﻿ 基于有限元法的箱型梁极限强度影响因素及敏感分析
 舰船科学技术  2019, Vol. 41 Issue (8): 28-33, 54 PDF

1. 山东省船舶控制工程与智能系统工程技术研究中心，山东 荣成 264300;
2. 中国海洋大学 工程学院，山东 青岛 266100;
3. 威海海洋职业学院，山东 荣成 264300

Ultimate strength and sensitive analysis of box girder based on finite element method
WANG Bao-sen1,2, FENG Liang3, GENG Bao-yang1,2
1. Ship Control Engineering and Intelligent Systems Engineering Technology Research Center of Shandong Province, Rongcheng 264300, China;
2. College of Engineering, Ocean University of China, Qingdao 266100, China;
3. Weihai Ocean Vocational College, Rongcheng 264300, China
Abstract: Finite element（FE）method for ultimate strength of hull box girder is widely used, but the FE method has a certain degree of instability. This paper develops the ultimate strength study of the simplified model of box girder, calculate the ultimate strength of three typical box girder models based on nonlinear FE method, Comparing with existing experimental data, verify the reliability of the FE method. Analyze the sensitive factors such as the boundary condition type, grid density and initial defects of box girder, analyze the sensitive factors such as the boundary condition type, grid density and initial defects of box girder, found that the model calculation error without extended section reached 20%, rough grid calculation error reaches 30%, when the initial defect size is 0.01 to 0.02 times of the length of the box girder, the calculation has less sensitive.
Key words: box girder     ultimate strength     finite element method     sensitivity factor
0 引　言

1 弧长法

 $\{ P\} - \{ I\} = 0{\text{。}}$ (1)

 $\left[ {{K_T}} \right]\left\{ {\Delta u} \right\} = \left\{ {\Delta P} \right\} - \left\{ R \right\}{\text{。}}$ (2)

 ${\left\{ {\Delta P} \right\}_i} = \Delta {\lambda _i}\left\{ {{P_{ref}}} \right\}{\text{。}}$ (3)

 $\left[ {{K_T}} \right]\left\{ {\Delta u} \right\} = \Delta {\lambda _i}\left\{ {{P_{ref}}} \right\} - {\left\{ R \right\}_i}{\text{。}}$ (4)

 图 1 弧长法原理示意图 Fig. 1 Principle diagram of RIKS
 $\left| {\Delta {l_i}} \right| = \sqrt {{{\left| {\left\{ {\Delta {u_i}} \right\}} \right|}^2} + {{\left| {\Delta {\lambda _i}\left\{ {{P_{ref}}} \right\}} \right|}^2}} {\text{。}}$ (5)

2 有限元模型

3种典型箱型梁即Nshihara的方形梁MST-3模型（简称Nshihara3模型）、Dowling2箱型梁模型、Reckling23箱型梁模型的剖面结构形式如图2所示。

 图 2 三种典型箱型梁剖面尺寸图 Fig. 2 Dimensions of three typical box girders

3种模型构件的详细尺寸和材料特性见表1表3，且3种模型的跨长L分别为540 mm，787 mm，500 mm。

 图 3 Nshihara 3箱型梁模型 Fig. 3 Model of Nshihara 3 box girder

 图 4 Nshihara3箱型梁损伤变形、应力云图及弯矩-转角曲线 Fig. 4 Damage deformation and stress cloud diagram bending moment - angle curve of Nshihara3 box girders

3种箱型梁有限元计算结果和实验值比对如表4所示，3种箱型梁有限元解和实验值的误差分别为0.92%，0.84%，3.6%，满足精度要求，验证了有限元算法的可信性。

3 有限元计算

3.1 边界条件

 图 5 无延长段和1+1+1边界条件下Nshihara3箱型梁损伤变形、应力云图 Fig. 5 Damage deformation and stress cloud diagram of no extension and 1+1+1 Boundary conditions

 图 6 两种边界条件下各箱型梁的弯矩-转角曲线 Fig. 6 Bending moment - angle curve of each box beam under two boundary conditions

3.2 初始缺陷因子

 图 7 Nshihara3模型屈曲模态及损伤变形、应力云图 Fig. 7 Buckling mode of Nshihara3 model and Damage deformation、stress cloud diagram

 图 9 Reckling23箱型梁模型屈曲模态及损伤变形、应力云图 Fig. 9 Buckling mode of Reckling23 model and Damage deformation、stress cloud diagram

 图 8 Dowling2箱型梁模型屈曲模态及损伤变形、应力云图 Fig. 8 Buckling mode of Dowling2 model and Damage deformation、stress cloud diagram

 图 10 Nshihara 3箱型梁不同缺陷下的弯矩-转角曲线 Fig. 10 Bending moment - angle curve of Nshihara 3 box girder under different defect

3.3 网格密度

 图 11 不同网格密度下Nshihara3箱型梁模型损伤变形、应力云图 Fig. 11 Damage deformation and stress cloud diagram of Nshihara3 box girder model under different grid densities

 图 12 四种网格密度下Nshihara箱型梁模型弯矩-转角曲线 Fig. 12 Bending moment - Angle curve of Nshihara box girder under four kind of grid densities

4 结　语

1）在相同荷载条件下，有延长段模型比无延长段模型极限弯矩值更接近实验值，且无延长段的Dowling2箱型梁模型计算值误差达到了20%，说明采用延长段的边界条件模拟箱型极限破坏得到的计算值更准确。

2）比例因子取5～10 mm时，3个模型在不同初始缺陷下计算误差为0.71%～6%，Nshihara模型和Reckling23模型最适合缺陷值为8 mm，Dowling2为10 mm，均在0.01～0.02倍箱型梁跨长范围内。

3）在2.5～15 cm网格密度内，有限元结果在大于5 cm时出现跳跃，此时Nshihara箱型梁模型极限强度误差值达到36%，当网格密度在0.1倍箱型梁跨长值以内时，计算结果更精确。

 [1] NISHIHARA S. Analysis of ultimate strength of stiffened rectangular plate (4th report) on the ultimate bending moment of ship hull girders[J]. Journal of the Society of Naval Architects of Japan, 1983, 154: 367-375. [2] NISHIHARA S. Ultimate longitudinal strength of midship cross section[J]. Naval Arch. Ocean Eng, 1984, 22: 200-214. [3] DOWLING P J, MOOLANI F M, FRIEZ PA. The effect of shear lag on the ultimate Strength of box girder[C]// Proc. Int. Con. On Steel Plated Structures. London, 1976: 108~147. [4] REKLING K A. Behaviour of box girder under bending and shear[A]. proc. ISSC[C], Paris 1997. Ⅱ. 2.46-11.2.49 [5] HANSEN A M. Strength of midship section[J]. Marine Structures, 1996, 9: 471-494P. DOI:10.1016/0951-8339(95)00040-2 [6] GORDO J M, SOARES C G, FAULKNER D. Approximate assessment of the ultimate longitudinal Strength of the hull girder[J]. Ship Research, 1996, 40(1): 60-59. [7] 徐向东, 崔维成, 冷建兴等. 箱型梁极限承载能力试验与现论研究[J]. 船舶力学. 2000, 4(5): 36~43 [8] 白勇, 徐向东, 崔维成. 船体结构极限强度的影响参数与敏感度探讨[J]. 船舶力学, 1998, 4(5): 35-43. [9] 贺双元, 吴卫国, 陆浩华, 运用MARC进行箱梁的极限强度分析[J]. 武汉理工大学学报(交通科学与工程版), 2006. 30(5): 889~891