Bernoulli-Euler beam model based on a modified couple stress theory
Bernoulli-Euler beam model based on a modified couple stress theory
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DOI：
10.1088/0960-1317/16/11/015
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发表时间：
2006-11-01
影响因子：
2.3
通讯作者：
Gao, X-L
中科院分区：
文献类型：
--
作者：
Park, S. K.;Gao, X-L
利用修正的偶应力理论建立了一个新的伯努利-欧拉梁弯曲模型。采用基于最小总势能原理的变分公式。与经典的Bernoulli-Euler梁模型不同，新模型包含了一个内部材料长度尺度参数，可以捕捉尺寸效应。在没有材料长度尺度参数的情况下，前者退化为后者。作为新模型的直接应用，求解了一个悬臂梁问题。研究发现，新模型预测的悬臂梁抗弯刚度大于经典梁模型预测的抗弯刚度。当梁厚度较小时，两种模型预测的挠度相差很大，但随着梁厚度的增加，两种模型预测的挠度相差不大。比较表明，预测的尺寸效应与实验观察到的相当好。
A new model for the bending of a Bernoulli-Euler beam is developed using a modified couple stress theory. A variational formulation based on the principle of minimum total potential energy is employed. The new model contains an internal material length scale parameter and can capture the size effect, unlike the classical Bernoulli-Euler beam model. The former reduces to the latter in the absence of the material length scale parameter. As a direct application of the new model, a cantilever beam problem is solved. It is found that the bending rigidity of the cantilever beam predicted by the newly developed model is larger than that predicted by the classical beam model. The difference between the deflections predicted by the two models is very significant when the beam thickness is small, but is diminishing with the increase of the beam thickness. A comparison shows that the predicted size effect agrees fairly well with that observed experimentally.