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A new shear and normal deformation theory for isotropic, transversely isotropic, laminated composite and sandwich plates

  • Atteshamuddin Shamshuddin Sayyad
  • Yuwaraj Marotrao Ghugal
Article

Abstract

In the present study, a sinusoidal shear and normal deformation theory taking into account effects of transverse shear as well as transverse normal is used to develop the analytical solution for the bidirectional bending analysis of isotropic, transversely isotropic, laminated composite and sandwich rectangular plates. The theory accounts for adequate distribution of the transverse shear strains through the plate thickness and traction free boundary conditions on the plate boundary surface, thus a shear correction factor is not required. The displacement field uses sinusoidal function in terms of thickness coordinate to include the effect of transverse shear and the cosine function in terms of thickness coordinate is used in transverse displacement to include the effect of transverse normal. The kinematics of the present theory is much richer than those of the other higher order shear deformation theories, because if the trigonometric term is expanded in power series, the kinematics of higher order theories 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 Navier solution for simply supported laminated composite plates has been developed. Results obtained for displacements and stresses of simply supported rectangular plates are compared with those of other refined theories and exact elasticity solution wherever applicable.

Keywords

Bidirectional bending Isotropic Transversely isotropic Composite plate Sandwich plate Transverse shear Transverse normal 

References

  1. Altenbach, H.: Mechanics of advanced materials for lightweight structures. J. Mech. Eng. Sci. 225, 2481–2496 (2011)CrossRefGoogle Scholar
  2. Aydogdu, M.: A new shear deformation theory for laminated composite plates. Compos. Struct. 89, 94–101 (2009)CrossRefGoogle Scholar
  3. Carrera, E.: Historical review of zig-zag theories for multilayered plates and shells. Appl. Mech. Rev. 56(3), 287–308 (2003)CrossRefGoogle Scholar
  4. Carrera, E., Buttner, A., Nalif, J.P., Wallmerperger, T., Kroplin, B.: A comparison of various two-dimensional assumptions in finite element analysis of multilayered plates. Int. J. Comput. Methods Eng. Sci. Mech. 11, 313–327 (2010)CrossRefMATHMathSciNetGoogle Scholar
  5. Cetkovic, M., Vuksanovic, D.: Bending, free vibrations and buckling of laminated composite and sandwich plates using a layerwise displacement model. Compos. Struct. 88, 219–227 (2009)CrossRefGoogle Scholar
  6. Civalek, O.: Analysis of thick rectangular plates with symmetric cross-ply laminates based on first-order shear deformation theory. J. Compos. Mater. 42, 2853–2867 (2008)CrossRefGoogle Scholar
  7. Daouadji, T.H., Henni, A.H., Tounsi, A., Abbes, A.B.E.: A new hyperbolic shear deformation theory for bending analysis of functionally graded plates. Model. Simul. Eng. 10, 1–10 (2012). doi: 10.1155/2012/159806 CrossRefGoogle Scholar
  8. Demasi, L.: 13 hierarchy plate theories for thick and thin composite plates: the generalized unified formulation. Compos. Struct. 84, 256–270 (2008)CrossRefGoogle Scholar
  9. Demasi, L.: 16 mixed plate theories based on the generalized unified formulation. Part I: governing equations. Compos. Struct. 87, 1–11 (2009a)CrossRefGoogle Scholar
  10. Demasi, L.: 16 mixed plate theories based on the generalized unified formulation. Part II: layerwise theories. Compos. Struct. 87, 12–22 (2009b)CrossRefGoogle Scholar
  11. Demasi, L.: 16 mixed plate theories based on the generalized unified formulation. Part III: advanced mixed high order shear deformation theories. Compos. Struct. 87, 183–194 (2009c)CrossRefGoogle Scholar
  12. Demasi, L.: 16 mixed plate theories based on the generalized unified formulation. Part IV: zig-zag theories. Compos. Struct. 87, 195–205 (2009d)CrossRefGoogle Scholar
  13. Demasi, L.: 16 mixed plate theories based on the generalized unified formulation. Part V: results. Compos. Struct. 88, 1–16 (2009e)CrossRefGoogle Scholar
  14. Demasi, L.: Three-dimensional closed form solutions and exact thin plate theories for isotropic plates. Compos. Struct. 80, 183–195 (2007)CrossRefGoogle Scholar
  15. Fares, M.E., Elmarghany, M.Kh.: A refined zigzag nonlinear first-order shear deformation theory of composite laminated plates. Compos. Struct. 82, 71–83 (2008)CrossRefGoogle Scholar
  16. Ferreira, A.J.M., Castro, L.M.S., Bertoluzza, S.: A high order collocation method for the static and vibration analysis of composite plates using a first-order theory. Compos. Struct. 89, 424–432 (2009)CrossRefGoogle Scholar
  17. Ferreira, A.J.M., Roque, C.M.C., Carrera, E., Cinefra, M., Polit, O.: Two higher order Zig-Zag theories for the accurate analysis of bending, vibration and buckling response of laminated plates by radial basis functions collocation and a unified formulation. J. Compos. Mater. 45(24), 2523–2536 (2011)CrossRefGoogle Scholar
  18. Ghugal, Y.M., Shimpi, R.P.: A review of refined shear deformation theories for isotropic and anisotropic laminated plates. J. Reinf. Plast. Compos. 21, 775–813 (2002)CrossRefGoogle Scholar
  19. Ghugal, Y.M., Sayyad, A.S.: Stress analysis of thick laminated plates using trigonometric shear deformation theory. Int. J. Appl. Mech. 5(1), 1–23 (2013)CrossRefGoogle Scholar
  20. Grover, N., Maiti, D.K., Singh, B.N.: A new inverse hyperbolic shear deformation theory for static and buckling analysis of laminated composite and sandwich plates. Compos. Struct. 95, 667–675 (2013)CrossRefGoogle Scholar
  21. Herakovich, C.T.: Mechanics of composites: a historical review. Mech. Res. Commun. 41, 1–20 (2012)CrossRefGoogle Scholar
  22. Karama, M., Afaq, K.S., Mistou, S.: Mechanical behavior of laminated composite beam by the new multilayered laminated composite structures model with transverse shear stress continuity. Int. J. Solids Struct. 40, 1525–1546 (2003)CrossRefMATHGoogle Scholar
  23. Karama, M., Afaq, K.S., Mistou, S.: A new theory for laminated composite plates. Proc. Inst. Mech. Eng. L 223, 53–62 (2009)CrossRefGoogle Scholar
  24. Kim, S.E., Thai, H.T., Lee, J.: A two variable refined plate theory for laminated composite plates. Compos. Struct. 89, 197–205 (2009)CrossRefGoogle Scholar
  25. Kreja, I.: A literature review on computational models for laminated composite and sandwich panels. Cent. Eur. J. Eng. 1(1), 59–80 (2011)CrossRefGoogle Scholar
  26. Kumari, P., Nath, J.K., Kapuria, S., Dumir, P.C.: Efficient global zigzag theory for elastic laminated plates. J. Reinf. Plast. Compos. 28, 1025–1047 (2009)CrossRefGoogle Scholar
  27. Liu, G.R., Zhao, X., Dai, K.Y., Zhong, Z.H., Li, G.Y., Han, X.: Static and free vibration analysis of laminated composite plates using the conforming radial point interpolation method. Compos. Sci. Technol. 68, 354–366 (2008)CrossRefGoogle Scholar
  28. Mallikarjuna, Kant, T.: A critical review and some results of recently developed refined theories of fiber-reinforced laminated composites and sandwiches. Compos. Struct. 23, 293–312 (1993)CrossRefGoogle Scholar
  29. Mantari, J.L., Oktem, A.S., Soares, C.G.: Static and dynamic analysis of laminated composite and sandwich plates and shells by using a new higher-order shear deformation theory. Compos. Struct. 94, 37–49 (2011)CrossRefGoogle Scholar
  30. Mindlin, R.D.: Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates. ASME J. Appl. Mech. 18, 31–38 (1951)MATHGoogle Scholar
  31. Meiche, N.E., Tounsi, A., Ziane, N., Mechab, I., Bedia, E.A.A.: A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate. Int. J. Mech. Sci. 53, 237–247 (2011)CrossRefGoogle Scholar
  32. Mouritz, A.P., Gellert, E., Burchill, P., Challis, K.: Review of advanced composite structures for naval ships and submarines. Compos. Struct. 53, 21–41 (2001)CrossRefGoogle Scholar
  33. Moleiro, F., Mota Soares, C.M., Mota Soares, C.A., Reddy, J.N.: Layerwise mixed least-squares finite element models for static and free vibration analysis of multilayered composite plates. Compos. Struct. 92, 2328–2338 (2010)CrossRefGoogle Scholar
  34. Moleiro, F., Mota Soares, C.M., Mota Soares, C.A., Reddy, J.N.: Mixed least-squares finite element model for the static analysis of laminated composite plates. Comput. Struct. 86, 826–838 (2008)CrossRefGoogle Scholar
  35. Nik, A.M.N., Tahani, M.: Bending analysis of laminated composite plates with arbitrary boundary conditions. J. Solid Mech. 1, 1–13 (2009)Google Scholar
  36. Noor, A.K., Burton, W.S.: Refinement of higher-order laminated plate theories. Appl. Mech. Rev. 42, 1–13 (1989)CrossRefGoogle Scholar
  37. Oktem, A.S., Chaudhuri, R.A.: Levy type analysis of cross-ply plates based on higher-order theory. Compos. Struct. 78, 243–253 (2007)CrossRefGoogle Scholar
  38. Pandit, M.K., Sheikh, A.H., Singh, B.N.: Analysis of laminated sandwich plates based on an improved higher order zigzag theory. J. Sandw. Struct. Mat. 12, 307–326 (2010)CrossRefGoogle Scholar
  39. Pagano, N.J.: Exact solutions for bidirectional composites and sandwich plates. J. Compos. Mater. 4, 20–34 (1970)Google Scholar
  40. Reddy, J.N.: A simple higher order theory for laminated composite plates. ASME J. Appl. Mech. 51, 745–752 (1984)CrossRefMATHGoogle Scholar
  41. Reddy, J.N., Arciniega, R.A.: Shear deformation plate and shell theories: from Stavsky to present. Mech. Adv. Mater. Struct. 11(6), 535–582 (2004)CrossRefGoogle Scholar
  42. Reissner, E.: The effect of transverse shear deformation on the bending of elastic plates. ASME J. Appl. Mech. 12, 69–77 (1945)MathSciNetGoogle Scholar
  43. Reissner, E.: Reflection on the theory of elastic plates. Appl. Mech. Rev. 38, 1453–1464 (1985)CrossRefGoogle Scholar
  44. Sayyad, A.S., Ghugal, Y.M.: Bending and free vibration analysis of thick isotropic plates by using exponential shear deformation theory. Appl. Comput. Mech. 6(1), 65–82 (2012a)Google Scholar
  45. Sayyad, A.S., Ghugal, Y.M.: Buckling analysis of thick isotropic plates by using exponential shear deformation theory. Appl. Comput. Mech. 6(2), 185–196 (2012b)Google Scholar
  46. Sayyad, A.S.: Flexure of thick orthotropic plates by exponential shear deformation theory. Lat. Am. J. Solids Struct. 10, 473–490 (2013)CrossRefGoogle Scholar
  47. Saidi, A.R., Atashipour, S.R., Keshavarzi, H.: Bending analysis of thick laminated rectangular plates using a boundary layer function. Proc. Inst. Mech. Eng. C 224, 2073–2081 (2010)CrossRefGoogle Scholar
  48. Shooshtari, A., Razavi, S.: A closed form solution for linear and nonlinear free vibrations of composite and fiber metal laminated rectangular plates. Compos. Struct. 92, 2663–2675 (2010)CrossRefGoogle Scholar
  49. Shi, G.: A new simple third-order shear deformation theory of plates. Int. J. Solids Struct. 44, 4399–4417 (2007)CrossRefMATHGoogle Scholar
  50. Sturzenbecher, R., Hofstetter, K.: Bending of cross-ply laminated composites: an accurate and efficient plate theory based upon models of Lekhnitskii and Ren. Compos. Struct. 93, 1078–1088 (2011)CrossRefGoogle Scholar
  51. Soldatos, K.P.: A transverse shear deformation theory for homogeneous monoclinic plates. Acta Mech. 94, 195–220 (1992)CrossRefMATHMathSciNetGoogle Scholar
  52. Valek, O.C., Baltacioglu, A.K.: Three-dimensional elasticity analysis of rectangular composite plates. J. Compos. Mater. 44, 2049–2066 (2010)CrossRefGoogle Scholar
  53. Versino, D., Gherlone, M., Mattone, M., Sciuva, M.D., Tessler, A.: C0 triangular elements based on the Refined Zigzag Theory for multilayer composite and sandwich plates. Compos. B 44, 218–230 (2013)CrossRefGoogle Scholar
  54. Wanji, C., Zhen, W.: A selective review on recent development of displacement-based laminated plate theories. Recent Pat. Mech. Eng. 1, 29–44 (2008)CrossRefGoogle Scholar
  55. Xiang, S., Kang, G.W.: A nth-order shear deformation theory for the bending analysis on the functionally graded plates. Eur. J. Mech. A 37, 336–343 (2013)CrossRefMathSciNetGoogle Scholar
  56. Zenkour, A.M.: Three-dimensional elasticity solution for uniformly loaded cross-ply laminates and sandwich plates. J. Sandw. Struct. Mater. 9, 213–238 (2007)CrossRefGoogle Scholar
  57. Zenkour, A.M.: The effect of transverse shear and normal deformations on the thermo-mechanical bending of functionally graded sandwich plates. Int. J. Appl. Mech. 1(4), 667–707 (2009)CrossRefMathSciNetGoogle Scholar
  58. Zhen, W., Cheung, Y.K., Lo, S.H., Wanji, C.: Effects of higher-order global–local shear deformations on bending, vibration and buckling of multilayered plates. Compos. Struct. 82, 277–289 (2008)CrossRefGoogle Scholar
  59. Zhong, Y., Li, R., Liu, Y., Tian, B.: On new symplectic approach for exact bending solutions of moderately thick rectangular plates with two opposite edges simply supported. Int. J. Solids Struct. 46, 2506–2513 (2009)CrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Atteshamuddin Shamshuddin Sayyad
    • 1
  • Yuwaraj Marotrao Ghugal
    • 2
  1. 1.Department of Civil EngineeringSRES’s College of EngineeringKopargaonIndia
  2. 2.Department of Applied MechanicsGovernment Engineering CollegeKaradIndia

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