## 留言板

 引用本文: 陆健炜，鲍四元，沈峰. 阶梯柱屈曲的改进Fourier级数分析 [J]. 应用数学和力学，2021，42（12）：1229-1237
LU Jianwei, BAO Siyuan, SHEN Feng. Buckling Analysis of Stepped Columns Based on the Improved Fourier Series Method[J]. Applied Mathematics and Mechanics, 2021, 42(12): 1229-1237. doi: 10.21656/1000-0887.410373
 Citation: LU Jianwei, BAO Siyuan, SHEN Feng. Buckling Analysis of Stepped Columns Based on the Improved Fourier Series Method[J]. Applied Mathematics and Mechanics, 2021, 42(12): 1229-1237.

## 阶梯柱屈曲的改进Fourier级数分析

##### doi: 10.21656/1000-0887.410373

###### 作者简介:陆健炜(1993—)，男，硕士生(E-mail：337246553@qq.com)鲍四元(1980—)，男，副教授，硕士生导师(通讯作者. E-mail：bsiyuan@126.com)沈峰(1984—)，男，副教授，硕士生导师
• 中图分类号: O317.3

## Buckling Analysis of Stepped Columns Based on the Improved Fourier Series Method

• 摘要:

该文对阶梯柱的弹性屈曲问题进行了研究。首先基于改进Fourier级数法采用局部坐标逐段建立阶梯柱的位移函数表达式，然后由带约束的势能变分原理得到含屈曲荷载的线性方程组，利用线性方程组有非零解的条件把问题转化为矩阵特征值问题得到临界载荷，最后讨论方法中的参数取值，并把结果与已有文献和有限元的结果比较，从而验证方法的精度。所提模型在阶梯柱的两端和变截面处引入横向弹簧和旋转弹簧，通过改变弹簧的刚度值模拟不同的边界。所提方法在工程设计中能比较精确地确定各种弹性边界条件下阶梯柱的临界载荷。

• 图  1  阶梯柱的屈曲模型

Figure  1.  The buckling model for the stepped column

图  2  一端弹性一端自由阶梯柱的临界载荷随刚度参数对数的变化图

Figure  2.  Change of buckling loads of the elastic-free stepped column with non-dimensional spring stiffness on a logarithmic scale

图  3  三阶对称阶梯柱

Figure  3.  A three-step symmetric column

图  4  三阶对称阶梯柱的屈曲模态

Figure  4.  The buckling modes of a three-stepped symmetric column

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##### 出版历程
• 收稿日期:  2020-12-07
• 录用日期:  2021-07-31
• 修回日期:  2021-07-30
• 网络出版日期:  2021-11-25
• 刊出日期:  2021-12-01

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