SEARCH

SEARCH BY CITATION

References

  • [1]
    J. Aboudi, A continuum theory for fiber-reinforced elastic-visoplastic composites, Int. J. Eng. Sci. 20(5), 605621 (1982).
  • [2]
    J. Aboudi, Micromechanical analysis of composites by the method of cells, Appl. Mech. Rev. 42(7), 193221 (1989).
  • [3]
    M.L. Accorsi and S. Nemat-Nasser, Bounds on the overall elastic and instantaneous elastoplastic moduli of periodic composites, Mechanics of Materials 5(3), 209220 (1986).
  • [4]
    A. Atilgan and D. Hodges, On the strain energy of laminated composite plates, Int. J. Solids Struct. 29, 25272543 (1992).
  • [5]
    B. Banerjee and D. Adams, On predicting the effective elastic properties of polymer bonded explosive using the recursive cell method, Int. J. Solids Struct. 41(2), 481509 (2004).
  • [6]
    A. Bensoussan, J. Lions, and G. Papanicolaou, Asymptotic Analysis for Periodic Structures (North-Holland, Amsterdam, 1978).
  • [7]
    V. Berdichevsky, Variational-asymptotic method of constructing a theory of shells, PMM 43(4), 664687 (1979).
  • [8]
    N. Buannic and P. Cartraud, Higher-order effective modeling of periodic heterogeneous beams. I. Asymptotic expansion method, Int. J. Solids Struct. 38, 71397161 (2001).
  • [9]
    D. Caillerie, Thin elastic and periodic plates, Math. Methods Appl. Sci. 6, 159191 (1984).
  • [10]
    D. Danielson and D. Hodges, Nonlinear beam kinematics by decomposition of the rotation tensor, J. Appl. Mech. 54, 258262 (1987).
  • [11]
    G. Dvorak and Y. Bahei-El-Din, Elastic-plastic behavior of fibrous composites, J. Mech. Phys. Solids 27, 5172 (1979).
  • [12]
    Z. Hashin and S. Shtrikman, A variational approach to the theory of the elastic behaviour of polycrystals, J. Mech. Phys. Solids 10, 343352 (1962).
  • [13]
    R. Hill, Theory of mechanical properties of fibre-strengthened materials III. Self-consistent model, J. Mech. Phys. Solids 13, 189198 (1965).
  • [14]
    D. Hodges, A. Atilgan, and D. Danielson, A geometrically nonlinear theory of elastic plates, J. Appl. Mech. 60(1), 109116 (1993).
  • [15]
    S.J. Hollister and N. Kikuchi, A comparison of homogenization and standard mechanics analyses for periodic porous composites, Comput. Mech. 10(2), 7395 (1992).
  • [16]
    A.L. Kalamkarov, I.V. Andrianov, and V.V. Danishevs'kyy, Asymptotic homogenization of composite materials and structures, Appl. Mech. Rev. 62, 030802 (2009).
  • [17]
    A. Kalamkarov, Composite and Reinforced Elements of Construction (Wiley, Chichester, 1992).
  • [18]
    A. Kalamkarov and A. Kolpakov, Analysis, Design and Optimization of Composite Structures (Wiley, Chichester, 1997).
  • [19]
    P. Kanouté, D. Boso, J.L. Chaboche, and B. Schrefler, Multiscale methods for composites: A review, Arch. Comput. Methods Eng. 16, 3175 (2009).
  • [20]
    R. Kohn and M. Vogelius, A new model for thin plates with rapidly varying thickness, Int. J. Solids Struct. 20(4), 333350 (1984).
  • [21]
    C.Y. Lee and W. Yu, Homogenization and dimensional reduction of composite plates with in-plane heterogeneity, Int. J. Solids Struct. 48(10), 14741484 (2011).
  • [22]
    T. Lewiński, Effective models of composite periodic plates – part i. asymptotic solution, Int. J. Solids Struct. 27(8), 11551172 (1991).
  • [23]
    A. LokTat-Seng and Q.H. Cheng, Elastic stiffness properties and behavior of truss-core sandwich panel, J. Struct. Eng. 126(5), 552559 (2000).
  • [24]
    G. Milton, Theory of Composites (Cambridge University Press, 2001).
  • [25]
    H. Murakami and A. Toledano, A higer-order mixture homogenization of bi-laminated composites, J. Appl. Mech. 57, 388396 (1990).
  • [26]
    M. Paley and J. Aboudi, Micromechanical analysis of composites by the generalized cells model, Mech. Mater. 14, 127139 (1992).
  • [27]
    J. Romanoff and P. Varsta, Bending response of web-core sandwich plates, Compos. Struct. 81, 292302 (2007).
  • [28]
    E. Sanchez-Palencia, Non-homogeneous Media and Vibration Theory (Springer, Berlin, 1980).
  • [29]
    A. Sharma, B.V. Sankar, and R.T. Haftka, Homogenization of Plates with Microstructure and Application to Corrugated Core Sandwich Panels, in: Proceedings of the 51st AIAA/ASME/ASCE /AHS/ASC Structures, Structural Dynamics, and Materials Conference, Apr. 12–15, 2010 (AIAA, Orlando, Florida, 2010).
  • [30]
    C. Sun and R. Vaidya, Prediction of composite properties from a representative volume element, Compos. Sci. Technol. 56, 171179 (1996).
  • [31]
    V. Sutyrin, Derivation of plate theory accounting asymptotically correct shear deformation, J. Appl .Mech. 64, 905915 (1997).
  • [32]
    T. Williams, A two-dimensional, higher-oder, elasticity-based micromechanics model, Int. J. Solids Struct. 42, 10091038 (2005).
  • [33]
    W. Yu, Variational Asymptotic Modeling of Composite Dimensionally Reducible Structures, PhD thesis (Aerospace Engineering Georgia Institute of Technology, Georgia, 2002).
  • [34]
    W. Yu, A Variational-Asymptotic Cell Method for Periodically Heterogeneous Materials, in: Proceedings of the 2005 ASME International Mechanical Engineering Congress and Exposition, Nov. 5–11, 2005 (ASME, Orlando, Florida, 2005).
  • [35]
    W. Yu, D. Hodges, and V. Volovoi, Asymptotic construction of Reissner-like models for composite plates with accurate strain recovery, Int. J. Solids Struct. 39(17), 51855203 (2002).
  • [36]
    W. Yu and T. Tang, Variational asymptotic method for unit cell homogenization of periodically heterogeneous materials, Int. J. Solids Struct. 44, 37383755 (2007).