Structural Engineering and Mechanics

  • 제51권5호
  • /
  • Pages.867-891
  • /
  • 2014
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  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Flexure of cross-ply laminated plates using equivalent single layer trigonometric shear deformation theory

  • Sayyad, Atteshamuddin S. (Department of Civil Engineering, SRES’s College of Engineering, University of Pune) ;
  • Ghugal, Yuwaraj M. (Department of Applied Mechanics, Government Engineering College)
  • 투고 : 2012.02.25
  • 심사 : 2014.07.20
  • 발행 : 2014.09.10
⟨ 이전 논문 다음 논문 ⟩

초록

An equivalent single layer trigonometric shear deformation theory taking into account transverse shear deformation effect as well as transverse normal strain effect is presented for static flexure of cross-ply laminated composite and sandwich plates. The inplane displacement field uses sinusoidal function in terms of thickness coordinate to include the transverse shear deformation effect. The cosine function in thickness coordinate is used in transverse displacement to include the effect of transverse normal strain. The kinematics of the present theory is much richer than those of the other higher order shear deformation theories, because if the trigonometric term (involving thickness coordinate z) is expanded in power series, the kinematics of higher order theories (which are usually obtained by power series in thickness coordinate z) are implicitly taken into account to good deal of extent. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. The closed-form solutions of simply supported cross-ply laminated composite and sandwich plates have been obtained. The results of present theory are compared with those of the classical plate theory (CPT), first order shear deformation theory (FSDT), higher order shear deformation theory (HSDT) of Reddy and exact three dimensional elasticity theory wherever applicable. The results predicted by present theory are in good agreement with those of higher order shear deformation theory and the elasticity theory.

키워드

참고문헌

  1. Akavci, S.S. (2007), "Buckling and free vibration analysis of symmetric and antisymmetric laminated composite plates on an elastic foundation", J. Reinf. Plast. Compos., 26, 1907-1919. https://doi.org/10.1177/0731684407081766
  2. Brischetto, S., Carrera, E. and Demasi, L. (2009), "Improved response of unsymmetrically laminated sandwich plates by using zig-zag functions", J. Sandw. Struct. Mater., 11, 257-267. https://doi.org/10.1177/1099636208099379
  3. Chalak, H.D., Chakrabarti, A., Iqbal M.A. and Sheikh, A.H. (2012), "An improved C0 FE model for the analysis of laminated sandwich plate with soft core", Finite Elem. Anal. Des., 56, 20-31. https://doi.org/10.1016/j.finel.2012.02.005
  4. Dehkordi, M.B., Cinefra, M., Khalili, S.M.R. and Carrera, E. (2013), "Mixed LW/ESL models for the analysis of sandwich plates with composite faces", Compos. Struct., 98, 330-339. https://doi.org/10.1016/j.compstruct.2012.11.016
  5. Doong, J.L., Lee, C. and Fung, C.T. (1991), "Vibration and stability of laminated plates based on modified plate theory", J. Sound Vib., 151, 193-30. https://doi.org/10.1016/0022-460X(91)90851-A
  6. Ghugal, Y.M. and Shimpi, R.P. (2002), "A review of refined shear deformation theories for isotropic and anisotropic laminated plates", J. Reinf. Plast. Compos., 21, 775-813. https://doi.org/10.1177/073168402128988481
  7. Ghugal, Y.M. and Kulkarni, S.K. (2011), "Thermal stress analysis of cross-ply laminated plates using refined shear deformation theory", J. Exp. App. Mech., 2(1), 47-66.
  8. Ghugal, Y.M. and Sayyad, A.S. (2010), "A flexure of thick isotropic plate using trigonometric shear deformation theory", J. Solid Mech., 2(1), 79-90.
  9. Ghugal, Y.M. and Sayyad, A.S. (2011a), "Free vibration of thick isotropic plates using trigonometric shear deformation theory", J. Solid Mech., 3(2), 172-182.
  10. Ghugal, Y.M. and Sayyad, A.S. (2011b), "Free vibration of thick orthotropic plates using trigonometric shear deformation theory", Lat. Am. J. Solid. Struct., 8, 229-243. https://doi.org/10.1590/S1679-78252011000300002
  11. Ghugal, Y.M. and Sayyad, A.S. (2013a), "Static flexure of thick orthotropic plates using trigonometric shear deformation theory", J. Struct. Eng., 39(5), 512-521.
  12. Ghugal, Y.M. and Sayyad, A.S. (2013b), "Stress analysis of thick laminated plates using trigonometric shear deformation theory", Int. J. Appl. Mech., 5(1), 1-23.
  13. Grover, N., Maiti, D.K. and Singh, B.N. (2013), "A new inverse hyperbolic shear deformation theory for static and buckling analysis of laminated composite and sandwich plates", Compos. Struct., 95, 667-675. https://doi.org/10.1016/j.compstruct.2012.08.012
  14. Jones, R.M. (1975), Mechanics of Composite Materials, McGraw Hill Kogakusha, Ltd, Tokyo.
  15. Kant, T. and Swaminathan, K. (2002), "Analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory", Compos. Struct., 56, 329-344. https://doi.org/10.1016/S0263-8223(02)00017-X
  16. Kapuria, S. and Nath, J.K. (2013), "On the accuracy of recent global-local theories for bending and vibration of laminated plates", Compos. Struct., 95, 163-172. https://doi.org/10.1016/j.compstruct.2012.06.018
  17. Karama, M., Afaq, K.S. and Mistou, S. (2009), "A new theory for laminated composite plates", Proc. IMechE Part L: J. Materials: Des. Appl., 223, 53-62.
  18. Kreja, I. (2011), "A literature review on computational models for laminated composite and sandwich panels", Centr. Eur. J. Eng., 1(1), 59-80 https://doi.org/10.2478/s13531-011-0005-x
  19. Krishna Murty, A.V. (1986), "Towards a consistent plate theory", AIAA J., 24, 1047-1048. https://doi.org/10.2514/3.9388
  20. Krishna Murty, A.V. (1987), "Theoretical modeling of laminated composite plates", Sadhana, 11(3/4), 357-365. https://doi.org/10.1007/BF02811362
  21. Leung, A.Y.T., Niu, J., Lim, C.W. and Song, K. (2003), "A new unconstrained third-order plate theory for Navier solutions of symmetrically laminated plates", Compos. Struct., 81, 2539-2548. https://doi.org/10.1016/S0045-7949(03)00290-6
  22. Levy, M. (1877), "Memoire sur la theorie des plaques elastique planes", J. des Math. Pures et Appl., 3, 219-306.
  23. Lo, K.H., Christensen, R.M. and Wu, E.M. (1977a), "A high-order theory of plate deformation, part-1: homogeneous plates", ASME J. Appl. Mech., 44, 663-668. https://doi.org/10.1115/1.3424154
  24. Lo, K.H., Christensen, R.M. and Wu, E.M. (1977b), "A high-order theory of plate deformation, part-2: laminated plates", ASME J. Appl. Mech., 44, 669-676. https://doi.org/10.1115/1.3424155
  25. Mantari, J.L., Oktem, A.S. and Soares, C.G. (2012), "A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates", Int. J. Solids and Struct., 49, 43-53. https://doi.org/10.1016/j.ijsolstr.2011.09.008
  26. Metin, A. (2006), "Comparison of various shear deformation theories for bending, buckling, and vibration of rectangular symmetric cross-ply plate with simply supported edges", J. Compos. Mater., 40, 2143-2155. https://doi.org/10.1177/0021998306062313
  27. Metin, A. (2009), "A new shear deformation theory for laminated composite plates", Compos. Struct., 89, 94-101. https://doi.org/10.1016/j.compstruct.2008.07.008
  28. Mindlin, R.D. (1951), "Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates", ASME J. Appl. Mech., 18, 31-38.
  29. Nik, A.M.N and Tahani, M. (2010), "Free vibration analysis of moderately thick rectangular laminated composite plates with arbitrary boundary conditions", Struct. Eng. Mech., 35(2), 217-240. https://doi.org/10.12989/sem.2010.35.2.217
  30. Noor, A.K. and Burton, W.S. (1989), "Assessment of shear deformation theories for multilayered composite plates", Appl. Mech. Rev., 42, 1-13. https://doi.org/10.1115/1.3152418
  31. Pagano, N.J. (1970), "Exact solutions for bidirectional composites and sandwich plates", J. Compos. Mater., 4, 20-34. https://doi.org/10.1177/002199837000400102
  32. Pandit, M.K., Sheikh, A.H. and Singh, B.N. (2010), "Analysis of laminated sandwich plates based on an improved higher order zigzag theory", J. Sandw. Struct. Mater., 12, 307-326. https://doi.org/10.1177/1099636209104517
  33. Reddy, J.N. (1984), "A simple higher order theory for laminated composite plates", ASME J. Appl. Mech., 51, 745-752. https://doi.org/10.1115/1.3167719
  34. Reddy, J.N. and Phan, N.D. (1985), "Stability and vibration of isotropic, orthotropic and laminated plates according to higher order shear deformation theory", J. Sound Vib., 98, 157-170. https://doi.org/10.1016/0022-460X(85)90383-9
  35. Reissner, E. (1944), "On the theory of bending of elastic plates", J. Math. Phy., 23, 184-191. https://doi.org/10.1002/sapm1944231184
  36. Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", ASME J. Appl. Mech., 12, 69-77.
  37. Sahoo, R. and Singh, B.N. (2013a), "A new inverse hyperbolic zigzag theory for the static analysis of laminated composite and sandwich plates", Compos. Struct., 105, 385-397. https://doi.org/10.1016/j.compstruct.2013.05.043
  38. Sahoo, R. and Singh, B.N. (2013a), "A new shear deformation theory for the static analysis of laminated composite and sandwich plates", Int. J. Mech. Sci., 75, 324-336. https://doi.org/10.1016/j.ijmecsci.2013.08.002
  39. Savithri, S. and Varadan, T.K. (1992), "A simple higher order theory for homogeneous plates", Mech. Res. Comm., 19, 65- 71. https://doi.org/10.1016/0093-6413(92)90014-2
  40. Sayyad, A.S. and Ghugal, Y.M. (2011), "Effect of transverse shear and transverse normal strain on bending analysis of cross-ply laminated beams", Int. J. Appl. Math. Mech., 7(12), 85-118.
  41. Sayyad, A.S. and Ghugal, Y.M. (2014a), "A new shear and normal deformation theory for isotropic, transversely isotropic, laminated composite and sandwich plates", Int. J. Mech. Mater. Des., DOI 10.1007/s10999-014-9244-3.
  42. Sayyad, A.S. and Ghugal, Y.M. (2014b), "On the buckling of isotropic, transversely isotropic and laminated composite rectangular plates", Int. J. Struct. Stab. Dyn., 14(6), 1-32. https://doi.org/10.1007/s13296-014-1001-9
  43. Sayyad, A.S. and Ghugal, Y.M. (2013), "Effect of stress concentration on laminated plates", Cambridge J. Mech., 29, 241-252. https://doi.org/10.1017/jmech.2012.131
  44. Shimpi, R.P. and Ghugal, Y.M. (2000), "A layerwise trigonometric shear deformation theory for two layered cross-ply laminated Plates", Mech. Adv. Mater. Struct., 7, 331-353. https://doi.org/10.1080/10759410050201690
  45. Shimpi, R.P. and Ainapure, A.V. (2004), "Free vibration of two-layered cross-ply laminated plates using layer-wise trigonometric shear deformation theory", J. Reinf. Plast. Compos., 23(4), 389-405. https://doi.org/10.1177/0731684404031893
  46. Soldatos, K.P. (1988), "On certain refined theories for plate bending", ASME J. Appl. Mech., 55, 994-995. https://doi.org/10.1115/1.3173757
  47. Stein, M. (1986), "Nonlinear theory for plates and shells including effect of transverse shearing", AIAA J., 24, 1537-1544. https://doi.org/10.2514/3.9477
  48. Thai, N.D., D'Ottavio, M. and Caron, J.F. (2013), "Bending analysis of laminated and sandwich plates using a layer-wise stress model", Compos. Struct., 96, 135-142. https://doi.org/10.1016/j.compstruct.2012.08.032
  49. Todhunter, I. and Pearson, K. (1893), A History of the Theory of Elasticity, Vol-II, Part-I, and Vol-II, Part-II, Dover Publications, Inc., New York.
  50. Wanji, C. and Zhen, W. (2008), "A selective review on recent development of displacement-based laminated plate theories", Rec. Pat. Mech. Eng., 1, 29-44. https://doi.org/10.2174/2212797610801010029
  51. Zhen, W. and Wanji, C. (2010), "A $C^0$-type higher-order theory for bending analysis of laminated composite and sandwich plates", Compos. Struct., 92, 653-661. https://doi.org/10.1016/j.compstruct.2009.09.032

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