复合材料加筋板的屈曲与后屈曲研究综述

胡媛媛; 张桂嘉; 陈普会; 童明波; 王芳丽

复合材料加筋板的屈曲与后屈曲研究综述

1.
南京航空航天大学　航空学院, 南京 210016
2.
金陵科技学院　机电学院, 南京 211169

基金项目: 航空科学基金 (20230009052004)

详细信息

通讯作者:
童明波，博士，教授，博士生导师，研究方向为复合材料飞机结构设计与分析　E-mail: tongw@nuaa.edu.cn

中图分类号: TB332
计量
- 文章访问数: 27
- HTML全文浏览量: 22
- 被引次数: 0
出版历程
- 收稿日期: 2024-08-14
- 修回日期: 2024-10-07
- 录用日期: 2024-10-23
- 网络出版日期: 2024-11-01

Review on buckling and post-buckling of stiffened composite panels

1.
College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
2.
College of Mechanical and Electrical Engineering, Jinling Institute of Technology, Nanjing 211169, China

Funds: Aeronautical Science Foundation of China (20230009052004)

摘要

摘要: 复合材料加筋板因其卓越的轻质、高强度和高刚度特性，在航空航天领域的飞机承力构件中得到了广泛应用。随着对材料性能要求的不断提升，深入理解这类结构的屈曲与后屈曲行为变得尤为重要。本文综述了国内外复合材料加筋板屈曲及后屈曲性能的研究进展，系统归纳了理论方法、有限元仿真技术及实验研究方法。研究表明，加筋板的几何参数(如加筋高度和间距)以及层合板的铺层顺序显著影响其屈曲性能；同时，考虑材料非线性和几何非线性对准确预测后屈曲行为至关重要。此外，本文探讨了预测复合材料加筋板屈曲和后屈曲失效模式及载荷的关键技术难点。通过分析现有研究的局限性，本文指出了未来可能的研究方向，为复合材料加筋板的屈曲与后屈曲研究及其工程应用提供了理论基础和实践指导。
- 复合材料 /
- 加筋板 /
- 屈曲与后屈曲 /
- 理论方法 /
- 有限元 /
- 试验
Abstract: Composite stiffened panels are widely used in aircraft load-bearing components in the aerospace field due to their excellent lightweight, high strength and high stiffness properties. With the continuous improvement of material performance requirements, it is particularly important to have a deep understanding of the buckling and post-buckling behavior of such structures. This article reviews the research progress on buckling and post-buckling properties of composite stiffened panels, and systematically summarizes theoretical approach, finite element simulation technology and experimental research methods. Studies have shown that the geometric parameters (such as height and spacing of stiffeners) and lay-up sequence of stiffened panels significantly affect the buckling performance; at the same time, considering material nonlinearity and geometric nonlinearity is crucial to accurately predict post-buckling behavior. In addition, this article explores the key technical difficulties in predicting buckling and post-buckling failure modes and loads of composite stiffened panels. By analyzing the limitations of existing researches, this article points out possible future research directions, providing a theoretical basis and practical guidance for buckling and post-buckling research on composite stiffened panels and their engineering applications.
- composite materials /
- stiffened panels /
- buckling and post-buckling /
- theoretical approach /
- finite element /
- experiment

HTML全文

图 1 工程算法流程图^[8]

Figure 1. Flowchart of engineering calculation method^[8]

下载: 全尺寸图片幻灯片

图 2 有效宽度处理(a)试验曲板横截面(b)等效横截面^[15]

Figure 2. Effective width approach (a) Test curved panel cross section(b) Equivalent cross section^[15]

下载: 全尺寸图片幻灯片

图 3 帽型加筋板三种蒙皮有效宽度^[16]

Figure 3. Three skin effective widths for omega-stiffened panel^[16]

下载: 全尺寸图片幻灯片

图 4 加筋板筋条种类

Figure 4. Types of stiffeners for stiffened panels

下载: 全尺寸图片幻灯片

图 5 后屈曲渐进损伤分析流程图

Figure 5. Flowchart of post-buckling progressive damage analysis

下载: 全尺寸图片幻灯片

图 6 双线性本构模型^[31]

Figure 6. Bilinear constitutive model^[31]

下载: 全尺寸图片幻灯片

图 7 冲击损伤有限元模型^[54]

Figure 7. Finite element model of impact damage^[54]

下载: 全尺寸图片幻灯片

图 8 压缩试验夹具示意图(左)、刀口夹具(右)^[59]

Figure 8. Schematic diagram of compression test fixture (left), knife edge fixture (right)^[59]

下载: 全尺寸图片幻灯片

图 9 压缩试验夹具示意图^[7]

Figure 9. Schematic diagram of compression test fixture^[7]

下载: 全尺寸图片幻灯片

图 10 剪切试验夹具示意图^[7]

Figure 10. Schematic diagram of shear test fixture^[7]

下载: 全尺寸图片幻灯片

图 11 剪切试验夹具现场图^[63]

Figure 11. Field diagram of shear test fixture^[63]

下载: 全尺寸图片幻灯片

图 12 压剪混合试验夹具示意图

Figure 12. Schematic diagram of compression-shear test fixture

下载: 全尺寸图片幻灯片

图 13 破坏模式：(a)工字型；(b) J型；(c) T型^[70]

Figure 13. Failure mode: (a) I-type; (b) J-type; (c) T-type^[70]

下载: 全尺寸图片幻灯片

图 14 数字图像相关(Digital image correlation, DIC)测量的屈曲模态：(a)未屈曲；(b)局部屈曲；(c)局部屈曲；(d)屈曲模式转变^[71]

Figure 14. Buckling modes measured by Digital image correlation (DIC): (a) Before buckling; (b) local buckling; (c) local buckling; (d) buckling mode transition. ^[71]

下载: 全尺寸图片幻灯片

图 15 加筋板剪切破坏^[70]

Figure 15. Shear failure of stiffened panel^[70]

下载: 全尺寸图片幻灯片

图 16 加筋板冲击损伤^[55]

Figure 16. Impact damage of stiffened panel^[55]

下载: 全尺寸图片幻灯片

图 17 含冲击损伤加筋板的破坏现象 (a)筋条侧；(b)蒙皮侧^[55]

Figure 17. Failure phenomenon of stiffened panel with impact damage (a) Stiffeners side; (b) Skin side^[55]

下载: 全尺寸图片幻灯片

图 18 开裂模式：(a)厚度-1.2 mm，载荷-60 Kn；(b)厚度-1.5 mm，载荷-80 kN^[98]

Figure 18. Cracking mode:(a) thickness-1.2 mm, load-60 kN; (b) thickness-1.5 mm, load-80 kN^[98]

下载: 全尺寸图片幻灯片

表 1 Camanho和Matthews的材料性能折减模型

Table 1. Material property reduction model of Camanho and Matthews

Failure mode	Degradation coefficient
Fiber tensile failure	$ E_{11}^d = 0.07{E_{11}} $
Fiber compression failure	$ E_{11}^d = 0.14{E_{11}} $
Matrix tensile/shear failure	$ E_{22}^d = 0.2{E_{22}} $ $ G_{12}^d = 0.2{G_{12}} $,$ G_{23}^d = 0.2{G_{23}} $
Matrix compression/shear failure	$ E_{22}^d = 0.4{E_{22}} $ $ G_{12}^d = 0.4{G_{12}} $,$ G_{23}^d = 0.4{G_{23}} $
Notes:$ {E_{11}} $ and $ {E_{22}} $ are the elastic moduli in the fiber and matrix directions; $ {G_{12}} $ and $ {G_{23}} $ are the shear moduli; $ d $ stands for degradation.

下载: 导出CSV

表 2 Chang和Lessard的材料性能折减模型

Table 2. Material property reduction model of Chang and Lessard

Failure mode	Degradation coefficient
Fiber failure	$ E_{11}^d = 0 $,$ E_{22}^d = 0 $,$ G_{12}^d = 0 $
Matrix failure	$ E_{22}^d = 0 $,$ \nu _{21}^d = 0 $
Fiber-matrix shear failure	$ G_{12}^d = 0 $,$ \nu _{12}^d = 0 $,$ \nu _{21}^d = 0 $
Notes: $ E_{11}^d $ and $ E_{22}^d $ are the elastic moduli in the fiber and matrix directions after degradation; $ G_{12}^d $is the shear moduli after degradation; $ \nu _{12}^d $ and $ \nu _{21}^d $ are poisson’s ratios after degradation; $ d $ stands for degradation.

下载: 导出CSV

[1]	CHAGRAOUI H, LAZGHAB T, SOULA M. Buckling optimization and post-buckling analysis of omega sub-stiffened composite panels using different cohesive interface properties[J]. Thin-Walled Structures, 2023, 189: 110944. doi: 10.1016/j.tws.2023.110944
[2]	WANG Y, WANG F, JIA S, et al. Experimental and numerical studies on the stability behavior of composite panels stiffened by tilting hat-stringers[J]. Composite Structures, 2017, 174: 187-195. doi: 10.1016/j.compstruct.2017.04.039
[3]	ABRAMOVICH H, WELLER T. Buckling and postbuckling behavior of laminated composite stringer stiffened curved panels under axial compression: Experiments and design guidelines[J]. Journal of Mechanics of Materials and Structures, 2009, 4(7): 1187-1207.
[4]	王海燕, 段世慧, 孙侠生. 复合材料加筋板后屈曲设计技术欧盟研究综述[J]. 航空工程进展, 2015, 6(2): 139-148. doi: 10.3969/j.issn.1674-8190.2015.02.002 WANG Haiyan, DUAN Shihui, SUN Xiasheng. Review on the EU Research Projects of Design and Analysis of Stiffened Composite Panels Including Post-buckling[J]. Advances in Aeronautical Science and Engineering, 2015, 6(2): 139-148(in Chinese). doi: 10.3969/j.issn.1674-8190.2015.02.002
[5]	朱菊芬, 陈浩然, 陈绍杰, 等. 复合材料加筋板后屈曲强度工程分析方法探讨[J]. 航空学报, 1991, (12): 639-642. doi: 10.3321/j.issn:1000-6893.1991.12.019 ZHU Jufen, CHEN Haoran, CHEN Shaoxing, et al. Engineering Method Research of Post-buckling[J]. Acta Aeronautica et Astronautica Sinica, 1991, (12): 639-642(in Chinese). doi: 10.3321/j.issn:1000-6893.1991.12.019
[6]	张雅倩, 刘轶轩, 吴泳芙等. 反对称铺设复合材料层合板非线性后屈曲分析[J]. 应用力学学报, 2023, 40(4): 778-787. ZHANG Yaqian, LIU Yixuan, WU Yongfu, et al. Nonlinear post-buckling analysis of composite laminates with antisymmetric angle-ply[J]. Chinese journal of applied mechanics, 2023, 40(4): 778-787(in Chinese).
[7]	邹建超. 纤维复合材料冲击后压缩/剪切的损伤机理及性能预测研究[D]. 大连理工大学, 2023. ZOU Jianchao. Study on Damage Mechanism and Performance Prediction of Fiber Composites under Compression/Shear After Impact[D]. Dalian University of Technology, 2023(in Chinese).
[8]	孙振亚. 基于人工神经网络的复合材料加筋板失效行为预测研究[D]. 大连理工大学, 2022. SUN Zhenya. Prediction of Failure Behavior of Composite Stiffened Panels Using Artificial Neural Network[D]. Dalian University of Technology, 2022(in Chinese).
[9]	王彬文, 艾森, 张国凡等. 考虑不确定性的复合材料加筋壁板后屈曲分析模型验证方法[J]. 航空学报, 2020, 41(8): 280–287. WANG Binwen, AI Sen, ZHANG Guofan, et al. Validation method for post-buckling analysis model of stiffened composite panel considering uncertainties[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(8): 223987(in Chinese).
[10]	FENG Y, LIU S, ZHANG T, et al. Experimental and theoretical investigation on the shear performance of stiffened composite panel with I-shaped stiffeners[J]. Composite Structures, 2022, 284: 115234. doi: 10.1016/j.compstruct.2022.115234
[11]	HAYATDAVOODI, A, SHANMUGAM N E. Web buckling and ultimate strength of composite plate girders subjected to shear and bending[J]. International Journal of Structural Stability and Dynamics, 2015, 1450047.
[12]	HAYATDAVOODI A, NAZARI M, JAVADI PORDESARI A. Investigation on the collapse behavior of diagonal stiffened composite plate girders subjected to shear loading[J]. International Journal of Steel Structures, 2020, 20(2): 386-399. doi: 10.1007/s13296-019-00291-7
[13]	王菲菲, 崔德刚, 熊强等. 复合材料加筋板后屈曲承载能力工程分析方法[J]. 北京航空航天大学学报, 2013, 39(4): 494-497. WANG Feifei, CUI Degang, XIONG Qiang, et al. Engineering analysis of post-buckling loading capability for composite stiffened panels[J]. Journal of Beijing University of Aeronautics and Astronautics, 2013, 39(4): 494-497(in Chinese).
[14]	王春寿, 张笑宇, 詹志新等. 复合材料厚板结构压缩稳定性和承载能力分析[J]. 北京航空航天大学学报, 2023, 1–11. WANG Chunshou, ZHANG Xiaoyu, ZHAN Zhixin, et al. The analysis of compression stability and load capacity of the thick composite plate structures[J]. Journal of Beijing University of Aeronautics and Astronautics, 2023, 1–11(in Chinese).
[15]	PEVZNER P, ABRAMOVICH H, WELLER T. Calculation of the collapse load of an axially compressed laminated composite stringer-stiffened curved panel–An engineering approach[J]. Composite Structures, 2008, 83(4): 341-353. doi: 10.1016/j.compstruct.2007.05.001
[16]	黄晓笛. 复合材料帽形加筋壁板轴压承载能力工程分析[D]. 大连理工大学, 2023. HUANG Xiaodi. Engineering analysis of axial compression load bearing capacity of composite omega stiffened panels[D]. Dalian University of Technology, 2023(in Chinese).
[17]	ZHAO W, KAPANIA R K. Buckling analysis of unitized curvilinearly stiffened composite panels[J]. Composite Structures, 2016, 135: 365-382. doi: 10.1016/j.compstruct.2015.09.041
[18]	钟博, 王新峰, 于健. 石英纤维与碳纤维混杂加筋壁板剪切后屈曲性能研究[J]. 南京航空航天大学学报, 2023, 55(6): 1111-1117. ZHONG Bo, WANG Xinfeng, YU Jian. Shear post-buckling behavior of quartz fiber and carbon fiber hybrid stiffened panels[J]. Journal of Nanjing University of Aernautics & Astrnautics, 2023, 55(6): 1111-1117(in Chinese).
[19]	FERREIRA F P V, TSAVDARIDIS K D, MARTINS C H, et al. Buckling and post-buckling analyses of composite cellular beams[J]. Composite Structures, 2021, 262: 113616. doi: 10.1016/j.compstruct.2021.113616
[20]	袁坚锋. 基于显式有限元的复合材料加筋板后屈曲分析方法研究[J]. 机械设计与制造工程, 2021, 50(4): 73-76. doi: 10.3969/j.issn.2095-509X.2021.04.016 YUAN Jianfeng. Research on post-buckling for composite stiffened panel based on explicit FEM[J]. Machine Design and Manufacturing Engineering, 2021, 50(4): 73-76(in Chinese). doi: 10.3969/j.issn.2095-509X.2021.04.016
[21]	刘存, 张磊, 杨卫平. 舰载机壁板剪切后屈曲承载能力预测与试验验证[J]. 航空学报, 2019, 40(4): 49–57. LIU Cun, ZHANG Lei, YANG Weiping. Post-buckling study and test verification of carrier-based aircraft wing stiffened panels under shear load[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40(4): 622300(in Chinese).
[22]	张连青. 压剪组合载荷下复合材料壁板屈曲性能及后屈曲承载能力分析[D]. 哈尔滨工业大学, 2021. ZHANG Lianqing. Analysis of buckling behavior and post-buckling bearing capacity of composite panels under combined compression and shear loads[D]. Harbin Institute of Technology, 2021(in Chinese).
[23]	林国伟, 李新祥. 复合材料加筋板后屈曲分析方法及实验验证[J]. 航空材料学报, 2021, 41(4): 149-156. doi: 10.11868/j.issn.1005-5053.2021.000013 LIN Guowei, LI Xinxiang. Post-buckling analysis method of stiffened composite panels and test verification[J]. Journal of Aeronautical Materials, 2021, 41(4): 149-156(in Chinese). doi: 10.11868/j.issn.1005-5053.2021.000013
[24]	CAMANHO P P, MATTHEWS F L. A progressive damage model for mechanically fastened joints in composite laminates[J]. Journal of composite materials, 1999, 33(24): 2248-2280. doi: 10.1177/002199839903302402
[25]	CHANG F K, Lessard L B. Damage tolerance of laminated composites containing an open hole and subjected to compressive loadings: Part I—Analysis[J]. Journal of composite materials, 1991, 25(1): 2-43. doi: 10.1177/002199839102500101
[26]	崔进, 肖文莹, 李想. 船体复合材料帽型加筋板渐进破坏分析[J]. 舰船科学技术, 2021, 43(3): 20-25. doi: 10.3404/j.issn.1672-7649.2021.02.004 CUI Jin, XIAO Wen-ying, LI Xiang. Progressive failure of hat-stringer-stiffened composite panel in the hull[J]. Ship Science and Technology, 2021, 43(3): 20-25(in Chinese). doi: 10.3404/j.issn.1672-7649.2021.02.004
[27]	邹华民. 含初始分层缺陷复合材料加筋壁板承载性能分析[D]. 大连理工大学, 2018. ZOU Huamin. Bearing Capacity Analysis of Composite Stiffened Panels with Initial Delamination Defects [D]. Dalian University of Technology, 2018(in Chinese).
[28]	邹华民, 崔向斌, 任明法, 等. 含初始脱粘缺陷复合材料加筋壁板渐进压溃过程的数值模拟[J]. 玻璃钢/复合材料, 2017, (11): 12-18. ZOU Hua-min, CUI Xiangbin, REN Mingfa, et al. Numerical simulation on progressive collapse process of composite stiffened panel with initial debonding defect[J]. FRP/CM, 2017, (11): 12-18(in Chinese).
[29]	韩庆, 宋恩鹏, 陆华等. 复合材料加筋结构后屈曲的自开发程序[J]. 复合材料学报, 2017, 34(7): 1443-1450. HAN Qing, SONG Enpeng, LU Hua, et al. Self-developed program for post-buckling of composite stiffened structures[J]. Acta Materiae Compositae Sinica, 2017, 34(7): 1443-1450(in Chinese).
[30]	ORIFICI A C, HERSZBERG I, THOMSON R S. Review of methodologies for composite material modelling incorporating failure[J]. Composite Structures, 2008, 86(1): 194-210.
[31]	王涛. 基于筋元界面的复合材料帽型加筋板失效分析[D]. 大连理工大学, 2023. WANG Tao. Failure analysis of composite hat-stiffened panels based on interface failure behavior of stiffener element [D]. Dalian University of Technology, 2023(in Chinese).
[32]	李乐坤, 张铁军, 支乐等. 湿热环境下复合材料加筋壁板压缩屈曲与后屈曲行为的有限元模拟[J]. 机械工程材料, 2023, 47(8): 93-99. doi: 10.11973/jxgccl202308015 LI Lekun, ZHANG Tiejun, ZHI Le, et al. Finite Element Modelling for Buckling and Post-Buckling Behavior of Composite Stiffened Panel during Compression in Hygrothermal Environment[J]. Materials for Mechanical Engineering, 2023, 47(8): 93-99(in Chinese). doi: 10.11973/jxgccl202308015
[33]	JI R, ZHAO L, WANG K, et al. Effects of debonding defects on the postbuckling and failure behaviors of composite stiffened panel under uniaxial compression[J]. Composite Structures, 2021, 256: 113121. doi: 10.1016/j.compstruct.2020.113121
[34]	YE Y, ZHU W, JIANG J, et al. Computational modelling of post-buckling behavior of composite T-stiffened panels with different bonding methods[J]. Composites Part B: Engineering, 2019, 166: 247-256. doi: 10.1016/j.compositesb.2018.11.137
[35]	胡波涛, 柴亚南, 陈向明等. 后屈曲复合材料加筋板筋条-蒙皮界面失效表征[J]. 机械强度, 2019, 41(6): 1473-1479. HU Botao, CHAI Yanan, CHEN Xiangming, et al. Stiffener-skin interface failure characterization of the stiffened composite panel at post-buckling stage[J]. Journal of Mechanical Strength, 2019, 41(6): 1473-1479(in Chinese).
[36]	VAN DOOREN K, BISAGNI C. Design, analysis and testing of thermoplastic welded stiffened panels to investigate skin-stringer separation in post-buckling[J]. Composites Part B: Engineering, 2023, 267: 111033. doi: 10.1016/j.compositesb.2023.111033
[37]	VAN DOOREN K S, TIJS B H A H, WALESON J E A, et al. Skin-stringer separation in post-buckling of butt-joint stiffened thermoplastic composite panels[J]. Composite Structures, 2023, 304: 116294. doi: 10.1016/j.compstruct.2022.116294
[38]	BERTOLINI J, CASTANIÉ B, BARRAU J-J, et al. An experimental and numerical study on omega stringer debonding[J]. Composite Structures, 2008, 86(1): 233-242.
[39]	RAIMONDO A, DOESBURG S A, BISAGNI C. Numerical study of quasi-static and fatigue delamination growth in a post-buckled composite stiffened panel[J]. Composites Part B: Engineering, 2020, 182: 107589. doi: 10.1016/j.compositesb.2019.107589
[40]	田甜, 张帆, 许健. 复合材料加筋壁板压缩试验研究与仿真分析[J]. 科技创新与应用, 2018, (5): 45-46. TIAN Tian, ZHANG Fan, XU Jian. Compression test research and simulation analysis of composite stiffened panel[J]. Technology Innovation and Application, 2018, (5): 45-46(in Chinese).
[41]	杜洪雨, 奚晓波, 孟力华等. 含分层损伤的复合材料层压板后屈曲及低周疲劳分层扩展有限元模拟研究[J]. 玻璃钢/复合材料, 2018, (6): 39-43. DU Hongyu, XI Xiaobo, MENG Lihua, et al. Finite element analysis of post-buckled delamination of composite laminate with preliminary debond subjected to static and fatigue loads[J]. FRP/CM, 2018, (6): 39-43(in Chinese).
[42]	DÁVILA C G, BISAGNI C. Fatigue life and damage tolerance of postbuckled composite stiffened structures with initial delamination[J]. Composite Structures, 2017, 161: 73-84. doi: 10.1016/j.compstruct.2016.11.033
[43]	唐劼尧, 柏敏建. 轴压载荷下复合材料蜂窝夹芯板的稳定性研究[J]. 兵器装备工程学报, 2020, 41(9): 242-246. doi: 10.11809/bqzbgcxb2020.09.045 TANG Jieyao, BAI Minjian. Stability evaluation on composite honeycomb sandwich panels subjected to compressive loadings[J]. Journal of Ordnance Equipment Engineering, 2020, 41(9): 242-246(in Chinese). doi: 10.11809/bqzbgcxb2020.09.045
[44]	李晓文, 朱兆一, 李妍等. 船舶复合材料加筋板屈曲和后屈曲行为研究[J]. 中国造船, 2020, 61(3): 186-194. doi: 10.3969/j.issn.1000-4882.2020.03.020 LI Xiaowen, ZHU Zhaoyi, LI Yan, et al. Research on buckling and post buckling behavior of composite stiffened panel for ships[J]. Shipbuilding of China, 2020, 61(3): 186-194(in Chinese). doi: 10.3969/j.issn.1000-4882.2020.03.020
[45]	KOLANU N R, RAJU G, RAMJI M. Experimental and numerical studies on the buckling and post-buckling behavior of single blade-stiffened CFRP panels[J]. Composite Structures, 2018, 196: 135-154. doi: 10.1016/j.compstruct.2018.05.015
[46]	孙中雷, 张国凡, 李军鹏. 轴压载荷下复合材料加筋板后屈曲承载能力研究[J]. 航空计算技术, 2016, 46(3): 63-66. doi: 10.3969/j.issn.1671-654X.2016.03.016 SUN Zhonglei, ZHANG Guofan, LI Junpeng. Study on loading capacity of composite panels under uniaxial compression[J]. Aeronautical Computing Technique, 2016, 46(3): 63-66(in Chinese). doi: 10.3969/j.issn.1671-654X.2016.03.016
[47]	张修路, 黄文超, 方采文等. 飞机复合材料加筋壁板结构屈曲和后屈曲研究[J]. 计算机仿真, 2020, 37(12): 230-234+408. doi: 10.3969/j.issn.1006-9348.2020.12.048 ZHANG Xiulu, HUANG Wenchao, Fang Caiwen, et al. The investigation on buckling and post buckling of aircraft composite panel structure[J]. Computer Simulation, 2020, 37(12): 230-234+408(in Chinese). doi: 10.3969/j.issn.1006-9348.2020.12.048
[48]	林国伟, 李新祥. 复合材料壁板后屈曲分析失效准则的适用性研究[J]. 机械强度, 2020, 42(3): 565-572. LIN Guowei, LI Xinxiang. Applicability investigation of failure criterion for post-buckling analysis of stiffened composite panels[J]. Journal of Mechanical Strength, 2020, 42(3): 565-572(in Chinese).
[49]	LIAN C, WANG P, ZHANG K, et al. Experimental and numerical research on the calculation methods for buckling and post-buckling of aircraft tail inclined stiffened panel under compression load[J]. Aerospace Science and Technology, 2024, 146: 108930. doi: 10.1016/j.ast.2024.108930
[50]	LIAN C, WANG P, CHEN X, et al. Experimental and numerical research on the analysis methods for buckling and post-buckling of inclined stiffened panel under shear load[J]. Thin-Walled Structures, 2024, 195: 111374. doi: 10.1016/j.tws.2023.111374
[51]	王维阳, 李伟, 曹奇凯. 复合材料加筋板轴压后屈曲及承载有限元分析[J]. 计算机仿真, 2022, 39(5): 474-479. doi: 10.3969/j.issn.1006-9348.2022.05.095 WANG Weiyang, LI Wei, CAO Qikai. Finite element analysis of post-buckling and bearing capability of composite stiffened plates under axial compression[J]. Computer Simulation, 2022, 39(5): 474-479(in Chinese). doi: 10.3969/j.issn.1006-9348.2022.05.095
[52]	李小乐. 含开口复合材料层合板的剪切承载及后屈曲渐进损伤研究[D]. 哈尔滨工业大学, 2019. LI Xiaole. Bearing characteristics and post-buckling progressive failure behavior of composite laminate with cutout under shear load [D]. Harbin Institute of Technology, 2019(in Chinese).
[53]	SUN W, GUAN Z, LI Z, et al. Modelling and simulating of the compressive behavior of T-stiffened composite panels subjected to stiffener impact[J]. Composite Structures, 2018, 186: 221-232. doi: 10.1016/j.compstruct.2017.11.079
[54]	黎汉华. 复合材料格栅加筋结构损伤对力学性能影响研究[D]. 哈尔滨工业大学, 2021. LI Hanhua. Influence of damage on mechanical properties of composite grid reinforced structure[D]. Harbin Institute of Technology, 2021(in Chinese).
[55]	杨钧超, 王雪明, 陈向明等. 低速冲击损伤对复材加筋板压缩性能的影响[J]. 航空学报, 2023, 44(20): 248-263. doi: 10.7527/S1000-6893.2023.28498 YANG Junchao, WANG Xueming, CHEN Xiangming, et al. Effect of low-velocity impact damage on compressive properties of composite stiffened panels[J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(20): 248-263(in Chinese). doi: 10.7527/S1000-6893.2023.28498
[56]	杨钧超, 陈向明, 邹鹏等. 复合材料层合板剪切稳定性试验及强度预测[J]. 复合材料学报, 2023, 40(3): 1707-1717. YANG Junchao, CHEN Xiangming, ZOU Peng, et al. Shear stability test and strength prediction of composite laminates[J]. Acta Materiae Compositae Sinica, 2023, 40(3): 1707-1717(in Chinese).
[57]	MASOOD S N, VISHAKH R, VISWAMURTHY S R, et al. Influence of stiffener configuration on post-buckled response of composite panels with impact damages[J]. Composite Structures, 2018, 194: 433-444. doi: 10.1016/j.compstruct.2018.04.005
[58]	WU Q, HU S, TANG X, et al. Compressive buckling and post-buckling behaviors of J-type composite stiffened panel before and after impact load[J]. Composite Structures, 2023, 304: 116339. doi: 10.1016/j.compstruct.2022.116339
[59]	胡少杰. J型复合材料加筋板压缩屈曲及后屈曲行为研究[D]. 哈尔滨工业大学, 2022. HU Shaojie. Research on compression buckling and post-buckling behavior of j-type composite stiffened plate[D]. Harbin Institute of Technology, 2022(in Chinese).
[60]	WANG X M, CAO W, DENG C H, et al. Experimental and numerical analysis for the post-buckling behavior of stiffened composite panels with impact damage[J]. Composite Structures, 2015, 133: 840-846. doi: 10.1016/j.compstruct.2015.08.019
[61]	付新卫, 刘瑞同, 戴瑛. 夹具对复合材料加筋板剪切试验屈曲载荷的影响[J]. 力学季刊, 2011, 32(4): 563-569. FU Xinwei, LIU Ruitong, DAI Ying. Effects of support fixture on the buckling loads in shear test of stiffened composites plate[J]. Chinese Quarterly of Mechanics, 2011, 32(4): 563-569(in Chinese).
[62]	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): 148-156. 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): 148-156 (in Chinese).
[63]	WANG Y, ZHU S. Effect of Stringer Design on the Stability of Stiffened Composite Panel Under In-plane Shear: An Experimental Study[J]. International Journal of Aeronautical and Space Sciences, 2021, 22(3): 590-601. doi: 10.1007/s42405-020-00332-0
[64]	YILDIRIM E G, ÜNAL R. A Review on Post – Buckling Behaviors of Composites: Crippling Phenomenon Kompozitlerin Son Burkulma Davranışı Üzerine Bir İnceleme: Burkulma Sonrası Dayanım Olgusu[J]. 2024.
[65]	FENG Y, WANG W, LU S, et al. Axial compressive performances of stiffened composite panels: Experimental and numerical study[J]. Alexandria Engineering Journal, 2023, 71: 115-130. doi: 10.1016/j.aej.2023.03.047
[66]	刘达. 加筋板屈曲及后屈曲行为的相移编码条纹投影测量方法研究[D]. 大连理工大学, 2022. LIU Da. Study on measurement method of buckling and post-buckling behavior of stiffened panels via phase-shift coding fringe projection profilometry[D]. Dalian University of Technology, 2022(in Chinese).
[67]	胡嘉桐, 余明. 国产T800H复合材料加筋壁板压缩破坏试验研究及数值仿真分析[J]. 机械设计与研究, 2022, 38(6): 98-103+109. HU Jiatong, YU Ming. Destruction test and numerical simulation analysis of homegrown t800h composite stiffened panel under compression[J]. Machine Design and Research, 2022, 38(6): 98-103+109(in Chinese).
[68]	高伟, 刘存, 张文军等. 不同长桁截面复合材料加筋板轴压屈曲分析[J]. 力学与实践, 2022, 44(5): 1143-1150. doi: 10.6052/1000-0879-21-521 GAO Wei, LIU Cun, ZHANG Wenjun, et al. Axial compression buckling of stiffened panel of composite materials with different stringer section[J]. Mechanics in Engineering, 2022, 44(5): 1143-1150(in Chinese). doi: 10.6052/1000-0879-21-521
[69]	FENG Y, MA B, CUI R, et al. Effects of hygrothermal environment on the buckling and postbuckling performances of stiffened composite panels under axial compression[J]. Composite Structures, 2020, 242: 112132. doi: 10.1016/j.compstruct.2020.112132
[70]	张国凡. 复合材料加筋壁板结构屈曲承载特性研究[D]. 西北工业大学, 2020. ZHANG Guofan. Study on buckling behavior of stiffened composite panels[D]. Northwestern Polytechnical University, 2020(in Chinese).
[71]	阳奥, 陈普会, 孔斌, 等. 数字图像相关技术在复合材料加筋曲板压缩试验中的应用[J]. 复合材料学报, 2020, 37(10): 2439-2451. YANG Ao, CHEN Puhui, KONG Bin, et al. Application of digital image correlation technology in compression test of stringer stiffened composite curved panels[J]. Acta Materiae Compositae Sinica, 2020, 37(10): 2439-2451(in Chinese).
[72]	王彩英, 白瑞祥, 雷振坤. 工字型加筋复合材料壁板的压缩屈曲行为实验研究[J]. 实验力学, 2018, 33(5): 725-733. doi: 10.7520/1001-4888-18-030 WANG Caiying, BAI Ruixiang, LEI Zhen-kun. Experimental study on compression buckling behavior of I-shaped rib stiffened composite panel[J]. Journal of Experimental Mechanics, 2018, 33(5): 725-733(in Chinese). doi: 10.7520/1001-4888-18-030
[73]	Laurin F, Charrier J-S, Lévêque D, et al. Determination of the Properties of Composite Materials Thanks to Digital Image Correlation Measurements[J]. Procedia IUTAM, 2012, 4: 106-115. doi: 10.1016/j.piutam.2012.05.012
[74]	NADEEM MASOOD S, VISWAMURTHY S R, GADDIKERI K M. Composites airframe panel design for post-buckling – An experimental investigation[J]. Composite Structures, 2020, 241: 112104. doi: 10.1016/j.compstruct.2020.112104
[75]	汪厚冰, 李新祥, 魏景超等. 复合材料曲面帽形加筋壁板在内压-轴压联合载荷下的屈曲及承载性能[J]. 航空制造技术, 2020, 63(18): 55-64+81. WANG Houbing, LI Xinxiang, WEI Jingchao, et al. Buckling and post-buckling of curved hat-stiffened composite panels under combined internal pressure and axial compression[J]. Aeronautical Manufacturing Technology, 2020, 63(18): 55-64+81(in Chinese).
[76]	高志刚, 冯宇, 马斌麟等. 航空复合材料加筋板压缩屈曲及后屈曲力学性能[J]. 航空材料学报, 2020, 40(1): 53-61. doi: 10.11868/j.issn.1005-5053.2019.000067 GAO Zhigang, FENG Yu, MA Binlin, et al. Compressive bucking and post-bucking mechanical properties of aeronautic composite stiffened panel[J]. Journal of Aeronautical Materials, 2020, 40(1): 53-61(in Chinese). doi: 10.11868/j.issn.1005-5053.2019.000067
[77]	汪厚冰, 陈昊, 雷安民等. 复合材料帽形加筋壁板轴压屈曲与后屈曲性能[J]. 复合材料学报, 2018, 35(8): 2014-2022. WANG Houbing, CHEN Hao, LEI Anming, et al. Buckling and post-buckling performance of hat-stiffened composite panels under axial compression load[J]. Acta Materiae Compositae Sinica, 2018, 35(8): 2014-2022(in Chinese).
[78]	MO Y, GE D, HE B. Experiment and optimization of the hat-stringer-stiffened composite panels under axial compression[J]. Composites Part B: Engineering, 2016, 84: 285-293. doi: 10.1016/j.compositesb.2015.08.039
[79]	张浩宇, 何宇廷, 冯宇, 等. 先进复合材料薄壁加筋板轴压屈曲特性及后屈曲承载性能[J]. 航空材料学报, 2016, 36(4): 55-63. doi: 10.11868/j.issn.1005-5053.2016.4.008 ZHANG Haoyu, HE Yuting, FENG Yu, et al. Buckling and post-buckling performance of advanced composite stiffened panel under compression[J]. Journal of Aeronautical Materials, 2016, 36(4): 55-63(in Chinese). doi: 10.11868/j.issn.1005-5053.2016.4.008
[80]	谭翔飞, 何宇廷, 冯宇, 等. 航空碳纤维树脂基复合材料加筋板压缩屈曲及后屈曲性能[J]. 航空动力学报, 2016, 31(10): 2359-2369. TAN Xiangfei, HE Yuting, FENG Yu, et al. Buckling and post-buckling performance of aeronautic carbon fiber reinforced resin composite stiffened panel under compression[J]. Journal of Aerospace Power, 2016, 31(10): 2359-2369(in Chinese).
[81]	ZHU S, YAN J, CHEN Z, et al. Effect of the stiffener stiffness on the buckling and post-buckling behavior of stiffened composite panels–Experimental investigation[J]. Composite Structures, 2015, 120: 334-345. doi: 10.1016/j.compstruct.2014.10.021
[82]	石经纬, 赵娟, 刘传军, 等. 复合材料翼面壁板剪切稳定性[J]. 复合材料学报, 2020, 37(7): 1590-1600. SHI Jingwei, ZHAO Juan, LIU Chuanjun, et al. Stability of composite stiffened panels in plane shear[J]. Acta Materiae Compositae Sinica, 2020, 37(7): 1590-1600(in Chinese).
[83]	杨钧超, 柴亚南, 陈向明, 等. 复合材料加筋板剪切屈曲与后屈曲承载特性[J]. 科学技术与工程, 2019, 19(7): 289-293. doi: 10.3969/j.issn.1671-1815.2019.07.048 YANG Junchao, CHAI Yanan, CHEN Xiangming, et al. Shear buckling and post-buckling behavior of composite stiffened panels[J]. Science Technology and Engineering, 2019, 19(7): 289-293(in Chinese). doi: 10.3969/j.issn.1671-1815.2019.07.048
[84]	谭翔飞, 何宇廷, 冯宇, 等. 航空复合材料加筋板剪切稳定性及后屈曲承载性能[J]. 复合材料学报, 2018, 35(2): 320-331. TAN Xiangfei, HE Yuting, FENG Yu, et al. Stability and post-buckling carrying capacity of aeronautic composite stiffened panel under shear loading[J]. Acta Materiae Compositae Sinica, 2018, 35(2): 320-331(in Chinese).
[85]	张国凡, 孙侠生, 孙中雷. 复合材料加筋壁板剪切破坏试验与后屈曲分析[J]. 机械科学与技术, 2016, 35(8): 1280-1285. ZHANG Guofan, SUN Xiasheng, SUN Zhonglei. Failure test and post-buckling analysis of composite stiffened panels under shear load[J]. Mechanical Science and Technology for Aerospace Engineering, 2016, 35(8): 1280-1285(in Chinese).
[86]	RAY B C. Temperature effect during humid ageing on interfaces of glass and carbon fibers reinforced epoxy composites[J]. Journal of Colloid and Interface Science, 2006, 298(1): 111-117. doi: 10.1016/j.jcis.2005.12.023
[87]	CHEN L, ZHUO Y, XU R, et al. Buckling and Post-buckling Characteristics of Stiffened Panels Under Compression-Shear Load[J]. Journal of Physics: Conference Series, IOP Publishing, 2022, 2403(1): 012008. doi: 10.1088/1742-6596/2403/1/012008
[88]	党乐, 郑洁, 杜凯, 等. 复合材料多墙盒段弯扭耦合下的屈曲和后屈曲[J]. 力学季刊, 2022, 43(2): 271-280. DANG Le, ZHENG Jie, DU Kai, et al. Buckling and post buckling of composite multi-wall box section under bending-torsion coupled loads[J]. Chinese Quarterly Of Mechanics, 2022, 43(2): 271-280(in Chinese).
[89]	袁菲, 柴亚南, 张阿盈. 复合材料多墙盒段后屈曲的破坏预测方法[J]. 机械强度, 2018, 40(5): 1090-1096. YUAN Fei, CHAI YaNan, ZHANG AYing. Prediction and damage analysis of the postbuckling for multi-spar composite box[J]. Journal of Mechanical Strength, 2018, 40(5): 1090-1096(in Chinese).
[90]	BISAGNI C, DÁVILA C G. Experimental investigation of the postbuckling response and collapse of a single-stringer specimen[J]. Composite Structures, 2014, 108: 493-503. doi: 10.1016/j.compstruct.2013.09.018
[91]	LIU X, HAN K, BAI R, et al. Buckling measurement and numerical analysis of M-type ribs stiffened composite panel[J]. Thin-Walled Structures, 2014, 85: 117-124. doi: 10.1016/j.tws.2014.08.008
[92]	FENG Y, ZHANG H, TAN X, et al. Effect of impact damage positions on the buckling and post-buckling behaviors of stiffened composite panel[J]. Composite Structures, 2016, 155: 184-196. doi: 10.1016/j.compstruct.2016.08.012
[93]	SUN W, GUAN Z, OUYANG T, et al. Effect of stiffener damage caused by low velocity impact on compressive buckling and failure modes of T-stiffened composite panels[J]. Composite Structures, 2018, 184: 198-210. doi: 10.1016/j.compstruct.2017.09.084
[94]	MEEKS C, GREENHALGH E, FALZON B G. Stiffener debonding mechanisms in post-buckled CFRP aerospace panels[J]. Composites Part A: Applied Science and Manufacturing, 2005, 36(7): 934-946. doi: 10.1016/j.compositesa.2004.12.003
[95]	TAN R, XU J, GUAN Z, et al. Experimental study on effect of impact locations on damage formation and compression behavior of stiffened composite panels with L-shaped stiffener[J]. Thin-Walled Structures, 2020, 150: 106707. doi: 10.1016/j.tws.2020.106707
[96]	FENG Y, HE Y, TAN X, et al. Experimental investigation on different positional impact damages and shear-after-impact (SAI) behaviors of stiffened composite panels[J]. Composite Structures, 2017, 178: 232-245. doi: 10.1016/j.compstruct.2017.06.053
[97]	肖浩, 胡伟平, 张淼, 等. 薄板的后屈曲损伤分析与疲劳寿命预估[J]. 北京航空航天大学学, 2015, 41(3): 523-529. XIAO Hao, HU Weiping, ZHANG Miao, et al. Post-buckling damage analysis and fatigue life prediction of thin plate[J]. Journal of Beijing University of Aeronautics and Astronautics, 2015, 41(3): 523-529(in Chinese).
[98]	张彦军, 朱亮, 杨卫平, 等. 舰载机机身加筋壁板屈曲疲劳试验[J]. 航空学报, 2019, 40(4): 40-48. ZHANG Yanjun, ZHU Liang, YANG Weiping, et al. Buckling fatigue test of fuselage stiffened panel for carrier-based aircraft[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40(4): 40-48(in Chinese).
[99]	薛景川, 贺恭泰, 宋湘臣, 等. 薄壁结构剪切屈曲疲劳研究[J]. 航空学报, 1989, (12): 607-613. doi: 10.3321/j.issn:1000-6893.1989.12.008 XUE Jingchuan, HE Gongtai, SONG Xiangchen, et al. A study of shear-buckling fatigue for thin-walled structures[J]. Acta Aeronautica et Astronautica Sinica, 1989, (12): 607-613(in Chinese). doi: 10.3321/j.issn:1000-6893.1989.12.008
[100]	成传贤. 飞机壁板屈曲疲劳试验与结果分析[J]. 机械强度, 1988, (3): 48-51+47. CHENG Chuanxian. Buckling fatigue testing and analysis of results of aircraft plate[J]. Mechanical Strength, 1988, (3): 48-51+47(in Chinese).
[101]	苏少普, 常文魁, 陈先民. 飞机典型壁板结构剪切屈曲疲劳试验与分析方法[J]. 航空学报, 2022, 43(5): 274–283. SU Shaopu, CHANG Wenkui, CHEN Xian-ming. Fatigue buckling test and analytical ap-proach of aircraft typical panel structures[J]. Acta Aeronautica et Astronauti-ca, Sinica, 2022, 43(5): 225219 (in Chinese).