关于弹性板弯曲变形的Reissner理论
On the Reissner Theory of Bending of an Elastic Plate
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摘要: 本文根据不完全广义余能原理重新推导了Reissner方程,使应力函数ψ以拉格朗日乘子的方式从变分中自然引出,同时明确了Reissner方程的解的结构.在此基础上提出了一个简化理论,它只需求解一个类似于经典薄板理论的四阶方程,即可得到计及剪力对弯曲变形影响的令人满意的结果.Abstract: Reissner equations of elastic plate are derived on the bases of incomplete generalized variational principle of complementary energy.The stress function ψ is obtained from the variational calculation in the form of Lagrange multiplier.The structure of solution of Reissner equations is thus determined.On the bases of these discussions,we obtained a simplified theory,in which the equations of equilibrium involving the shearing influence can be reduced into a fourth order differential equation similar to those of classic plate theory.
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[1] Reissner,E.,On the theory of bending of elastic plates,J.Math,Phys,23,184(1944). [2] Reissner,E.,The effect of transverse shear deformation on the bending of elastic plates,J.Appl.Mech,12,A69(1945). [3] Reissner,E.,On bending of elastic plates,Quart,Appl.Math,55(I947). [4] Salerno V.L.,and Goldberg,M.A.,Effect of shear deformations on the bending of rectangular plates,J.Appl.Mech.27,54(1960). [5] Koeller,R.C.,and Essenburg,F.,Shear deformation in rectangular plates,proc,4th U,S,Nat.Cong,Appl.Mech 1,555(1962). [6] Frederick,D.,Thick rectangular plates On an elastic foundation,Trans,A,S,C,E.122 1.67(1957). -
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