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横观各向同性板的弹性理论和弹性改进理论及一种新的厚板理论

钟正华 罗建辉

钟正华, 罗建辉. 横观各向同性板的弹性理论和弹性改进理论及一种新的厚板理论[J]. 应用数学和力学, 1988, 9(4): 341-354.
引用本文: 钟正华, 罗建辉. 横观各向同性板的弹性理论和弹性改进理论及一种新的厚板理论[J]. 应用数学和力学, 1988, 9(4): 341-354.
Zhong Zheng-hua, Luo Jian-hui. Theory and Refined Theory of Elasticity for Transversely Isotropic Plates and a New Theory for Thick Plates[J]. Applied Mathematics and Mechanics, 1988, 9(4): 341-354.
Citation: Zhong Zheng-hua, Luo Jian-hui. Theory and Refined Theory of Elasticity for Transversely Isotropic Plates and a New Theory for Thick Plates[J]. Applied Mathematics and Mechanics, 1988, 9(4): 341-354.

横观各向同性板的弹性理论和弹性改进理论及一种新的厚板理论

Theory and Refined Theory of Elasticity for Transversely Isotropic Plates and a New Theory for Thick Plates

  • 摘要: 本文从横观各向同性体弹性力学位移形式的基本方程出发,考虑板面承受横向荷载,建立了横观各向同性板弯曲的弹性理论.并由此建立了一个在板的每边能满足三个边界条件的弹性改进理论和一种新的厚板理论.文中求得了周边简支多边形板的弹性改进理论解,数值结果与三维弹性理论精确解的结果非常接近.新的厚板理论和以往的中厚板理论的系统比较表明,我们提出的厚板理论最靠近弹性理论的结果.
  • [1] Lur'E,A.I.,Three-Dimensional Problems of the Theory of Elasticity,Interscience Publisher,New York (1964).
    [2] Cheng,S.,Elasticity theory of plates and a refined theory,J.Appl.Mech.,46,3 (1979).
    [3] 王飞跃,横观各向同性板的弹性精化理论,上海力学,6, 2 (1985), 10-21.
    [4] 张鸿庆,弹性力学方程组一般解的统一理论,大连工学院学报,3 (1979), 23-47.
    [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.
    [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.
    [7] Reissner,E.,The effect of transverse shear deformation on the bending of elastic plates,J.Appl.Mech.,12(1945),69-77.
    [8] Hencky,H.,Über die Bercksichtigung der Schubverrug in ebenen Platten,Ing-Arch,16 (1947),72.
    [9] Mindlin,R.D.,Influence of rotatory inertia and shear on flexural motions of isotropic elastic plates,J.Appl.Mech.,18 (1951),31.
    [10] Panc,V.,Theories of Elastic Plates,Noordhoff International Publishing,the Netherlands (1975).
    [11] Vlasov,V.Z.,On the equations of bending theory for plates,Izvest.Akad.Nauk SSSR Otdel.Tekh.Nauk,12 (1957),51.(in Russian).
    [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.
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出版历程
  • 收稿日期:  1986-11-17
  • 刊出日期:  1988-04-15

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