功能梯度双材料复合悬臂梁受集中剪力作用的弹性力学解

Elastic Solutions for a Bilayer Functionally Graded Cantilever Beam under Concentrated Shear Loads

采用应力函数的方法,求解了功能梯度双材料层合悬臂梁在端部受集中剪力作用下的弹性解.该梁中含有两个功能梯度层,每层的弹性模量均可以沿厚度方向独立变化,对任意的变化梯度均成立,当退化至各向同性材料时,与已有的单层悬臂梁理论解一致.该方法具有一般性,可推广至功能梯度夹芯梁的求解.

An elastic solution for a laminated beam composed of two functionally graded layers subjected to the concentrated shear force at the free end is explored. The beam is treated as a plane problem by means of Airy stress function and its modulus of each graded layer varies with the thickness as an arbitrary function respectively. When assuming the elastic compliance parameters to be constant, this solution can degenerate into the classical solution derived by Timoshenko. Furthermore,this method presented here can be extended to the sandwich functionally graded beam.