基于牛顿迭代算法的大型有面外支撑杆X撑结构的屈曲分析

康元顺; 张伟为; 刘梦娟; 曾晓辉

doi:10.6052/j.issn.1000-4750.2021.05.S053

基于牛顿迭代算法的大型有面外支撑杆X撑结构的屈曲分析

doi: 10.6052/j.issn.1000-4750.2021.05.S053

康元顺^{1, 2,},
张伟为^{1, 2, 3,},
刘梦娟^{1, 2,},
曾晓辉^{1, 2, ,}

1.
中国科学院力学研究所，北京 100190
2.
中国科学院大学工程科学学院，北京 100049
3.
中国科学院大学未来技术学院，北京 100049

基金项目: 国家自然科学基金项目(11672306)

详细信息

作者简介:
康元顺(1997−)，男，贵州人，博士生，主要从事工程力学研究(E-mail: kangyuanshun@imech.ac.cn)

张伟为(1996−)，男，江苏人，博士生，主要从事工程力学研究(E-mail: zhangweiwei@imech.ac.cn)

刘梦娟(1998−)，女，河南人，硕士生，主要从事工程力学研究(E-mail: liumengjuan@imech.ac.cn)

通讯作者:
曾晓辉(1972−)，男，湖南人，研究员，博士，博导，从事结构动力响应、稳定性和流固耦合领域研究(E-mail: zxh@imech.ac.cn)

中图分类号: TB12
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- HTML全文浏览量: 14
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- 被引次数: 0
出版历程
- 收稿日期: 2021-05-30
- 修回日期: 2022-02-23
- 网络出版日期: 2022-03-23
- 刊出日期: 2022-06-06

BUCKLING ANALYSIS OF A LARGE X-SUPPORTED STRUCTURE WITH OUT-OF-PLANE BRACES BASED ON NEWTON'S ITERATION

KANG Yuan-shun^{1, 2
,},
ZHANG Wei-wei^{1, 2, 3
,},
LIU Meng-juan^{1, 2
,},
ZENG Xiao-hui^{1, 2
, ,}

1.
Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
2.
School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China
3.
School of Future Technology, University of Chinese Academy of Sciences, Beijing 100049, China

摘要

摘要: 该文从理论分析和数值计算的角度研究了一种有面外支撑的X支撑系统的稳定性问题，提出了一种简单高效的计算方法，这种X支撑的两条支撑对角线的交点处连接了一个面外撑杆。考虑有面外撑杆的非对称交叉支撑体系在一般情况下的弹性屈曲，即不同长度、截面和载荷的连续对角，面外撑杆与X支撑平面可以有不同角度，并且X支撑的交叉点不固定在跨中。建立了两端固接的双跨受压杆件跨中任意线弹性的特征值矩阵，利用迭代算法进行屈曲载荷计算，详述了新型X支撑系统的屈曲荷载理论计算方法。推导了两端固接的双跨受拉(压)杆件跨中任意位置处的转动刚度计算公式，并通过数值计算讨论了不同受力形式转动刚度对X支撑的屈曲长度系数的影响，阐释了在实际结构中转动刚度对屈曲载荷的影响可忽略。进行比例加载屈曲分析，分析的目的是建立受压杆件的有效长度因子与压缩杆件和拉伸杆件的力比之间的关系。得到了任意位置处的非对称交叉支撑系统有效长度因子的数值解，并通过已有文献的退化结果验证了其有效性。结合工程实际，给出了屈曲长度系数的理论推荐值。
- 结构工程 /
- 屈曲分析 /
- 理论推导 /
- 数值计算 /
- 有面外支撑的X支撑系统 /
- 有效长度系数 /
- 结构设计
Abstract: Studies the stability of an X-brace system with out-of-plane support using theoretical analysis and numerical calculation, and proposes a simple and efficient calculation method. An out-of-plane brace is connected at the intersection of the two diagonals of the X-brace. The elastic buckling of an asymmetric cross bracing system with out-of-plane struts is considered, i.e., continuous diagonals of different lengths, sections and loads. Out-of-plane struts and X-brace planes can have different angles, and the intersection point of the X-brace is not fixed in the middle of the span. The eigenvalue matrix of any linear elasticity in the middle of the double-span compression member fixed at both ends is established, and the buckling load is calculated by an iterative algorithm and the buckling of the new X-brace system is described in details. The calculation formula for the rotational stiffness of a double-span tension (compression) member fixed at both ends is deduced at any position in the span, and the influence of the rotational stiffness of different force forms on the buckling length coefficient of the X-brace is discussed based on numerical calculation, which shows that the influence of the rotational stiffness on the buckling load is negligible in actual structure. Then proportional load buckling analysis is carried out to establish the relationship between the effective length factor of the compression member and the force ratio of the compression member and the tension member. The numerical solution of the effective length factor of the asymmetric cross bracing system at any position is obtained, and its effectiveness is verified using the results in the literature. The theoretical value of buckling length coefficient is recommended to engineering practice.
- structural engineering /
- buckling analysis /
- theoretical derivation /
- numeral calculations /
- X-brace system with out-of-plane support /
- effective length coefficient /
- structural design

HTML全文

图 1 带面外支撑的交叉系统

Figure 1. Cross system with out-of-plane support

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图 2 压缩杆AB的屈曲形状

Figure 2. Buckling shape of compression rod AB

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图 3 连续压缩杆件的分析模型

Figure 3. Analytical model for continuous compression members

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图 4 与数值结果和实验结果的对比

Figure 4. Comparison between numerical and experimental results

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图 5 转动刚度计算模型

Figure 5. Rotational stiffness calculation model

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图 6 不同受力条件下X撑交点位置与弹性刚度因子的关系

Figure 6. The relationship between the position of the X brace intersection and the elastic stiffness factor under different stress conditions

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图 7 弹性支点的位置与屈曲长度系数的关系

Figure 7. The relationship between the position of the elastic fulcrum and the buckling length factor

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图 8 不同转动刚度对屈曲载荷的影响

Figure 8. Effect of different rotational stiffness on buckling load

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图 9 与数值结果进行对比

Figure 9. Compare with numerical results

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图 10 跨中无量纲因子与屈曲长度系数的关系

Figure 10. Relationship between dimensionless factor in midspan and buckling length factor

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图 11 不同支承刚度时拉压比与屈曲长度系数的关系

Figure 11. Relationship between tension-compression ratio and buckling length coefficient with different bearing stiffness

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