平面单元和壳单元在复合有限条法中模拟加劲肋的应用

doi:10.16183/j.cnki.jsjtu.2021.071

摘要/Abstract

摘要：

有限条法是一种经典的分析薄壁构件屈曲的方法,传统的有限条法在长度方向采用三角函数,无法分析沿长度方向间隔布置加劲肋的构件的屈曲问题,而复合有限条法恰好能弥补这一缺陷.基于复合有限条法,使用平面单元和壳单元分别模拟加劲肋对分析结果的影响.相比于壳单元,平面单元的自由度数量更少, 矩阵组合更简便.而壳单元因为考虑到面外的位移自由度而更全面.分别采用两种加劲肋单元分布带加劲肋的构件,发现壳单元和平面单元对屈曲结果的影响甚小,两者之间差异的绝对平均值在0.75%以内,并且屈曲承载力和模态与有限元结果皆能良好吻合.两种形式的复合有限条法与有限元差异的绝对平均值控制在5%以内.平面单元加劲肋的精度已经满足预期要求,有助于减少程序计算量和简化分析的复杂程度;在划分单元较密的情况下,能显著提升计算速度.

关键词: 复合有限条法, 屈曲, 平面单元, 壳单元, 加劲肋

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

中图分类号:

侯彦果, 李占杰, 龚景海. 平面单元和壳单元在复合有限条法中模拟加劲肋的应用[J]. 上海交通大学学报, 2022, 56(6): 710-721.

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.

图/表 19

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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