不同模量功能梯度悬臂梁集中剪力作用下的弹性力学解

Elastic solution of a functionally graded cantilever beam with different modulus in tension and compression under a concentrated shear load

利用半逆解法,求解了不同模量功能梯度悬臂梁在自由端受集中剪力作用下的弹性力学解.该模型的拉压弹性模量分别以各自的功能梯度函数进行变化,泊松比为常数.当假定模型的拉压模量均为常数且相等时,该弹性力学解与经典平面梁的解一致.最后依照该方法,对材料为指数形式变化时的功能梯度梁进行了计算,并分析了其相关力学性能.

A functionally graded cantilever beam with different modulus in tension and compression under con-centrated shear loads was considered by using the semi-inverse method. The modulus of tension and compression of the model varied with the thickness as an arbitrary linear or non-linear function and the Poisson’s ratio was assumed to be constant. If the model decayed into a homogeneous state, its solutions coincided with the classical ones of the beams. Finally, according to this approach, an example was calculated, where the modulus varied with the exponential form, and its behaviors of mechanics was illustrated.