一维周期性梁结构等效性能计算方法讨论

Discussion of effective properties prediction methods for 1D periodic beam structure

具有轴向周期微结构的复合梁结构,通常在宏观上简化为一维欧拉-伯努利梁。由于缺乏基于严格数学理论、同时考虑降维及均匀化的等效性能计算方法,已有研究或采用基于平截面假定的弯曲能量近似方法,或采用基于三维周期性介质等效性质的方法。本文首先介绍了基于一维周期性梁的渐近均匀化理论求解新方法,并在此基础上与上述两种方法进行比较。结果表明,基于平截面假定的近似方法忽视了这类梁结构内的三维应力状态,过高地估计了梁的等效性质。

The periodic composite beam with microstructure arranged along the axis is generally simplified to an Euler-Bernoulli beam in macro.Due to the lack of the method considering both the strict mathematical base and the dimension reduction and homogenization to calculating the effective stiffness,the bending energy approximate method based on the plane cross-section assumption or the asymptotic homogenization based on 3D periodic medium is usually utilized in the literature.In this paper,the method of asymptotic homogenization theory for one dimensional periodic beam is introduced and compared with the other two methods.The results indicate that the bending energy method overestimates the effective bending stiffness of the beam,because the three-dimensional stress state in the beam is neglected based on the plane cross-section assumption.