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.

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

• Publish Date: 1988-04-15
• 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.
•  [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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