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Theory and refined theory of elasticity for transversely isotropic plates and a new theory for tnick plates

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Abstract

A theory of elasticity for the bending of transversely isotropic plates has been developed from the basic equations of elasticity in terms of displacements for transversely isotropic bodies, which takes into account the loads distributed over the surfaces of the plates. Based on this theory, a refined theory of plates which can satisfy three boundary conditions along each edge of the plates and a new theory of thick plates are established. The solution of the refined theory for simply supported polygonal plates has been obtained; and its numerical result is very close to the exact solution of the three-dimensional theory of elasticity. A systematic comparison with the former theories of thick plates shows that the present theory of thick plates is closest to the result of the theory of elasticity.

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References

  1. Lur'E A.I.,Three-Dimensional Problems of the Theory of Elasticity, Interscience Publisher, New York (1964).

    Google Scholar 

  2. Cheng, S., Elasticity theory of plates and a refined theory,J. Appl. Mech.,46, 3 (1979).

    Google Scholar 

  3. Wang Fei-yue, A refined theory of transversely isotropic plates,Mechanics of Shanghai, 2 (1985), (in Chinese)

  4. Zhang Hong-qing, A united theory on general solution of systems of elasticity equations,Journal of Dalian Institute of Technology, 3 (1979), 23–47 (in Chinese)

    Google Scholar 

  5. Sundara, K.T., Raja Iyegar, K. Chandrashekhara and V.K. Sebastian, On the analysis of thick rectangular plates,Ingenieur-Archiv,43, (1974), 317–330.

    Article  Google Scholar 

  6. Srinivas, S., A.K. Rao and C.V. Joga Rao, Flexure of simply supported thick homogeneous and laminated rectangular plates,Z. Angew, Math. Mech.,49 (1969), 449.

    MATH  Google Scholar 

  7. Reissner, E., The effect of transverse shear deformation on the bending of elastic plates,J. Appl. Mech.,12 (1945), 69–77.

    MathSciNet  Google Scholar 

  8. Hencky, H., Über die Berücksichtigung der Schubverrug in ebenen Platten,Ing-Arch,16 (1947), 72.

    Article  MATH  MathSciNet  Google Scholar 

  9. Mindlin, R.D., Influence of rotatory inertia and shear on flexural motions of isotropic elastic plates,J. Appl. Mech.,18 (1951) 31.

    MATH  Google Scholar 

  10. Panc, V.,Theories of Elastic Plates, Noordhoff International Publishing, the Netherlands (1975).

    Google Scholar 

  11. Vlasov, V.Z., On the equations of bending theory for plates,Izvest. Akad. Nauk SSSR Otdel. Tekh. Nauk, 12 (1957), 51 (in Russian)

    Google Scholar 

  12. Reissner, E., On transverse bending of plates including the effect of transverse shear deformation,Int. J. of Solids and Structures,11 (1975), 569–573.

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Human University, Changsha

    Zhong Zheng-hua & Luo Jian-hui

Authors
  1. Zhong Zheng-hua
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  2. Luo Jian-hui
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Communicated by Tang Ren-ji

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Zheng-hua, Z., Jian-hui, L. Theory and refined theory of elasticity for transversely isotropic plates and a new theory for tnick plates. Appl Math Mech 9, 375–389 (1988). https://doi.org/10.1007/BF02456118

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  • DOI: https://doi.org/10.1007/BF02456118

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