Application of Plane Elements and Shell Elements in Imitating Ribs of Members in Compound Strip Method

doi:10.16183/j.cnki.jsjtu.2021.071

Abstract

Abstract:

Finite strip method (FSM) is a classical method to analyze the buckling of thin-walled members. The traditional FSM adopting trigonometric functions longitudinally can hardly analyze the members with spaced ribs along the longitudinal direction, while the compound strip method (CSM) can compensate for this shortcoming. Based on the CSM, the influence of utilizing plane elements and shell elements to respectively imitate stiffeners on buckling is investigated. Compared with the shell-element ribs, the plane-element ribs are prone to assembling the stiffener matrices with fewer degrees of freedom. But the shell-element ribs are more comprehensive as the out-plane displacement of ribs are taken into consideration. It is found that plane element ribs and shell element ribs have little difference on the buckling capacity of members. The buckling capacity has a small difference of mean absolute error (MAE) underneath 0.75% between the two types of CSMs, and the buckling capacity and modes are in good agreement with the finite element results. The buckling loads of the two types of CSMs are close to the FEM with a MEA less than 5%. The accuracy of the plane elements satisfies the predicted requirements, which helps to reduce the program computation and simplify the analysis complexity. The efficiency of analysis can be dramatically improved for fine meshing elements.

Key words: compound strip method (CSM), buckling, plane element, shell element, ribs

CLC Number:

HOU Yanguo, LI Zhanjie, GONG Jinghai. Application of Plane Elements and Shell Elements in Imitating Ribs of Members in Compound Strip Method[J]. Journal of Shanghai Jiao Tong University, 2022, 56(6): 710-721.

Figures/Tables 19

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References 23

[1]	CHEUNG Y. Finite strip method in structural analysis[M]. Oxford: Pergamon Press, 1976: 1-24.
[2]	BRADFORD M A, AZHARI M. Buckling of plates with different end conditions using the finite strip method[J]. Computers & Structures, 1995, 56(1): 75-83. doi: 10.1016/0045-7949(94)00528-B URL
[3]	SCHAFER B W, ÁDÁNY S. Buckling analysis of cold-formed steel members using CUFSM: Conventional and constrained finite strip methods[C]∥18th International Specialty Conference on Cold-Formed Steel Structures. Rolla, USA: United States University of Missouri Rolla, 2006.
[4]	LI Z J, SCHAFER B. Buckling analysis of cold-formed steel members with general boundary conditions using CUFSM: Conventional and constrained finite strip methods[C]∥20th International Specialty Conference on Cold-Formed Steel Structures. St. Louis, MO, USA: Missouri University of Science and Technology, 2010.
[5]	申富林, 蔡长青. 基于集成有限条法的大跨度斜拉桥的地震响应研究[J]. 山东农业大学学报(自然科学版), 2020, 51(2): 316-319.
	SHEN Fulin, CAI Changqing. Study on seismic response of long-span cable-stayed bridge based on integrated finite strip method[J]. Journal of Shandong Agricultural University (Natural Science Edition), 2020, 51(2): 316-319.
[6]	葛威延, 何斌, 安逸, 等. 矩形薄板屈曲分析的高阶有限条传递矩阵法[J]. 应用力学学报, 2018, 35(3): 558-563.
	GE Weiyan, HE Bin, AN Yi, et al. Higher-order finite strip transfer matrix for buckling analysis of rectangular thin plate[J]. Chinese Journal of Applied Mechanics, 2018, 35(3): 558-563.
[7]	龙跃凌, 盘创汉, 范文浩. 基于有限条法的带约束拉杆方形钢管混凝土柱局部屈曲模型[J]. 工业建筑, 2017, 47(12): 174-180.
	LONG Yueling, PAN Chuanghan, FAN Wenhao. Local buckling model of square cft columns with binding bars based on finite strip method[J]. Industrial Construction, 2017, 47(12): 174-180.
[8]	孙冰. 冷弯薄壁卷边型钢构件有限条法屈曲计算误差分析[J]. 科学技术与工程, 2017, 17(14): 173-178.
	SUN Bing. Error analysis of elastic buckling for cold-formed steel members by finite strip method[J]. Science Technology and Engineering, 2017, 17(14): 173-178.
[9]	刘冬梅, 何斌, 方媛, 等. 单支开口薄壁梁屈曲分析的Riccati有限条传递矩阵法[J]. 应用力学学报, 2019, 36(3): 588-594.
	LIU Dongmei, HE Bin, FANG Yuan, et al. Buckling analysis of single-branched open cross-section thin-walled beams via Riccati finite strip transfer matrix method[J]. Chinese Journal of Applied Mechanics, 2019, 36(3): 588-594.
[10]	高亚南. 矫直过程的弹塑性B样条有限条分析[D]. 秦皇岛: 燕山大学, 2016.
	GAO Yanan. Plastoelastic B spline finite strip analysis of leveling process[D]. Qinhuangdao: Yanshan University, 2016.
[11]	FAN S C, CHEUNG Y K. Analysis of shallow shells by spline finite strip method[J]. Engineering Structures, 1983, 5(4): 255-263. doi: 10.1016/0141-0296(83)90004-4 URL
[12]	FAN S C. Spline finite strip in structural analysis[D]. Hong Kong: The University of Hong Kong, 1982.
[13]	SEIF A E, KABIR M Z. Spline finite strip modelling of post-buckling behaviour in the notched tensioned sheets considering analytical approaches for fracture and fatigue[J]. Thin-Walled Structures, 2019, 137: 541-560. doi: 10.1016/j.tws.2019.01.028 URL
[14]	王宗木, 沈鹏程. 样条能量法解加肋板壳的静力问题[J]. 安徽建筑工业学院学报(自然科学版), 1995, 3(1): 11-14.
	WANG Zongmu, SHEN Pengcheng. Static analysis of ribbed plates and shells by using b-spline functions[J]. Journal of Anhui Institute of Architecture, 1995, 3(1): 11-14.
[15]	ZHEN L, QIAO P Z, ZHONG J B, et al. Design of steel pipe-jacking based on buckling analysis by finite strip method[J]. Engineering Structures, 2017, 132: 139-151. doi: 10.1016/j.engstruct.2016.11.016 URL
[16]	WANG Y L, QIAO P Z, LU L J. Buckling analysis of steel jacking pipes embedded in elastic tensionless foundation based on spline finite strip method[J]. Thin-Walled Structures, 2018, 130: 449-457. doi: 10.1016/j.tws.2018.06.010 URL
[17]	CHEN C J, GUTKOWSKI R M, PUCKETT J A. B-spline compound strip analysis of stiffened plates under transverse loading[J]. Computers & Structures, 1990, 34(2): 337-347. doi: 10.1016/0045-7949(90)90378-F URL
[18]	WANG Y L, QIAO P Z. Improved buckling analysis of stiffened laminated composite plates by spline finite strip method[J]. Composite Structures, 2021, 255: 112936. doi: 10.1016/j.compstruct.2020.112936 URL
[19]	ABBASI M, KHEZRI M, RASMUSSEN K J R, et al. Elastic buckling analysis of cold-formed steel built-up sections with discrete fasteners using the compound strip method[J]. Thin-Walled Structures, 2018, 124: 58-71. doi: 10.1016/j.tws.2017.11.046 URL
[20]	HOANG T, ÁDÁNY S. Torsional buckling of thin-walled columns with transverse stiffeners: Analytical studies[J]. Periodica Polytechnica Civil Engineering, 2020, 64: 370-386.
[21]	ZHEN L, CHEN J J, WANG J H, et al. Effect of orthogonal stiffeners on the stability of axially compressed steel jacking pipe[J]. Journal of Shanghai Jiao Tong University (Science), 2017, 22(5): 536-540.
[22]	HOU Y G, LI Z J, GONG J H. A compound strip method for static and buckling analyses of thin-walled members with transverse stiffeners[J]. Thin-Walled Structures, 2021, 165: 107829. doi: 10.1016/j.tws.2021.107829 URL
[23]	MOAVENI S. Finite element analysis theory and application with ANSYS[M]. 3rd ed. Upper Saddle River, New Jersey, USA: Prentice Hall, 1999.

L	l₁	l₂
30	10	20
50	15	35
100	30	70
300	100	200
500	160	340
800	272	528
1000	350	650
1500	500	1000
2000	650	1350
3000	1000	2000
4000	1360	2640
5000	1600	3400

L	l₁	l₂	l₃
30	7.5	15	22.5
50	12.5	25	37.5
100	25	50	75
300	75	150	225
500	125	250	375
800	200	400	600
1000	250	500	750
1500	375	750	1125
2000	500	1000	1500
3000	750	1500	2250
4000	1000	2000	3000
5000	1250	2500	3750

肋板数量	受力类型	d_SM/%
1个加劲肋	轴力	1.20×10^-3
	弯曲	6.10×10^-5
2个加劲肋	轴力	7.00×10^-2
	弯曲	8.70×10^-3
3个加劲肋	轴力	1.20×10^-2
	弯曲	1.70×10^-2

肋板数量	受力类型	d_SM/%
单加劲肋	轴力	1.30E-01
	弯曲	5.00E-01
双加劲肋	轴力	7.40E-01
	弯曲	4.80E-01

构件	差异对比项	轴力		弯曲
构件	差异对比项	单肋板	双肋板	单肋板	双肋板
槽钢	FEM-CSM2D	1.550	1.348	0.865	1.229
	FEM-CSM3D	1.550	1.286	0.865	1.226
卷边槽钢	FEM-CSM2D	0.956	1.889	1.236	1.599
	FEM-CSM3D	0.956	1.851	1.218	1.526