拱脚沉降下3D打印拱的非线性失稳研究

文新钧; 刘爱荣; 毛吉化

doi:10.6052/j.issn.1000-4750.2021.05.S003

拱脚沉降下3D打印拱的非线性失稳研究

1.
广州大学风工程与工程振动研究中心，广东，广州 510006
2.
广州广检建设工程检测中心有限公司，广东，广州 510030

基金项目: 国家自然科学基金项目(51878188)；高等学校学科创新引智计划项目(111计划D21021)；广州市科技计划项目(20212200004)

详细信息

作者简介:
文新钧(1995−)，男，湖南人，硕士生，主要从事打印材料拱的稳定性研究(E-mail: wxjvenn@foxmail.com)

毛吉化(1978−)，男，安徽人，高工，硕士，常务副总经理，主要从事土木工程检测研究(E-mail: 1750358980@qq.com)

通讯作者:
刘爱荣(1972−)，女，山西人，教授，博士，主任，主要从事新型桥梁结构的静动力稳定性研究(E-mail: liuar@gzhu.edu.cn)

中图分类号: U441；TU31
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出版历程
- 收稿日期: 2021-05-25
- 修回日期: 2022-03-17
- 网络出版日期: 2022-05-05
- 刊出日期: 2022-06-05

STUDY ON NONLINEAR INSTABILITY OF 3D PRINTING ARCH UNDER SETTLEMENT OF ARCH FOOT

1.
Research Center for Wind Engineering and Engineering Vibration, Guangzhou University, Guangzhou, Guangdong 510006, China
2.
Guangzhou Guangjian Construction Engineering Testing Center Co. LTD, Guangzhou, Guangdong 510030, China

摘要

摘要: 该文以3D打印材料ABS-M30作为试验载体，开展了拱脚沉降下3D打印拱的非线性失稳研究。基于最小势能原理推导了失稳临界荷载的解析表达式，得到了拱脚竖向和水平变位下拱径向位移沿拱轴线的分布图；设计了可控制拱脚沉降的加载系统，试验得到了拱在加载过程中的平衡路径，并通过有限元模拟对解析与试验结果进行了验证；分析了拱脚沉降量、矢跨比和长细比对3D打印拱失稳临界荷载的影响。研究结果表明：非线性失稳临界荷载随着拱脚沉降量的增大而减小；在拱脚沉降量一定的前提下，非线性失稳荷载随着矢跨比的增大而增大，随着长细比的增大而减小，且长细比的影响最为显著。
- 3D打印拱 /
- 拱脚沉降 /
- 非线性面内失稳 /
- 理论推导 /
- 试验研究 /
- 有限元模拟
Abstract: Presents an investigation on nonlinear instability of 3D printing arch made of 3D printing material ABS-M30 under the settlement of arch foot. Based on the principle of minimum potential energy, the analytical expression of instability critical load is derived, and the distribution of arch radial displacement along the arch axis under vertical and horizontal displacements of arch foot is obtained. The loading system which is capable of controlling the settlement of arch foot is designed. Then the equilibrium path of arch in the loading process is obtained experimentally, which is verified by analytical and finite element simulation. Meanwhile, the influence of rise span ratio and slenderness ratio on the critical load of 3D printing arch is analyzed. The results show that the nonlinear instability load decreases with the increase of arch foot settlement; with a certain arch foot settlement, the nonlinear instability load increases with the increase of rise span ratio, while decreases with the increase of slenderness ratio which has the most significant effect on the nonlinear instability load.
- 3D printing arch /
- settlement of arch foot /
- nonlinear instability /
- analytical solution /
- experiment /
- finite element simulation

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图 1 拱脚变位时圆弧拱受力图

Figure 1. Stress diagram of circular arch during displacement of arch foot

下载: 全尺寸图片幻灯片

图 2 拱脚竖向变位下拱径向位移沿拱轴线分布图

Figure 2. Distribution of arch radial displacement along arch axis under vertical displacement of arch foot

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图 3 拱脚水平变位下拱径向位移沿拱轴线分布图

Figure 3. Distribution of arch radial displacement along arch axis under horizontal displacement of arch foot

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图 4 加载试验全过程(以工况1为例)

Figure 4. Whole process of loading test (taking condition 1 as an example)

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图 5 拱的上下极值点试验值随着拱脚竖向变位的折线图

Figure 5. Line chart of the test value of the upper and lower extreme points of the arch with the vertical displacement of the arch foot

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图 6 拱的上下极值点试验值随着矢跨比变化的折线图

Figure 6. Line chart of the variation of the test value of the upper and lower extreme points of the arch with the rise span ratio

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图 7 拱的上下极值点试验值随着长细比变化的折线图

Figure 7. Line chart of the variation of the test value of the upper and lower extreme points of the arch with the slenderness ratio

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图 8 拱脚沉降量对失稳荷载的影响

Figure 8. Influence of arch foot settlement on instability load

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图 9 矢跨比对失稳荷载的影响

Figure 9. Influence of rise span ratio on instability load

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图 10 长细比对失稳荷载的影响

Figure 10. Influence of slenderness ratio on instability load

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表 1 试件材性试验结果

Table 1 Material property test results of test piece

项目	拉伸弹性模量/MPa	泊松比	拉伸强度/MPa
平均值	1540	0.3164	13.63
标准差	0.10	0.0040	0.17
离散系数/(%)	6.58	1.2700	1.25

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表 2 3D打印拱试件设计参数

Table 2 Design parameters of 3D printing of arch specimen

工况组	矢跨比f/L	跨径L/mm	矢高f/mm	截面宽度b/mm	截面高度h/mm	支撑截面高度b^'/mm	支撑截面高度h^'/mm	长细比λ	拱脚变位量X/mm
1	1/8	300	37.50	6.00	3.00	6.00	1.41	88.36	−4.46
2	1/8	300	37.50	6.00	3.00	6.00	1.41	88.36	0.00
3	1/8	300	37.50	6.00	3.00	6.00	1.41	88.36	3.12
4	1/8	300	37.50	6.00	3.00	6.00	1.41	88.36	6.25
5	1/8	300	37.50	6.00	3.00	6.00	1.41	88.36	8.92
6	1/10	300	30.00	6.00	3.00	6.00	1.15	70.19	6.25
7	1/9	300	33.33	6.00	3.00	6.00	1.27	78.22	6.25
8	1/8	300	37.50	6.00	3.00	6.00	1.41	88.36	6.25
9	1/7	300	42.86	6.00	3.00	6.00	1.58	101.57	6.25
10	1/6	300	50.00	6.00	3.00	6.00	1.80	119.54	6.25
11	1/8	300	37.50	6.00	3.00	6.00	1.41	88.36	6.25
12	1/8	300	37.50	6.20	3.10	6.20	1.46	85.51	6.25
13	1/8	300	37.50	6.40	3.20	6.40	1.51	82.83	6.25
14	1/8	300	37.50	6.60	3.30	6.60	1.55	80.32	6.25
15	1/8	300	37.50	6.80	3.40	6.80	1.60	77.96	6.25
注：表中负号表示拱脚向上变位量。

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表 3 3D打印拱临界失稳荷载误差分析表

Table 3 Error analysis table of 3D printing arch critical load

误差分析项	上极值点临界荷载				下极值点临界荷载
误差分析项	理论值X₁/N	试验值X₂/N	有限元值X₃/N	误差率 ${\varDelta _1}$ /(%)	理论值Y₁/N	试验值Y₂/N	有限元值Y₃/N	误差率 ${\varDelta _2}$ /(%)
工况1	24.60	23.88	23.76	0.50	9.79	10.19	10.04	1.47
工况2	24.59	24.20	23.89	1.28	9.55	10.12	10.01	1.09
工况3	24.55	24.02	23.83	0.79	9.78	10.17	10.03	1.38
工况4	24.05	23.79	23.65	0.59	10.08	10.22	10.07	1.47
工况5	23.67	23.56	23.41	0.64	10.23	10.38	10.12	2.50
工况6	19.58	19.99	19.20	3.95	7.44	8.49	8.69	−2.36
工况7	21.34	21.82	21.32	2.29	8.76	9.49	9.29	2.11
工况8	24.05	23.79	23.65	0.59	10.08	10.22	10.07	1.47
工况9	27.41	27.29	26.79	1.83	10.28	11.25	10.95	2.67
工况10	31.32	30.82	30.31	1.65	12.26	12.40	12.10	2.42
工况11	24.05	23.79	23.65	0.59	10.08	10.22	10.07	1.47
工况12	27.65	27.57	27.03	1.96	10.34	11.90	11.53	3.11
工况13	31.25	31.18	30.57	1.96	12.52	13.83	13.19	4.63
工况14	35.12	36.00	34.41	4.42	14.65	16.03	15.04	6.18
工况15	39.39	40.28	38.59	4.20	16.38	17.68	17.09	3.34

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