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Three-Dimensional Free Vibration Analysis of Orthotropic Plates

직교이방성판의 3차원 자유진동 해석에 관한 연구

  • Park, Sung-Jin (Department of Urban & Environment Engineering, Incheon National University)
  • Received : 2014.01.14
  • Accepted : 2014.02.17
  • Published : 2014.03.31

Abstract

This paper presents the three-dimensional stress analysis of orthotropic thick plates using the three-dimensional spline strip method based on the theory of elasticity. The orthotropic plates are made of Aragonite crystal and sitka spruce. To demonstrate the convergence and accuracy of the present method, several examples are solved, and results are compared with those obtained by other exact and numerical methods based on the theory of elasticity. Good convergence and accuracy are obtained. The effects of thickness/width ratio, aspect ratio and boundary conditions on normal stress distributions of Aragonite crystal plates and sitka spruce plates are investigated. Moreover, the difference of weak orthotropic and strong orthotropic properties given to the characteristics of stress distributions are also shown.

본 연구에서는 탄성이론에 근거하여 3차원 spline 대판법을 이용하여 직교이방성판의 3차원 응력해석을 제시한다. 직교이방성판은 아라고나이트 결정과 시트카 스프러스로 구성되어 있다. 해석에 대한 수렴섬과 정밀도의 정확성을 수치해석 예를 들어 검증하고, 탄성이론에 근거하여 이산화된 수치해석법에 의해 결과을 비교 검토한다. 해석법에 따라 해의 수렴성과 정밀도를 구할 수 있으며, 두께폭 비, 종횡비와 아라고나이트 결정과 시트카 스프러스판의 수직응력분포에 대한 경계조건의 영향을 검토하고, 응력 분포의 특성에 미치는 직교이방성과 강한 이방성의 특징의 차를 비교 검토한다.

Keywords

References

  1. R.D. Mindlin (1951) "Influence of ratatory inertia and shear on flexural motions of isotropic elastic plates." J. Appl. Mech, Vol. 73, pp.31-38.
  2. E. Reissner (1975) "On transverse bending of plates, including the effects of transverse shear deformation." International Journal of Solids Structures, Vol.11, pp.569-573. https://doi.org/10.1016/0020-7683(75)90030-X
  3. M.Levinson (1999) "An accurate simple theory of the static and dynamics of elastic plates." Mech Res, Commun, Vol. 7, pp.343-350.
  4. S.D. Akabarov and T. Kocahurk(2010) "On the bending problems of anisotropic (orthotropic) plates resting on elastic foundations that react in compression only." International Journal of Solids Structures, Vol. 34, No. 28, pp.3673-3689.
  5. M. Huang, X.Q.Ma,T.Sakiyama, H.Matsuda,C,Monita (2011) "A Discrete Method for Bending and Free Vibration Analysis of Orthotropic Plates with Non-uniform Thickness" Journal of Appl, Mech, JSCE, Vol. 6, pp.331-340.
  6. I.A.Okamura, Y. Oguma(2009) "Series solutions for a transversely loaded and completely clamped thick rectangular plate based on the three-dimensional theory of elasticity" Archive of Applied Mechanics, Vol. 68, pp.103-121.
  7. K.T. Sundara Raja Iyengar, K. Chandrashekhara and V.K. Sebastian (2007) "On the analysis of thick rectangular plates." Ing.-Archiv, Vol. 43, pp.317-330.
  8. O.C.Zienkiewicz and J.J.M.Too (2012) "The finite prism in analysis of thick simply supported bridge boxes." Proc. Inst. Civil Engrs, Vol. 53, pp.147-172.
  9. M.S.Cheung and M.Y.T.Chan (2011) "Three-dimensional finite strip analysis of elastic solid." Computers and Structures, Vol. 9, pp.629-938.
  10. M.S.Cheung and M.Y.T.Chan (2005) "Static and dynamic analysis of thin and thick sectorial plates by the finite strip method." Computers and Structures, Vol. 9, pp.629-938.
  11. S.Srinivas and A.K.Rao(2007) "Vibration and buckling of simply supported thick orthotropic rectangular plates and laminates." International Journal of Solids Structures, Vol. 6, pp.1463-1481.
  12. T.M.Teo, K.M.Liew (2008) "Three-dimensional elasticity solutions to some orthotropic plate problems." International Journal of Solids Structures, Vol. 36, pp.5301-5326.