Acta Mechanica Solida Sinica

, Volume 30, Issue 1, pp 75–86 | Cite as

A size-dependent composite laminated skew plate model based on a new modified couple stress theory

Article

Abstract

In this study, a size-dependent composite laminated skew Mindlin plate model is proposed based on a new modified couple stress theory. This plate model can be viewed as a simplified couple stress theory in engineering mechanics. Governing equations and related boundary conditions are derived based on the principle of minimum potential energy. The Rayleigh—Ritz method is employed to obtain the numerical solutions of the center deflections of simply supported plates with different ply orientations. Numerical results show that the normalized center deflections obtained by the proposed model are always smaller than those obtained by the classical one, i.e. the present model can capture the scale effects of microstructures. Moreover, a phenomenon reveals that the ply orientation would make a significant influence on the magnitude of scale effects of composite laminated plates at micro scale. Additionally, the present model of thick skew plate can be degenerated to the model of Kirchhoff plate based on the modified couple stress theory by adopting the assumptions in Bernoulli—Euler beam and material isotropy.

Keywords

Modified couple stress theory Composite laminated plates Scale effects Ply orientation Rayleigh—Ritz method 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M.A. Haque, M.T.A Saif, Strain gradient effect in nanoscale thin films, Acta Mater. 51 (11) (2003) 3053–3061.CrossRefGoogle Scholar
  2. 2.
    Z.C. Leseman, T.J Mackin, Indentation testing of axisymmetric freestanding nanofilms using a MEMS load cell, Sens. Actuators, A 134 (1) (2007) 264–270.Google Scholar
  3. 3.
    M.A. Haque, M.T.A Saif, Microscale materials testing using MEMS actuators, J. Microelectromech. Syst. 10 (1) (2001) 146–152.CrossRefGoogle Scholar
  4. 4.
    W.M.A.J. Andrew, Role of material microstructure in plate stiffness with relevance to microcantilever sensors, J. Micromech. Microeng. 15 (5) (2005) 1060.CrossRefGoogle Scholar
  5. 5.
    J.S. Stölken, A.G Evans, A microbend test method for measuring the plasticity length scale, Acta Mater. 46 (14) (1998) 5109–5115.CrossRefGoogle Scholar
  6. 6.
    Q Ma, D.R Clarke, Size dependent hardness of silver single crystals, J. Mater. Res. 10 (04) (1995) 853–863.CrossRefGoogle Scholar
  7. 7.
    N.A. Fleck, G.M. Muller, M.F. Ashby, J.W Hutchinson, Strain gradient plasticity: theory and experiment, Acta Metall. Mater. 42 (2) (1994) 475–487.CrossRefGoogle Scholar
  8. 8.
    D.C.C. Lam, F. Yang, A.C.M. Chong, J. Wang, P Tong, Experiments and theory in strain gradient elasticity, J. Mech. Phys. Solids 51 (8) (2003) 1477–1508.CrossRefGoogle Scholar
  9. 9.
    M. Kouzeli, A Mortensen, Size dependent strengthening in particle reinforced aluminium, Acta Mater. 50 (1) (2002) 39–51.CrossRefGoogle Scholar
  10. 10.
    N.A. Fleck, J.W Hutchinson, Strain gradient plasticity, Adv. Appl. Mech. 33 (1997) 295–361.CrossRefGoogle Scholar
  11. 11.
    E. Cosserat, F Cosserat, Théorie Des Corps Déformables, Paris, 1909.Google Scholar
  12. 12.
    Toupin R.A. Elastic materials with couple-stresses. 1962;11(1):385–414.Google Scholar
  13. 13.
    Mindlin R.D., Tiersten H.F. Effects of couple-stresses in linear elasticity. 1962;11(1):415–448.Google Scholar
  14. 14.
    W. Koiter, Couple-stresses in the theory of elasticity[J], Dictionary Geotechnical Engineering/wörterbuch Geotechnik 67 (1964) 1385.MathSciNetMATHGoogle Scholar
  15. 15.
    J. Altenbach, H. Altenbach, V.A. Eremeyev, On generalized Cosserat-type theories of plates and shells: a short review and bibliography, Arch. Appl. Mech. 80 (1) (2010) 73–92.CrossRefGoogle Scholar
  16. 16.
    C. Cosserat, F. Cosserat, Théorie des corps déformables, Nature 81 (2072) (1909) 67.MATHGoogle Scholar
  17. 17.
    Neuber H. On the General Solution of Linear-Elastic Problems in Isotropic and Anisotropic Cosserat Continua. 1966, pp. 153–158.CrossRefGoogle Scholar
  18. 18.
    R.D. Mindlin, Influence of couple-stresses on stress concentrations, Exp. Mech. 3 (1) (1963) 1–7.CrossRefGoogle Scholar
  19. 19.
    F. Yang, A.C.M Chong, D.C.C Lam, P Tong, Couple stress based strain gradient theory for elasticity, Int. J. Solids Struct. 39 (10) (2002) 2731–2743.CrossRefGoogle Scholar
  20. 20.
    S.K. Park, X Gao, Bernoulli–Euler beam model based on a modified couple stress theory, J. Micromech. Microeng. 16 (11) (2006) 2355.CrossRefGoogle Scholar
  21. 21.
    H.M. Ma, X.L. Gao, J.N Reddy, A microstructure-dependent Timoshenko beam model based on a modified couple stress theory, J. Mech. Phys. Solids 56 (12) (2008) 3379–3391.MathSciNetCrossRefGoogle Scholar
  22. 22.
    G.C. Tsiatas, A new Kirchhoff plate model based on a modified couple stress theory, Int. J. Solids Struct. 46 (13) (2009) 2757–2764.CrossRefGoogle Scholar
  23. 23.
    L. Yin, Q. Qian, L. Wang, W Xia, Vibration analysis of microscale plates based on modified couple stress theory, Acta Mech. Solida Sin. 23 (5) (2010) 386–393.CrossRefGoogle Scholar
  24. 24.
    Chen W., Li X. A new modified couple stress theory for anisotropic elasticity and microscale laminated Kirchhoff plate model. 2014;84(3):323–341.Google Scholar
  25. 25.
    W. Chen, J Si, A model of composite laminated beam based on the global–local theory and new modified couple-stress theory, Compos. Struct. 103 (0) (2013) 99–107.CrossRefGoogle Scholar
  26. 26.
    C. Wanji, W. Chen, K.Y Sze, A model of composite laminated Reddy beam based on a modified couple-stress theory, Compos. Struct. 94 (8) (2012) 2599–2609.CrossRefGoogle Scholar
  27. 27.
    W. Chen, M Xu, L Li, A model of composite laminated Reddy plate based on new modified couple stress theory, Compos. Struct. 94 (7) (2012) 2143–2156.CrossRefGoogle Scholar
  28. 28.
    W. Chen, L. Li, M Xu, A modified couple stress model for bending analysis of composite laminated beams with first order shear deformation, Compos. Struct. 93 (11) (2011) 2723–2732.CrossRefGoogle Scholar
  29. 29.
    J. Bin, C Wanji, A new analytical solution of pure bending beam in couple stress elasto-plasticity: theory and applications, Int. J. Solids Struct. 47 (6) (2010) 779–785.CrossRefGoogle Scholar
  30. 30.
    C.M.C. Roque, D.S. Fidalgo, A.J.M. Ferreira, J.N Reddy, A study of a microstructure-dependent composite laminated Timoshenko beam using a modified couple stress theory and a meshless method, Compos. Struct. 96 (2013) 532–537.CrossRefGoogle Scholar
  31. 31.
    M. Mohammadabadi, A.R. Daneshmehr, M Homayounfard, Size-dependent thermal buckling analysis of micro composite laminated beams using modified couple stress theory, Int. J. Eng. Sci. 92 (2015) 47–62.MathSciNetCrossRefGoogle Scholar
  32. 32.
    M. Mohammad Abadi, A.R Daneshmehr, An investigation of modified couple stress theory in buckling analysis of micro composite laminated Euler–Bernoulli and Timoshenko beams, Int. J. Eng. Sci. 75 (2014) 40–53.MathSciNetCrossRefGoogle Scholar
  33. 33.
    J.N. Reddy, Mechanics of Laminated Composite plates: Theory and Analysis, CRC Press, Boca Raton, 1997.MATHGoogle Scholar
  34. 34.
    J.N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, 2004.Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2014

Authors and Affiliations

  1. 1.Key Laboratory of Liaoning Province for Composite Structural Analysis of Aerocraft and SimulationShenyang Aerospace UniversityShenyangChina

Personalised recommendations