基于平铺刚度法的弧形加筋板的轻量化设计

刘宸宇; 骆烜赫; 刘康翔; 孟增; 肖山

doi:10.21656/1000-0887.430342

基于平铺刚度法的弧形加筋板的轻量化设计

doi: 10.21656/1000-0887.430342

刘宸宇^1,,
骆烜赫¹,
刘康翔¹,
孟增^1, ,,
肖山²

1.
合肥工业大学土木与水利工程学院，合肥 230009
2.
中国航空工业集团有限公司沈阳飞机设计研究所，沈阳 110034

基金项目:

国家自然科学基金(面上项目) 11972143

详细信息

作者简介:
刘宸宇(2001—)，男(E-mail: 2019210816@mail.hfut.edu.cn)

通讯作者:
孟增(1987—)，男，副教授，博士，博士生导师(通讯作者. E-mail: mengz@mail.dlut.edu.cn)

中图分类号: TB114.3;O213.2
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- 文章访问数: 339
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- PDF下载量: 57
- 被引次数: 0
出版历程
- 收稿日期: 2022-10-28
- 修回日期: 2022-12-08
- 刊出日期: 2023-08-01

Lightweight Design of Arc Rib Stiffened Plates Based on the Smeared Stiffener Method

1.
College of Civil Engineering, Hefei University of Technology, Hefei 230009, P.R.China
2.
Shenyang Aircraft Design and Research Institute, Aviation Industry Corporation of China, Ltd., Shenyang 110034, P.R.China

摘要

摘要: 加筋板结构是航空航天结构设计中常见的承载部件，可以在保证加筋板性能的基础上减轻其结构质量，能够带来巨大的实际效益. 因此，加筋板结构的轻量化设计一直是航空航天领域的研究重点. 基于同步失效的概念，设计了一种新型的弧形加筋板，旨在充分利用加筋肋的轴向承载能力. 同时，基于平铺刚度法，准确预测了弧形加筋板的临界屈曲载荷. 最后采用粒子群优化算法对弧形加筋板进行了轻量化设计. 算例结果表明，弧型加筋板承载能力优异，轻量化设计效果显著，具有良好的优化效果.
- 弧形加筋板 /
- 平铺刚度法 /
- 临界屈曲荷载 /
- 轻量化
Abstract: Stiffened plates are common bearing components in aerospace structure design, which can bring great economic benefits and reduce the structure weight based on the insurance of the plate performance. Therefore, the lightweight design of stiffened plate structures is a research focus in the aerospace field. Based on the concept of synchronous failure, a new type of arc rib stiffened plate was proposed to sufficiently make use of the axial bearing capacity of ribs. Then, the critical buckling load of the arc rib stiffened plate was accurately predicted based on the smeared stiffener method. The lightweight design of arc rib stiffened plates was carried out by means of the particle swarm optimization algorithm. The results show that, the arc rib stiffened plate has excellent bearing capacity, significant lightweight design effects, and promising optimization results.
- arc rib stiffened plate /
- smeared stiffener method /
- critical buckling load /
- lightweight

HTML全文

图 1 正交网格加筋板示意图

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 1. Schematic diagram of the orthogonal grid stiffened plate

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图 2 传统网格加筋板

Figure 2. The traditional grid stiffened plate

下载: 全尺寸图片幻灯片

图 3 弧形网格加筋板

Figure 3. The arc grid stiffened plate

下载: 全尺寸图片幻灯片

图 4 带凸筋和凹筋的弧形加筋板示意图

Figure 4. Schematic diagram of the stiffened plate with convex and concave arc ribs

下载: 全尺寸图片幻灯片

图 5 优化历程

Figure 5. The optimization process

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表 1 弧形加筋板参数的验证与设计空间

Table 1. The validation and design space of parameters of arc rib stiffened cylindrical plates

	H/mm	t/mm	h_e1/mm	h_m1/mm	h_e2/mm	h_m2/mm	N_a	N_c
lowerbound	1	5	5	20	20	5	3	4
upperbound	4	15	20	80	80	20	10	10

下载: 导出CSV

表 2 传统加筋板和弧形加筋板优化

Table 2. Optimization of traditional and arc rib stiffened plates

	H/mm	t/mm	h_e1/mm	h_m1/mm	h_e2/mm	h_m2/mm	N_a	N_c	critical load P_cr/(kN/m)	structural mass M/kg
initial design	1.10	13.00	24.00	24.00	24.00	24.00	3	3	13.5	7.91
lightweight design (traditional)	1.00	8.13	25.40	25.40	25.40	25.40	3	4	14.1	6.82
lightweight design (arc rib stiffened)	1.00	6.00	5.00	66.14	25.08	13.35	3	4	14.1	5.42

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参考文献(30)

[1]	王伟, 吴梵. 单根加筋板整体屈曲临界应力计算与分析[J]. 舰船科学技术, 2010, 32(10): 3-7. https://www.cnki.com.cn/Article/CJFDTOTAL-JCKX201010001.htm WANG Wei, WU Fan. Calculating and analysising of the overall buckling's critical stress of single stiffened panels[J]. Ship Science and Technology, 2010, 32(10): 3-7. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JCKX201010001.htm
[2]	王伟, 吴梵. 加筋板整体屈曲临界应力计算与分析[J]. 中国舰船研究, 2011, 6(3): 21-27. https://www.cnki.com.cn/Article/CJFDTOTAL-JCZG201103005.htm WANG Wei, WU Fan. Computational analysis on the critical stress of stiffened plates' overall buckling[J]. Chinese Journal of Ship Research, 2011, 6(3): 21-27. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JCZG201103005.htm
[3]	李彦娜, 董科. 基于广义切线模量理论的铝合金加筋板结构轴压极限强度分析[J]. 船舶工程, 2016, 38(1): 78-81. https://www.cnki.com.cn/Article/CJFDTOTAL-CANB201601021.htm LI Yanna, DONG Ke. Analysis of ultimate axial compressive strength of stiffened aluminum panel structure based on generalized tangent modulus theory[J]. Ship Engineering, 2016, 38(1): 78-81. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-CANB201601021.htm
[4]	张振兴, 肖刚, 李四平. 横向纤维搭桥下的脱层屈曲数值模拟[J]. 上海交通大学学报, 2010, 44(1): 130-133. https://www.cnki.com.cn/Article/CJFDTOTAL-SHJT201412019.htm ZHANG Zhenxing, XIAO Gang, LI Siping. Simulation of delamination buckling by fiber bridges[J]. Journal of Shanghai Jiaotong University, 2010, 44(1): 130-133. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-SHJT201412019.htm
[5]	朱菊芬, 郑罡, 武金瑛. 层合板壳脱层屈曲的有限元分析[J]. 应用数学和力学, 2000, 21(3): 301-306. http://www.applmathmech.cn/article/id/2177 ZHU Jufen, ZHENG Gang, WU Jinying. FEM analysis of delamination buckling in composite plates & shells[J]. Applied Mathematics and Mechanics, 2000, 21(3): 301-306. (in Chinese) http://www.applmathmech.cn/article/id/2177
[6]	叶广宁, 邵青, 何宇廷, 等. 铝合金加筋板轴压屈曲稳定性的有限元分析[J]. 机械工程材料, 2013, 37(3): 83-86. https://www.cnki.com.cn/Article/CJFDTOTAL-GXGC201303023.htm YE Guangning, SHAO Qing, HE Yuting, et al. FEM analysis on compress buckling stability of stiffened aluminum alloy panels[J]. Materials for Mechanical Engineering, 2013, 37(3): 83-86. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-GXGC201303023.htm
[7]	江玮, 郁鼎文, 冯平法. 加筋板结构静态性能分析及优化设计[J]. 机械设计与制造, 2008, 2: 4-6. https://www.cnki.com.cn/Article/CJFDTOTAL-JSYZ200802004.htm JIANG Wei, YU Dingwen, FENG Pingfa. Static stiffness analysis and structure optimization of stiffened plate[J]. Machinery Design & Manufacture, 2008, 2: 4-6. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JSYZ200802004.htm
[8]	黄丕帅, 陈昆. 均匀受压加筋板的刚性加筋与柔性加筋临界点确定[J]. 起重运输机械, 2017, 5: 42-45. https://www.cnki.com.cn/Article/CJFDTOTAL-QZJJ201705011.htm HUANG Pishuai, CHEN Kun. Determination of critical point between rigid reinforcement and flexible reinforcement of stiffened plate under uniform pressure[J]. Hoisting and Conveying Machinery, 2017, 5: 42-45. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-QZJJ201705011.htm
[9]	黄丽华, 刘鹏洋, 曲激婷. 正交各向异性加筋板屈曲分析方法研究[J]. 计算力学学报, 2021, 38(1): 78-83. https://www.cnki.com.cn/Article/CJFDTOTAL-JSJG202101012.htm HUANG Lihua, LIU Pengyang, QU Jiting. Study on the buckling algorithm of orthotropic stiffened plate[J]. Chinese Journal of Computational Mechanics, 2021, 38(1): 78-83. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JSJG202101012.htm
[10]	刘毅, 聂坤, 戴瑛. 任意铺层复合材料加筋板屈曲/后屈曲行为的解析解[J]. 南京航空航天大学学报, 2018, 50(1): 1-10. https://www.cnki.com.cn/Article/CJFDTOTAL-NJHK201801001.htm LIU Yi, NIE Kun, DAI Ying. Analytical solution for buckling and postbuckling behavior of stiffened arbitrary laminated composite panels[J]. Journal of Nanjing University of Aeronautics & Astronautics, 2018, 50(1): 1-10. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-NJHK201801001.htm
[11]	高伟, 刘存, 陈顺强. 变厚度复合材料加筋板轴压试验及分析方法[J]. 航空学报, 2022, 43(11): 526764. https://www.cnki.com.cn/Article/CJFDTOTAL-HKXB202211008.htm GAO Wei, LIU Cun, CHEN Shunqiang. Axial compression test and analysis method of composite stiffened plates with variable thickness[J]. Acta Aeronautica et Astronautica Sinica, 2022, 43(11): 526764. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HKXB202211008.htm
[12]	石峰, 马洪英, 孙义真, 等. 基于n阶剪切变形理论的复合材料层合板屈曲分析[J]. 应用数学和力学, 2020, 41(12): 1346-1357. doi: 10.21656/1000-0887.410061 SHI Feng, MA Hongying, SUN Yizhen, et al. Buckling analysis of composite laminate plates based on the nth-order shear deformation theory[J]. Applied Mathematics and Mechanics, 2020, 41(12): 1346-1357. (in Chinese) doi: 10.21656/1000-0887.410061
[13]	吴菁, 胡明勇, 章向明, 等. 复合材料帽型加筋板等效弯曲刚度[J]. 复合材料学报, 2022, 39(12): 6088-6095. https://www.cnki.com.cn/Article/CJFDTOTAL-FUHE202212038.htm WU Jing, HU Mingyong, ZHANG Xiangming, et al. Equivalent bending stiffness of composite hat-stiffened panel[J]. Acta Materiae Compositae Sinica, 2022, 39(12): 6088-6095. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-FUHE202212038.htm
[14]	王平远, 李成, 姚林泉. 基于非局部应变梯度理论功能梯度纳米板的弯曲和屈曲研究[J]. 应用数学和力学, 2021, 42(1): 15-26. doi: 10.21656/1000-0887.410188 WANG Pingyuan, LI Cheng, YAO Linquan. Bending and buckling of functionally graded nanoplates based on the nonlocal strain gradient theory[J]. Applied Mathematics and Mechanics, 2021, 42(1): 15-26. (in Chinese) doi: 10.21656/1000-0887.410188
[15]	李若愚, 王天宏. 薄板热力耦合的屈曲分析[J]. 应用数学和力学, 2020, 41(8): 877-886. doi: 10.21656/1000-0887.400308 LI Ruoyu, WANG Tianhong. Thermo-mechanical buckling analysis of thin plates[J]. Applied Mathematics and Mechanics, 2020, 41(8): 877-886. (in Chinese) doi: 10.21656/1000-0887.400308
[16]	任慧龙, 马开开, 杨征, 等. 不同扶强材形式的纵骨贯穿舱壁结构疲劳试验[J]. 船舶工程, 2019, 41(2): 15-18. https://www.cnki.com.cn/Article/CJFDTOTAL-CANB201902006.htm REN Huilong, MA Kaikai, YANG Zheng, et al. Fatigue test of the cutout of bulkhead for longitudinals with different type of stiffeners[J]. Ship Engineering, 2019, 41(2): 15-18. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-CANB201902006.htm
[17]	万育龙, 朱旭光. 加筋板屈曲和极限强度有限元计算方法研究[J]. 船海工程, 2013, 42(6): 17-21. https://www.cnki.com.cn/Article/CJFDTOTAL-WHZC201306004.htm WAN Yulong, ZHU Xuguang. Studies on the nonlinear finite element method for buckling and ultimate strength of stiffened panels[J]. Ship & Ocean Engineering, 2013, 42(6): 17-21. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-WHZC201306004.htm
[18]	朴春雨, 章怡宁. 典型加筋板的优化设计[J]. 飞机设计, 2003, 4: 29-32. https://www.cnki.com.cn/Article/CJFDTOTAL-FJSJ200304006.htm PIAO Chunyu, ZHANG Yining. Optimal design of typical stiffened panels[J]. Aircraft Design, 2003, 4: 29-32. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-FJSJ200304006.htm
[19]	满林涛, 杨婵. 矩形加筋板结构优化设计[J]. 中国科技信息, 2018, 19: 45-48. https://www.cnki.com.cn/Article/CJFDTOTAL-XXJK201819018.htm MAN Lintao, YANG Chan. Rectangular stiffened plate structure optimization design[J]. China Science and Technology Information, 2018, 19: 45-48. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-XXJK201819018.htm
[20]	施利娟, 杨平. 高速船铝合金带筋板的力学性能优化设计[J]. 船海工程, 2011, 40(2): 36-39. https://www.cnki.com.cn/Article/CJFDTOTAL-WHZC201102009.htm SHI Lijuan, YANG Ping. Optimum design of mechanical properties of aluminum sheets-with-ribs of high speed ships[J]. Ship & Ocean Engineering, 40(2): 36-39. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-WHZC201102009.htm
[21]	王博, 周子童, 周演, 等. 薄壁结构多层级并发加筋拓扑优化研究[J]. 计算力学学报, 2021, 38(4): 487-497. https://www.cnki.com.cn/Article/CJFDTOTAL-JSJG202104012.htm WANG Bo, ZHOU Zitong, ZHOU Yan, et al. Concurrent topology optimization of hierarchical stiffened thin-walled structures[J]. Chinese Journal of Computational Mechanics, 38(4): 487-497. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JSJG202104012.htm
[22]	崔荣华, 崔天晨, 孙直, 等. 基于水平集法的薄板加强筋分布优化理论研究[J]. 固体力学学报, 2018, 39(6): 587-593. https://www.cnki.com.cn/Article/CJFDTOTAL-GTLX201806003.htm CUI Ronghua, CUI Tianchen, SUN Zhi, et al. Topology optimization for stiffener layout of thin plate structures based on level set method[J]. Chinese Journal of Solid Mechanics, 39(6): 587-593. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-GTLX201806003.htm
[23]	MENG Z, LUO X, ZHOU H. Lightweight design of arcuately stiffened cylindrical shells based on smeared stiffener method and active learning strategy[J]. Thin-Walled Structures, 2022, 174: 109167.
[24]	常楠, 杨伟, 赵美英. 典型复合材料加筋壁板优化设计[J]. 机械设计, 2007, 24(12): 46-48. https://www.cnki.com.cn/Article/CJFDTOTAL-JXSJ200712014.htm CHANG Nan, YANG Wei, ZHAO Meiying. Optimization design on typical reinforced wainscot of composite materials[J]. Journal of Machine Design, 2007, 24(12): 46-48. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JXSJ200712014.htm
[25]	赵群, 丁运亮, 金海波. 基于压弯刚度匹配论则的复合材料加筋板结构优化设计[J]. 南京航空航天大学学报, 2010, 42(3): 357-362. https://www.cnki.com.cn/Article/CJFDTOTAL-NJHK201003021.htm ZHAO Qun, DING Yunliang, JIN Haibo. Structural optimization design of composite stiffened panels based on matching regulations of compression and bending stiffnesses[J]. Journal of Nanjing University of Aeronautics & Astronautics, 2010, 42(3): 357-362. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-NJHK201003021.htm
[26]	王栋, 李正浩. 薄板结构加筋布局优化设计方法研究[J]. 计算力学学报, 2018, 35(2): 138-143. https://www.cnki.com.cn/Article/CJFDTOTAL-JSJG201802002.htm WANG Dong, LI Zhenghao. Layout optimization method for stiffeners of plate structure[J]. Chinese Journal of Computational Mechanics, 2018, 35(2): 138-143. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JSJG201802002.htm
[27]	郝鹏, 王博, 李刚, 等. 基于代理模型和等效刚度模型的加筋柱壳混合优化设计[J]. 计算力学学报, 2012, 29(4): 481-486. https://www.cnki.com.cn/Article/CJFDTOTAL-JSJG201204001.htm HAO Peng, WANG Bo, LI Gang, et al. Hybrid optimization of grid-stiffened cylinder based on surrogate model and smeared stiffener model[J]. Chinese Journal of Computational Mechanics, 2012, 29(4): 481-486. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JSJG201204001.htm
[28]	李刚, 孟增. 基于RBF神经网络模型的结构可靠度优化方法[J]. 应用数学和力学, 2014, 35(11): 1271-1279. doi: 10.3879/j.issn.1000-0887.2014.11.010 LI Gang, MENG Zeng. Reliability based design optimization with the RBF neural network model[J]. Applied Mathematics and Mechanics, 2014, 35(11): 1271-1279. (in Chinese doi: 10.3879/j.issn.1000-0887.2014.11.010
[29]	张洪波. 加筋板结构稳定优化设计研究[J]. 山西建筑, 2011, 37(3): 44-45. https://www.cnki.com.cn/Article/CJFDTOTAL-JZSX201103025.htm ZHANG Hongbo. Research on stability optimization design for stiffened plate structure[J]. Shanxi Architecture, 2011, 37(3): 44-45. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JZSX201103025.htm
[30]	郑俊锋, 姚卫星, 王磊. 均布平压下加筋板拓扑优化的工程方法[J]. 飞机设计, 2017, 37(2): 31-35. https://www.cnki.com.cn/Article/CJFDTOTAL-FJSJ201702008.htm ZHENG Junfeng, YAO Weixing, WANG Lei. Engineering algorithm for topology optimization of stiffened panel under uniform pressure[J]. Aircraft Design, 2017, 37(2): 31-35. (in Chinese)) https://www.cnki.com.cn/Article/CJFDTOTAL-FJSJ201702008.htm