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弹性支撑阶梯柱侧向位移与稳定性的精确分析

DOI: 10.3969/j.issn.1006-7043.201305059

Keywords: 微分方程法, 稳定性分析, 箱形伸缩臂, 弹性约束, 二阶效应, 阶梯柱, 侧向位移

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Abstract:

为了得到平面内弹性支撑阶梯柱刚度与稳定性问题的精确解,对箱形阶梯柱平面内受力模型进行了合理等效。基于纵横弯曲理论,建立了弹性支撑条件下变截面阶梯柱挠曲微分平衡方程,结合边界条件,得到了任意阶变截面阶梯柱端部挠度及结构失稳特征方程的精确递推表达式,从而给出工程中起重机常用节数箱形伸缩臂平面内失稳特征方程的显式表达。将所得的计算结果与ANSYS软件细分单元后的计算结果进行比较分析,验证了推导公式的正确性,从而为工程设计提供了简单、快捷、精确的变截面阶梯柱变形与屈曲临界力确定方法。

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