Being gradually softened approach for solving large deflection of cantilever beam subjected to distributed and tip loads
Being gradually softened approach for solving large deflection of cantilever beam subjected to distributed and tip loads
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DOI：
10.1016/j.mechmachtheory.2022.104879
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发表时间：
2022-04-27
影响因子：
5.2
通讯作者：
Wu, Xinyu
中科院分区：
文献类型：
--
作者：
Gao, Fei;Liao, Wei-Hsin;Wu, Xinyu
均匀悬臂梁的小挠度解已经得到了广泛的应用。然而，当挠度变大时，由于几何非线性的影响，求解十分困难，特别是对于变截面梁。为解决这一问题，本文提出了一种新的、有效的方法--逐渐软化方法(BGSA)来预测均匀和非均匀悬臂梁在分布荷载和端部荷载作用下的大挠度。将悬臂梁初始视为刚性梁，然后从自由端到固定端逐渐软化，以求解悬臂梁的挠度。随着悬臂梁的新刚性单元被软化，作用在先前软化单元上的力荷载的方向发生变化。正因为如此，之前被软化的单位的偏转需要进行相应的更新。实验结果表明，该方法能够较高精度地求解均匀悬臂梁和非均匀悬臂梁在分布荷载和端部荷载作用下的大挠度问题。
The solutions to small deflections of uniform cantilever beams have been obtained and widely used. However, when the deflections become large, it is quite challenging to derive the solutions due to the geometric nonlinearity, especially for non-uniform beams. To handle that, in this paper, a novel and an efficient method called being gradually softened approach (BGSA) is proposed to predict the large deflections of uniform and non-uniform cantilever beams subjected to distributed and tip loads. The cantilever beam is initially regarded as a rigid beam and then is gradually softened from the free end to the fixed end to solve the deflection of the cantilever beam. As new rigid units of the cantilever beam are softened, the direction of the force load acting on the previous softened units changes. Because of that, the deflections of the previous softened units need to be updated accordingly. Experimental results show that this method can solve the large deflections of uniform and non-uniform cantilever beams that experience distributed and tip loads with high accuracy.