论微极弹性板理论中的一些问题

On Some Problems in Micropolar Plate Theory

本文首先指出与经典平面弹性理论中的情况一样,平面应变和平面应力情况下的Eringen微极板方程之间有类似的转换关系。对于平面应力情况下的微极板横向运动方程、本文通过变量变换,使原耦合的方程组化为关于二个独立函数的非耦合的方程组,并且变换前后微分方程的总阶数不变。 本文还讨论了各种近似理论,指出由于微极板本身的特性,导致忽略横向剪切变形影响的方式的多样性,并对此进行了详细的讨论,指出了五种不同的方案。

In this paper it was showed that, under the transformation y→/(1-v) and E→E/(1-v2), Eringen's equations of micropolar plates theory in the case of t33 = 0 change into the equations of the theory in the case of e33 = 0 . we proved that the rotation vk , microrotations q φk. and displacement w can be represented asand the basic plates equations are equivalent to the following two uncupled equations:It was also pointed out that there exist five different ways of neglecting tansverse shear effects, and five sets of basic eqations are derived.