor, A.K. (1975), "Stability of multilayered composite plates", Fibre Sci. Technol., 8(2), 81-89. https://doi.org/10.1016/0015-0568(75)90005-6
  25. Noor, A.K., Burton, W.S. (1990), "Assessment of computational models for multilayered anisotropic plates", Compos. Struct., 14(3), 233-265. https://doi.org/10.1016/0263-8223(90)90050-O
  26. Noor, A.K., Burton, W.S. and Bert, C.W. (1996), "Computational model for sandwich panels and shells", Appl. Mech. Rev., 49, 155-199. https://doi.org/10.1115/1.3101923
  27. Reddy, J.N. (1993), "An evaluation of equivalent single layer and layerwise theories of composite laminates", Compos. Struct., 25, 21-35. https://doi.org/10.1016/0263-8223(93)90147-I
  28. Reddy, J.N. and Khdeir, A.A. (1989), "Buckling and vibration of laminated composite plates using various plate theories", AIAA J., 27(12),1808-1817. https://doi.org/10.2514/3.10338
  29. Reddy, J.N. and Phan, N.D. (1985), "Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory", J. Sound Vib., 98(2), 157-170. https://doi.org/10.1016/0022-460X(85)90383-9
  30. Reissner, E. (1984), "On a certain mixed variational theory and a proposed application", Int. J. Numer Meth. Eng., 20, 1366-1368. https://doi.org/10.1002/nme.1620200714
  31. Reissner, E. (1986a), "On a mixed variational theorem and on a shear deformable plate theory", Int. J. Numer Meth. Eng., 23(6), 193-198. https://doi.org/10.1002/nme.1620230203
  32. Reissner, E. (1986b), "On a certain mixed variational theorem and on laminated elastic shell theory", Proc. Euromech-Colloquium, 219, 17-27.
  33. Teo, T.M. and Liew, K.M. (1999a), "Three-dimensional elasticity solutions to some orthotropic plate problems", Int. J. Solids Struct., 36(3-4), 5301-5326. https://doi.org/10.1016/S0020-7683(98)00240-6
  34. Teo, T.M. and Liew, K.M. (1999b), "A differential quadrature procedure for three-dimensional buckling analysis of rectangular plates", Int. J. Solids Struct., 36(8), 1149-1168. https://doi.org/10.1016/S0020-7683(97)00344-2
  35. 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(7), 1738-1746. https://doi.org/10.1016/j.compstruct.2011.01.012
  36. Wu, C.P. and Chang, R.Y. (2012), "A unified formulation of RMVT-based finite cylindrical layer methods for sandwich circular hollow cylinders with an embedded FGM layer", Compos. Part B - Eng., 43(8), 3318-3333. https://doi.org/10.1016/j.compositesb.2012.01.084
  37. Wu, C.P. and Chen, C.W. (2001), "Elastic buckling of multilayered anisotropic conical shells", J. Aerospace Eng., 14(1), 29-36. https://doi.org/10.1061/(ASCE)0893-1321(2001)14:1(29)
  38. Wu, C.P. and Chen, W.Y. (1994), "Vibration and stability of laminated plates based on a local high order plate theory", J. Sound Vib., 177(4), 503-520. https://doi.org/10.1006/jsvi.1994.1448
  39. Wu, C.P., Chiu, K.H. and Wang, Y.M. (2008), "A review on the three-dimensional analytical approaches of multilayered and functionally graded piezoelectric plates and shells", Comput. Mater. Continua, 18, 93-132.
  40. Wu, C.P. and Chiu, S.J. (2001), "Thermoelastic buckling of laminated composite conical shells", J. Therm. Stresses, 24(9), 881-901. https://doi.org/10.1080/014957301750379649
  41. Wu, C.P. and Chiu, S.J. (2002), "Thermally induced dynamic instability of laminated composite conical shells", Int. J. Solids Struct., 39(11), 3001-3021. https://doi.org/10.1016/S0020-7683(02)00234-2
  42. Wu, C.P. and Li, H.Y. (2010), "The RMVT- and PVD-based finite layer methods for the three-dimensional analysis of multilayered composite and FGM plates", Compos. Struct., 92(10), 2476-2496. https://doi.org/10.1016/j.compstruct.2010.03.001
  43. Wu, Z., Chen, W. (2007), "Thermomechanical buckling of laminated composite and sandwich plates using global-local higher order theory", Int. J. Mech. Sci., 49(6), 712-721. https://doi.org/10.1016/j.ijmecsci.2006.10.006
  44. Wu, Z. and Chen, W. (2008), "An assessment of several displacement-based theories for the vibration and stability analysis of laminated composite and sandwich beams", Compos. Struct., 84(4), 337-349. https://doi.org/10.1016/j.compstruct.2007.10.005
  45. Wu, Z., Cheung, Y.K., Lo, S.H., Chen, W. (2008), "Effects of higher-order global-local shear deformations on bending, vibration and buckling of multilayered plates", Compos. Struct., 82(2), 277-289. https://doi.org/10.1016/j.compstruct.2007.01.017
  46. Zenkour, A.M. (2005), "A comprehensive analysis of functionally graded sandwich plates: Part 2-Buckling and free vibration", Int. J. Solids Struct. 42, 5243-5258. https://doi.org/10.1016/j.ijsolstr.2005.02.016
  47. Zenkour, A.M., Ai-Sheikh, K. (2001), "Buckling and free vibration of elastic plates using simple and mixed shear deformation theories", Acta Mech., 146(3-4), 183-197. https://doi.org/10.1007/BF01246732
  48. Zenkour, A.M. and Fares, M.E. (2001), "Bending, buckling and free vibration of non-homogeneous composite laminated cylindrical shells using a refined first-order theory", Compos. Part B - Eng., 32(3), 237-247. https://doi.org/10.1016/S1359-8368(00)00060-3
  49. Zhao, X., Lee, Y.Y. and Liew, K.M. (2009), "Mechanical and thermal buckling analysis of functionally graded plates", Compos. Struct., 90(2), 161-171. https://doi.org/10.1016/j.compstruct.2009.03.005

피인용 문헌

  1. A review of semi-analytical numerical methods for laminated composite and multilayered functionally graded elastic/piezoelectric plates and shells vol.147, 2016, https://doi.org/10.1016/j.compstruct.2016.03.031
  2. Assessment of higher order transverse shear deformation theories for modeling and buckling analysis of FGM plates using RBF based meshless approach pp.1573-6105, 2018, https://doi.org/10.1108/MMMS-07-2017-0069