考虑杆件初弯曲的弦支穹顶结构非线性屈曲分析

姜正荣; 邱俊明; 石开荣; 苏昌旺

doi:10.3969/j.issn.0258-2724.20230234

考虑杆件初弯曲的弦支穹顶结构非线性屈曲分析

doi: 10.3969/j.issn.0258-2724.20230234

姜正荣^{1, 2,},
邱俊明¹,
石开荣^{1, 2, ,},
苏昌旺¹

1.
华南理工大学土木与交通学院，广东广州 510640
2.
华南理工大学亚热带建筑科学国家重点实验室，广东广州 510640

基金项目: 广东省现代土木工程技术重点实验室课题（2021B1212040003）

详细信息

作者简介:
姜正荣（1971—），男，副教授，博士，研究方向为大跨度空间结构，E-mail：zhrjiang@scut.edu.cn

通讯作者:
石开荣（1978—），男，副教授，博士，研究方向为预应力钢结构，E-mail：krshi@scut.edu.cn

中图分类号: TU394
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出版历程
- 收稿日期: 2023-05-15
- 修回日期: 2023-09-19
- 网络出版日期: 2024-10-17

Nonlinear Buckling Analysis of Suspended Domes Considering Initial Curvature of Members

JIANG Zhengrong^{1, 2
,},
QIU Junming¹,
SHI Kairong^{1, 2
, ,},
SU Changwang¹

1.
School of Civil Engineering & Transportation, South China University of Technology, Guangzhou 510640, China
2.
State Key Laboratory of Subtropical Building Science, South China University of Technology, Guangzhou 510640, China

摘要

摘要:
为揭示杆件初弯曲对弦支穹顶结构稳定承载力的影响规律，以多段直梁法模拟杆件初弯曲，采用随机缺陷模态法引入不同形状及幅值的杆件初弯曲，对弦支穹顶结构进行非线性屈曲分析；引入整体缺陷与杆件初弯曲，考察2种缺陷的共同施加对结构稳定性能的影响. 结果表明：仅考虑杆件初弯曲时，弦支穹顶结构的稳定承载力系数平均值显著降低（最大降幅为33.84%），该结构对杆件初弯曲较为敏感；相比于正弦全波，以正弦半波为初弯曲形状来引入杆件初弯曲，对结构的稳定性更为不利；相比于理想结构，同时考虑整体缺陷与杆件初弯曲时，结构的稳定承载力系数进一步降低（最大降幅为44.80%），但其降幅小于两者分别引入的降幅之和，2种缺陷的同时施加，对结构的稳定承载力存在耦合影响，一定程度上削弱了两者单独引入时的不利影响.
- 弦支穹顶结构 /
- 杆件初弯曲 /
- 整体缺陷 /
- 非线性屈曲分析
Abstract:
In order to reveal the influence laws of the initial curvature of members on the stability bearing capacity of suspended domes, a nonlinear buckling analysis of suspended domes was carried out by applying the multi-beam method to simulate the initial curvature of members and the random imperfection mode method to introduce the initial curvature of members with different shapes and amplitudes. The overall imperfection and the initial curvature of members were introduced to investigate the effect of the two kinds of imperfections imposed jointly on the structural stability behaviors. The results show that the mean coefficients of stability bearing capacity of suspended domes are significantly reduced when only the initial curvature of members is considered, and the maximum reduction is 33.84%, which indicates that the structure is sensitive to the initial curvature of members. Compared with the sinusoidal full-wave, the sinusoidal half-wave as the shape of initial curvature is more unfavorable to the structural stability. When the overall imperfection and the initial curvature of members are both considered, the coefficients of stability bearing capacity are further reduced for the suspended domes compared with the perfect structure, with the maximum reduction being 44.80%, but the reductions are smaller than the sums of reductions when the two kinds of imperfections are introduced separately. The joint action of the two kinds of imperfections has coupling effects on the structural stability bearing capacity, which weakens the adverse effects when the two kinds of imperfections are introduced separately to some extent.
- suspended dome /
- initial curvature of member /
- overall imperfection /
- nonlinear buckling analysis

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图 1 杆件空间弯曲示意

Figure 1. Schematic diagram of spatial curvature of member

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图 2 多段直梁法示意

Figure 2. Schematic diagram of multi-beam method

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图 3 分析模型

Figure 3. Analytical model

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图 4 一次模拟所得的初弯曲幅值及方向角分布直方图

Figure 4. Distribution histograms of amplitudes and direction angles of initial curvature from one simulation

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图 5 理想结构引入杆件初弯曲分布（放大50倍）

Figure 5. Distributions of initial curvature of members introduced in perfect structure （enlarged by 50 times）

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图 6 稳定承载力系数分布直方图

Figure 6. Distribution histograms of coefficients of stability bearing capacity

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图 7 仅考虑杆件初弯曲的稳定承载力系数平均值对比

Figure 7. Comparison of mean coefficients of stability bearing capacity considering initial curvature of members only

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图 8 整体缺陷结构引入杆件初弯曲分布（放大50倍）

Figure 8. Distributions of initial curvature of members introduced in structures with overall imperfection （enlarged by 50 times）

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图 9 同时考虑2种缺陷的稳定承载力系数平均值对比

Figure 9. Comparison of mean coefficients of stability bearing capacity considering both kinds of imperfections

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图 10 不同模型对应的荷载-位移曲线对比

Figure 10. Comparison of load-displacement curves corresponding to different models

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表 1 构件和材料规格

Table 1. Specifications of members and materials

结构部位	构件		材质	规格
上部单层网壳	凯威特部分	径向杆	Q355B	ϕ219 × 12
		环向杆	Q355B	ϕ219 × 12
		斜杆	Q355B	ϕ203 × 10
	联方部分	环向杆	Q355B	ϕ203 × 10
	联方部分	斜杆	Q355B	ϕ194 × 10
	撑杆		Q355B	ϕ168 × 8
下部索杆体系	环向索	内圈	平行钢丝束，1670 级	ϕ5 × 61
		中圈	平行钢丝束，1670 级	ϕ5 × 91
		外圈	平行钢丝束，1670 级	ϕ5 × 139
	径向索		平行钢丝束，1670 级	ϕ5 × 55

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表 2 仅考虑杆件初弯曲的稳定承载力系数

Table 2. Coefficients of stability bearing capacity considering initial curvature of members only

初弯曲形状	稳定承载力系数
正弦半波	3.361，3.328，3.382，3.390，3.391，3.398， 3.377，3.345，3.338，3.355，3.343，3.367， 3.324，3.401，3.344，3.368，3.371，3.353， 3.375，3.350，3.387，3.379，3.340，3.389， 3.389，3.340，3.320，3.313，3.378，3.401， 3.282，3.378，3.404，3.369，3.370，3.331， 3.444，3.371，3.333，3.342，3.310，3.361， 3.394，3.402，3.338，3.314，3.377，3.348， 3.337，3.359，3.383，3.405，3.358，3.351， 3.360，3.383，3.391，3.329，3.349，3.421， 3.365，3.414，3.346，3.386，3.354，3.339， 3.357，3.393，3.418，3.364，3.339，3.361， 3.364，3.339，3.362，3.345，3.384，3.348， 3.346，3.336，3.356，3.403，3.346，3.350， 3.409，3.375，3.379，3.393，3.377，3.326， 3.355，3.312，3.336，3.397，3.382，3.351， 3.332，3.404，3.397，3.385
	${K_{\min }} = 3.282$ ， ${K_{\max }} = 3.444$ ， $\mu = 3.3642$ ， ${\sigma } = 0.028\;8$
正弦全波	3.424，3.416，3.406，3.416，3.395，3.387， 3.409，3.357，3.400，3.415，3.410，3.392， 3.406，3.395，3.370，3.369，3.390，3.409， 3.380，3.399，3.370，3.400，3.413，3.422， 3.398，3.385，3.405，3.422，3.424，3.423， 3.377，3.401，3.392，3.403，3.421，3.360， 3.408，3.393，3.407，3.411，3.397，3.440， 3.406，3.390，3.392，3.410，3.381，3.391， 3.411，3.397，3.388，3.397，3.409，3.419， 3.388，3.409，3.403，3.366，3.372，3.388， 3.410，3.399，3.367，3.386，3.427，3.412， 3.394，3.401，3.411，3.402，3.383，3.393， 3.400，3.415，3.392，3.427，3.398，3.421， 3.393，3.373，3.387，3.390，3.409，3.395， 3.384，3.395，3.406，3.414，3.401，3.416， 3.343，3.413，3.376，3.406，3.395，3.394， 3.400，3.410，3.387，3.410
	${K_{\min }} = 3.343$ ， ${K_{\max }} = 3.440$ ， $\mu = 3.3987$ ， ${\sigma } = 0.017\;0$

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表 3 仅考虑杆件初弯曲的稳定承载力系数对比

Table 3. Comparison of coefficients of stability bearing capacity considering initial curvature of members only

初弯曲幅值最大值	初弯曲形状	K_min	K_max	$\mu$	$\sigma$	是否满足 χ² 检验	$\mu - 3\sigma$
l_max/700	正弦半波	3.365	3.482	3.4243	0.0178	否
l_max/700	正弦全波	3.424	3.473	3.4453	0.0092	是	3.4177
l_max/600	正弦半波	3.344	3.469	3.4141	0.0216	是	3.3493
l_max/600	正弦全波	3.400	3.465	3.4401	0.0102	是	3.4095
l_max/500	正弦半波	3.356	3.461	3.4065	0.0192	是	3.3489
l_max/500	正弦全波	3.401	3.459	3.4334	0.0109	是	3.4007
l_max/400	正弦半波	3.305	3.476	3.3890	0.0305	是	3.2975
l_max/400	正弦全波	3.369	3.443	3.4215	0.0120	是	3.3855
l_max/300	正弦半波	3.282	3.444	3.3642	0.0288	是	3.2778
l_max/300	正弦全波	3.343	3.440	3.3987	0.0170	是	3.3477

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表 4 同时考虑2种缺陷的稳定承载力系数对比

Table 4. Comparison of coefficients of stability bearing capacity considering both kinds of imperfections

整体缺陷分布模式	初弯曲幅值最大值	K_min	K_max	$\mu$	$\sigma$	是否满足 χ² 检验	$\mu - 3\sigma$
随机缺陷	l_max/700	2.845	2.916	2.8840	0.0142	否
	l_max/600	2.841	2.914	2.8809	0.0125	是	2.8434
	l_max/500	2.843	2.940	2.8802	0.0137	是	2.8391
	l_max/400	2.841	2.913	2.8741	0.0164	是	2.8249
	l_max/300	2.833	2.912	2.8737	0.0153	是	2.8278
特征缺陷	l_max/700	2.773	2.848	2.8157	0.0129	否
	l_max/600	2.770	2.862	2.8151	0.0157	否
	l_max/500	2.769	2.859	2.8146	0.0186	否
	l_max/400	2.775	2.899	2.8162	0.0198	是	2.7568
	l_max/300	2.759	2.878	2.8077	0.0197	否

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