﻿ 整体壁板压弯成形等效计算模型
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Press bending equivalent simulation model of integrally reinforced panel
Li Weidong, Wan Min
School of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Abstract:The elastic and plastic deformation distribution of skin and stiffener were analyzed during press bending for integrally reinforced panel with inside ribs. According to the characteristics of plastic deformation on inside stiffener and mainly elastic deformation on skin, a geometrical equivalent method was proposed which simplified the skin component to stiffener with virtual material properties. The calculative formula of equivalent coefficient was educed based on inertia moment. For complicated integrally reinforced panel, the establishment process and calculative method of equivalent model were also introduced. The finite element analysis and experiment of Ⅰ -style single stiffener and gridding stiffener panels were carried out. The comparisons on efficient and precision between detailed model and equivalent model were made and verified by experimental data. The equivalent model for press bending was proved to be reliable and highly efficient which can be used for simulation and parameter optimization of large complicated gridding integrally reinforced panel.
Key words: integrally reinforced panel     press bend forming     equivalent model     virtual material     finite element analysis

1 压弯成形有限元模型

 参数 弹性模量/GPa 屈服强度/MPa 抗拉强度/MPa 延伸率/% 强度系数K 硬化指数n 数值 69.029 445.21 558.54 8.99 1 220.21 0.86

 图 1 压弯成形分析模型Fig. 1 Press bend forming model
2 压弯成形等效计算模型

 图 2 典型Ⅰ筋条截面弯曲正应力分布Fig. 2 Distribution of normal stress on bending of Ⅰ-section

 图 3 等效模型示意图Fig. 3 Scheme of equivalent model

 图 4 复杂截面等效方法Fig. 4 Equivalent method of complicated section

 图 5 网格筋条单元图Fig. 5 Cells with grid stiffene

1) 取零件待等效部位蒙皮厚度的平均值作为等效筋条的厚度,以降低网格剖分难度.大型复杂网格筋条壁板可分区域设置等效筋条厚度.

3) 对A和B间的等效筋条,宽度为b1,长度设为L1,设体积为VAB,其虚拟材料受到A部分和B部分各一半的影响,因此虚拟材料系数为A和B体积加权计算值:

4) 对A和C间的等效筋条,宽度为b2,长度设为L2,设体积为VAC，同理其虚拟材料系数为

5) 对A,B,C和D相邻的十字位置筋条,其虚拟材料系数可以取SAB,SAC,SBD,SCD的体积加权计算值,即

6) 当单元格形状不规则或者单元非闭合时,以上计算方法同样适用. 3 单筋条有限元分析与实验

 图 6 Ⅰ型单筋条等效塑性应变分布Fig. 6 Equivalent plastic strain distribution of Ⅰ-section sample

 图 7 单筋条压弯实验Fig. 7 Press bending experiment of Ⅰ-section sample

 对比项 下压3 mm 下压4 mm 下压力/kN 位移/mm 下压力/kN 位移/mm 回弹前 回弹后 回弹前 回弹后 实验测量 29.16 -2.82 -0.89 32.44 -3.79 -1.67 完整模型 27.94 -2.69 -0.94 31.23 -3.66 -1.73 等效模型J 28.79 -2.65 -0.97 29.66 -3.61 -1.80 等效模型V 28.84 -2.65 -0.97 29.61 -3.60 -1.81
4 网格筋条有限元分析与实验

 图 8 网格筋条试件毛料Fig. 8 Blank of grid reinforced panel

 图 9 等效筋条分区位置Fig. 9 Partitions of equivalent model

 位置 体积W 体积E 体积N 体积S 筋条体积 等效系数 A 0.0 493.2 0.0 340.8 115.9 4.718 0 B 0.0 0.0 0.0 2 612.7 600.0 5.354 5 C 493.2 493.2 340.8 340.8 121.8 4.537 6 D 0.0 0.0 2 612.7 2 612.7 240.0 11.886 3 E 493.2 493.2 340.8 340.8 51.8 9.316 8 F 0.0 2 307.9 0.0 0.0 375.0 7.154 5 G 2307.9 2 307.9 0.0 0.0 150.0 16.386 3

 图 10 压弯位置示意图Fig. 10 Sketch of press location

 模型 节点数 单元数目(C3D8R) 最小单元边长/mm 计算时间/s Y下压5.2 mm Y10下压5.2 mm 完整模型 93 756 72 340 0.881 2 403 2 339 等效模型 54 063 39 708 0.881 765 707

 图 11 Y和Y10试件等效塑性应变分布Fig. 11 Equivalent plastic strain distribution of Y and Y10 samplese

 图 12 网格壁板实验件Fig. 12 Press bending experiments of gridding stiffener panel samples

 对比项 Y Y10 下压力/kN 位移/mm 下压力/kN 位移/mm 回弹前 回弹后 回弹前 回弹后 实验测量 33.46 -5.19 -2.39 32.61 -5.19 -2.11 完整模型 32.19 -5.18 -2.52 31.52 -5.18 -2.35 等效模型 30.15 -5.19 -2.47 30.13 -5.18 -2.21
5 结 论

1) 整体壁板压弯成形过程中筋条承受主要塑性变形,蒙皮部分主要发生弹性变形,可以按弯曲变形等效为虚拟材料的筋条模型.

2) 根据抗弯刚度等效方法,计算虚拟材料等效弹性模量和塑性应力.复杂网格筋条壁板可以使用体积比的方法计算各区域等效材料参数.

3) 针对Ⅰ型单筋条和网格筋条,通过完整模型和等效模型的有限元分析和实验对比,表明提出的等效模型具有可靠的精度和数倍的计算效率,为实际网格筋条整体壁板压弯成形有限元分析和工艺参数优化提供了基础.

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#### 文章信息

Li Weidong, Wan Min

Press bending equivalent simulation model of integrally reinforced panel

Journal of Beijing University of Aeronautics and Astronsutics, 2014, 40(11): 1537-1542.
http://dx.doi.org/10.13700/j.bh.1001-5965.2013.0726