重力载荷作用下柔性梁的结构变形与承载力分析

柔性体在承受外载荷作用时，会通过自身变形，降低所承受的外载荷.为了研究重力载荷作用下柔性梁的结构变形与承载力之间的定量关系，首先建立模拟实验分析重力载荷在梁上的分布形式；基于Timoshenko梁的大变形本构方程，建立承受重力载荷作用下大变形梁的控制方程；通过量纲分析，确定研究两个无量纲变量，结构变形数与Cauchy数；数值求解控制方程，分析结构变形数与Cauchy数之间的定量关系；与实验结果对比，证实理论模型的可靠性，并结合文献中树枝承受雪载荷的实验数据，分析模型用于预测实际问题的可行性.所建理论模型可用于机械工程中柔性结构件的变形分析与承载力设计，也可用来预测自然界中风沙、大雪环境下植被的抗倒伏能力.

Analysis of Deformation and Bearing Capacity of Flexible Beams Under Gravitational Loads

The large deformation of flexible structure can decrease the load. The relation between the large deformation of the flexible beam and the gravitational load was studied. Based on the experiments, the distribution mode for the gravitational load was built. With the large deflection constitutive model for Timoshenko beams, the governing equation for the large-deformation beam under the gravitational load was derived. Two dimensionless parameters were defined, i.e. the Cauchy number and the deformation coefficient. Through numerical calculation of the governing equation, the quantitative relation between the Cauchy number and the deformation coefficient was discussed. The theoretical results are compared with the experimental data to confirm the reliability of the theoretical model. The model was used to analyze the snow load data in previous literatures to verify the applicability in reality. The research indicates that, the proposed method applies to the design of deflection and bearing capacity of flexible beams in engineering systems, as well as the prediction of the lodging resistance of vegetations in sand storm or snow storm.