刚性基底弹性转动约束矩形板各受载条件下屈曲分析

doi:10.16183/j.cnki.jsjtu.2020.353

摘要/Abstract

摘要：

为探究对于刚性基底上边界不同弹性转动约束刚度矩形板的单侧屈曲行为,研究了在刚性基底上弹性转动约束矩形薄板四边受线性压力和均布剪力屈曲的问题.采用Rayleigh-Ritz法,依据不同受载情况的屈曲形变提出合适的挠曲面函数,由板屈曲时能量的变分推得临界屈曲荷载理论解.运用相关性稳定验算公式,获得薄板在弯-剪复合应力下的屈曲公式.建立相关有限元模型,分析不同基底刚度和弯剪比对弯-剪复合屈曲应力的影响,并与一个半充填式钢箱-混凝土组合梁负弯矩区腹板屈曲试验结果比较.结果表明:半充填混凝土作刚性基底时可简化为刚度系数略低于5的弹性基底.

关键词: 矩形薄板, Ritz法, 刚性基底, 弹性转动约束, 临界屈曲系数, 弯-剪复合应力

Abstract:

In order to investigate the unilateral buckling behavior of rectangular plates with different elastic rotational restraint stiffnesses on the rigid foundation, the buckling of rectangular plates with elastic rotation constraints on the rigid foundation under linear pressure and uniform shear force is studied. According to the buckling deformation under different loading conditions, the appropriate deflection surface function is proposed, and the theoretical solution to critical buckling load is deduced from the energy variation of plate buckling by using the Rayleigh-Ritz method. The buckling formula of the thin plate at the combined bending-shear stress is obtained by using the correlation stability checking formula. A finite element model is established to analyze the influence of different base stiffnesses and bending-shear ratios on the bending shear composite buckling stress. The results are compared with the web buckling test result of a semi filled steel box concrete composite beam in the negative moment region. The results show that the rigid foundation of semi filled concrete can be simplified as an elastic foundation with a stiffness coefficient slightly lower than 5.

Key words: rectangular plate, Ritz method, rigid foundation, rotationally restrained boundary, critical buckling coefficient, combined bending-shear stress

中图分类号:

TB12
O343.9

吴韬, 莫时旭, 向勇斌, 邹泽群, 郑艳. 刚性基底弹性转动约束矩形板各受载条件下屈曲分析[J]. 上海交通大学学报, 2022, 56(1): 114-126.

WU Tao, MO Shixu, XIANG Yongbin, ZOU Zequn, ZHENG Yan. Explicit Buckling Analysis of Rotationally Restrained Plates on Rigid Base Under Various Loading Conditions[J]. Journal of Shanghai Jiao Tong University, 2022, 56(1): 114-126.

图/表 22

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参考文献 18

[1]	XIANG Y. Exact solutions for buckling of multispan rectangular plates[J]. Journal of Engineering Mechanics, 2003, 129(2):181-187. doi: 10.1061/(ASCE)0733-9399(2003)129:2(181) URL
[2]	詹豪, 邵旭东, 蒋志刚. 多跨弹性支承连续矩形薄板屈曲分析[J]. 工程力学, 2014, 31(11):25-30.
	ZHAN Hao, SHAO Xudong, JIANG Zhigang. Buckling analysis of continuous rectangular thin plates with multi-span elastic supports[J]. Engineering Mechanics, 2014, 31(11):25-30.
[3]	朱甚, 李四平. 横向纤维搭桥下矩形脱层热屈曲数值模拟[J]. 上海交通大学学报, 2014, 48(12):1784-1787.
	ZHU Shen, LI Siping. Numerical simulation of thermal buckling of rectangular-shaped delamination bridged by lateral fibers in 3D composites[J]. Journal of Shanghai Jiao Tong University, 2014, 48(12):1784-1787.
[4]	谈梅兰, 董经鲁. 余弦分布压力下矩形薄板的屈曲[J]. 工程力学, 2010, 27(5):32-35.
	TAN Meilan, DONG Jinglu. Buckling analysis of thin rectangular plates under cosine-distributed compressive loads[J]. Engineering Mechanics, 2010, 27(5):32-35.
[5]	史旭东, 王鑫伟. 受面内非均匀分布载荷的矩形板屈曲分析[J]. 航空学报, 2006, 27(6):1113-1116.
	SHI Xudong, WANG Xinwei. Analysis of buckling of rectangular plates subjected to non-uniformly distributed in-plane loadings[J]. Acta Aeronautica et Astronautica Sinica, 2006, 27(6):1113-1116.
[6]	甘立飞, 王鑫伟, 王爱军. 矩形薄板受面内非均匀分布载荷稳定性分析[J]. 宇航学报, 2008, 29(4):1457-1461.
	GAN Lifei, WANG Xinwei, WANG Aijun. Buckling analysis of rectangular thin-plates subjected to in-plane non-uniformly distributed loadings[J]. Journal of Astronautics, 2008, 29(4):1457-1461.
[7]	TIMOSHENKO S P, GERE J M. Theory of elastic stability[M]. 2nd ed. New York: McGraw-Hill, 1961.
[8]	QIAO P Z, SHAN L Y. Explicit local buckling analysis of rotationally restrained composite plates under biaxial loading[J]. International Journal of Structural Stability and Dynamics, 2007, 7(3):487-517. doi: 10.1142/S021945540700240X URL
[9]	QIAO P Z, HUO X P. Explicit local buckling analysis of rotationally-restrained orthotropic plates under uniform shear[J]. Composite Structures, 2011, 93(11):2785-2794. doi: 10.1016/j.compstruct.2011.05.026 URL
[10]	刘沐宇, 陈齐风, 张强. 弹性转动边界约束的组合梁腹板剪切屈曲分析[J]. 华中科技大学学报(自然科学版), 2014, 42(1):84-88.
	LIU Muyu, CHEN Qifeng, ZHANG Qiang. Wed plate buckling analysis in steel-concrete composite girder considering elastic rotational restraint boundary under shear[J]. Journal of Huazhong University of Science and Technology (Natural Science Edition), 2014, 42(1):84-88.
[11]	WRIGHT H D. Local stability of filled and encased steel sections[J]. Journal of Structural Engineering, 1995, 121(10):1382-1388. doi: 10.1061/(ASCE)0733-9445(1995)121:10(1382) URL
[12]	毛佳, 江振宇, 陈广南, 等. 弹性支承上边界转动约束矩形板屈曲分析[J]. 工程力学, 2010, 27(12):59-63.
	MAO Jia, JIANG Zhenyu, CHEN Guangnan, et al. Elastic buckling analysis of rectangle plate with rotation restraint on elastic support[J]. Engineering Mechanics, 2010, 27(12):59-63.
[13]	郑艳, 莫时旭, 赵剑光, 等. 转动约束受压矩形钢板单侧屈曲强度计算简化[J]. 广西大学学报(自然科学版), 2016, 41(1):99-106.
	ZHENG Yan, MO Shixu, ZHAO Jianguang, et al. Simplified calculation on unilateral buckling strength of rotationally-retrained compression rectangular steel plates[J]. Journal of Guangxi University (Natural Science Edition), 2016, 41(1):99-106.
[14]	莫时旭, 钟新谷, 赵人达. 刚性基底上弹性约束矩形板的屈曲行为分析[J]. 工程力学, 2005, 22(2):174-178.
	MO Shixu, ZHONG Xingu, ZHAO Renda. Buckling behavior of elastically constrained rectangular plate on rigid base[J]. Engineering Mechanics, 2005, 22(2):174-178.
[15]	AGGARWAL K, WU S, PAPANGELIS J. Finite element analysis of local shear buckling in corrugated web beams[J]. Engineering Structures, 2018, 162:37-50. doi: 10.1016/j.engstruct.2018.01.016 URL
[16]	REINALDO GONCALVES B, KARTTUNEN A, ROMANOFF J, et al. Buckling and free vibration of shear-flexible sandwich beams using a couple-stress-based finite element[J]. Composite Structures, 2017, 165:233-241. doi: 10.1016/j.compstruct.2017.01.033 URL
[17]	陈绍蕃. 钢结构稳定设计指南[M]. 北京: 中国建筑工业出版社, 1996.
	CHEN Shaofan. Guide to stability design of steel structures[M]. Beijing: China Architecture and Building Press, 1996.
[18]	BIJLAARD P P. Plastic buckling of simply supported plates subjected to combined shear and bending or eccentric compression in their plane[J]. Journal of the Aeronautical Sciences, 1957, 24(4):291-303. doi: 10.2514/8.3832 URL

应变片编号	高度/mm	应变值×10⁶
YY1-1	50	-1016.36
YY1-2	100	-874.56
YY1-3	150	-727.06
YY1-4	200	-575.86
YY1-5	250	-435.06

弯剪比β	弯曲压力/kN	剪力/kN
0	0	8087.65
0.1	743.46	7434.86
0.25	1643.64	6574.57
0.5	2706.99	5413.98
1	3840.12	3840.12
1.5	4323.32	2882.17
2	4539.25	2269.55
2.5	4647.50	1859.00
3	4708.85	1569.57
4	4771.77	1192.91
6	4817.67	802.95
10	4841.84	484.20
β→+∞	4772.20	0