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工程力学  2015 

柔性梁几何非线性/后屈曲分析的改进势能列式方法研究

DOI: 10.6052/j.issn.1000-4750.2014.04.0335, PP. 18-26

Keywords: 柔性梁,几何非线性分析,后屈曲,总势能,刚体运动检验,变形后节点受力平衡

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Abstract:

针对基于Updated-Lagrangian列式的能量方法存在:1)由于位移模型的近似性而带来虚假节点力;2)在分析节点空间转动效应上存在争议;3)势能高阶项由于物理概念不明确给简化列式带来困难等问题,提出描述柔性梁构件有限位移过程受力状态变化的势能列式方法。根据连续介质力学极分解定理,将典型增量步内单元内力势能分解为刚体变位下初始节点力势能和自然变形中积累的初始节点力势能和应变能,推导了满足刚体运动检验和变形后节点受力平衡的空间梁单元几何刚度矩阵。建立全面反映构件非线性大位移行为的增量割线刚度矩阵显式列式。数值分析结果表明,势能列式能准确预测任意荷载作用下结构非线性平衡路径,物理概念清晰,适应工程实践对一般杆系结构非线性分析需求。

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