关于弹性板弯曲变形的Reissner理论

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.

On the Reissner Theory of Bending of an Elastic Plate

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.