Please wait a minute...
Journal of ZheJiang University (Engineering Science)  2020, Vol. 54 Issue (7): 1341-1346    DOI: 10.3785/j.issn.1008-973X.2020.07.012
Design and performance analysis of variable stiffness multi-stable composite laminate structure
Zheng ZHANG1(),Hao ZHANG1,Hao CHAI2,Hua-ping WU1,Shao-fei JIANG1
1. College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou 310014, China
2. College of Mechanical Engineering, Zhijiang College of Zhejiang University of Technology, Shaoxing 312030, China
Download: HTML     PDF(972KB) HTML
Export: BibTeX | EndNote (RIS)      


Two variable stiffness multi-stable composite laminate structures were designed by analyzing the relationship between the theoretical model of regional fiber angle change and the stiffness change of composite structures. The variable stiffness multi-stable composite structure was modeled, and the stable configuration of the multi-stable composite structures with variable stiffness was obtained by solving different equilibrium equations with Matlab. The experimental specimens were prepared to measure the mechanical properties with different stable transformation. The cooling process were simulated by finite element software Abaqus, and the numerical results of equilibrium stable configuration were obtained. The stable configuration, the stable transformation maximum load and the load-displacement curvatures were analyzed by combining with the theoretical, numerical and experimental results.

Key wordsvariable stiffness      multi-stable composite structure      classical laminate theory      finite element analysis     
Received: 09 March 2019      Published: 05 July 2020
CLC:  TB 332  
Cite this article:

Zheng ZHANG,Hao ZHANG,Hao CHAI,Hua-ping WU,Shao-fei JIANG. Design and performance analysis of variable stiffness multi-stable composite laminate structure. Journal of ZheJiang University (Engineering Science), 2020, 54(7): 1341-1346.

URL:     OR


通过研究复合材料层合板结构局部纤维角变化的理论模型与刚度变化的关系,设计2种变刚度多稳态复合材料层合板结构. 对变刚度多稳态复合材料结构进行建模,运用Matlab求出不同的平衡方程解,得到变刚度多稳态复合材料结构的稳态构型. 制备相应的实验试件,测量变刚度多稳态复合材料结构不同稳态转变时的力学性能,通过有限元软件Abaqus模拟变刚度多稳态复合材料结构的降温冷却过程,得到平衡稳定状态的数值解. 结合理论、数值与试验,分析变刚度多稳态复合材料结构的稳态构型、稳态转变最大载荷及载荷-位移曲线的变化规律.

关键词: 变刚度,  多稳态复合材料,  经典层合板理论,  有限元分析 
参数 数值
E11/GPa 186
E22/GPa 88
v12 0.3
G12/GPa 7.1
ɑ11/(10?6°C?1 0.345
ɑ22/(10?6°C?1 15.3
Tab.1 Material properties of carbon fibre laminates
Fig.1 Schematic diagram of fiber direction of variable stiffness multi-stable composite laminate structures
Fig.2 Processing equipment with constant temperature and pressure
Fig.3 Stable diagram of specimen 1
Fig.4 Stable diagram of specimen 2
Fig.5 Experiment of stable state transformation
Fig.6 Indenter and fixture
Fig.7 Load-displacement curvatures of two specimens
Fig.8 Comparison of second stable configuration of theoretical and simulation results for specimen 1
Fig.9 Two different stable configurations of specimen 1 in simulation and experiment specimen
Fig.10 Two different stable configurations of specimen 2 in simulation and experiment specimen
Fig.11 Comparison of load-displacement with experiment and simulation for specimen 2
[1]   KUDER I K, ARRIETA A F, RIST M, et al Aeroelastic response of a selectively compliant morphing aerofoil featuring integrated variable stiffness bi-stable laminates[J]. Journal of Intelligent Material Systems and Structures, 2016, 27 (14): 1949- 1966
doi: 10.1177/1045389X15620038
[2]   SOUSA C S, CAMANHO P P, SULEMAN A Analysis of multistable variable stiffness composite plates[J]. Composite Structures, 2013, 98 (3): 34- 46
[3]   WALDHART C. Analysis of tow-placed, variable-stiffness laminates [D]. Virginia: Virginia Tech, 1996.
[4]   GURDAL Z, OLMEDO R In-plane response of laminates with spatially varying fiber orientations-variable stiffness concept[J]. American Institute of Aeronautics and Astronautics Journal, 1993, 31 (4): 751- 758
doi: 10.2514/3.11613
[5]   GURDAL Z, TATTING B F, WU C K Variable stiffness composite panels: effects of stiffness variation on the in-plane and buckling response[J]. Composites Part A: Applied Science and Manufacturing, 2008, 39 (5): 911- 922
doi: 10.1016/j.compositesa.2007.11.015
[6]   BLOM A W, STICKLER P B, GURDAL Z Optimization of a composite cylinder under bending by tailoring stiffness properties in circumferential direction[J]. Composites Part B: Engineering, 2010, 41 (2): 157- 165
doi: 10.1016/j.compositesb.2009.10.004
[7]   邵忠喜. 纤维铺放装置及其铺放关键技术研究[D]. 哈尔滨: 哈尔滨工业大学, 2010.
SHAO Zhong-xi. Research on fiber laying device and its key technologies [D]. Harbin: Harbin University of Technology, 2010.
[8]   LE H M, CAO L, DO T N, et al Design and modelling of a variable stiffness manipulator for surgical robots[J]. Mechatronics, 2018, 53: 109- 123
doi: 10.1016/j.mechatronics.2018.05.012
[9]   PEETERS D M J, HESSE S, ABDALLA M M Stacking sequence optimization of variable stiffness laminates with manufacturing constraints[J]. Composite Structures, 2015, 125: 596- 604
doi: 10.1016/j.compstruct.2015.02.044
[10]   NIK M A, FAYAZBAKHSH K, PASINI D, et al Optimization of variable stiffness composites with embedded defects induced by automated fiber placement[J]. Composite Structures, 2014, 107: 160- 166
doi: 10.1016/j.compstruct.2013.07.059
[11]   KUDER I K, ARRIETA A F, ERMANNI P Design space of embeddable variable stiffness bi-stable elements for morphing applications[J]. Composite Structures, 2015, 122: 445- 455
doi: 10.1016/j.compstruct.2014.11.061
[12]   KHANI A, IJSSELMUIDEN S T, ABDALLA M M, et al Design of variable stiffness panels for maximum strength using lamination parameters[J]. Composites Part B: Engineering, 2011, 42 (3): 546- 552
doi: 10.1016/j.compositesb.2010.11.005
[13]   孔斌, 顾杰斐, 陈普会, 等 变刚度复合材料结构的设计、制造与分析[J]. 复合材料学报, 2017, 34 (10): 2121- 2133
KONG Bin, GU Jie-fei, CHEN Pu-hui, et al Design, manufacture and analysis of variable stiffness composite structures[J]. Journal of Composite Materials, 2017, 34 (10): 2121- 2133
[14]   DURAN A V, FASANELLA N A, SUNDARARAGHAVAN V, et al Thermal buckling of composite plates with spatial varying fiber orientations[J]. Composite Structures, 2015, 124: 228- 235
doi: 10.1016/j.compstruct.2014.12.065
[15]   RAHMAN T, IJSSELMUIDEN S T, ABDALLA M M, et al Postbuckling analysis of variable stiffness composite plates using a finite element-based perturbation method[J]. International Journal of Structural Stability and Dynamics, 2011, 11 (4): 735- 753
doi: 10.1142/S0219455411004324
[16]   ARRIETA A F, KUDER I K, RIST M, et al Passive load alleviation aerofoil concept with variable stiffness multi-stable composites[J]. Composite Structures, 2014, 116: 235- 242
doi: 10.1016/j.compstruct.2014.05.016
[17]   COBURN B H, WU Z, WEAVER P M Buckling analysis of stiffened variable angle tow panels[J]. Composite Structures, 2014, 111 (11): 259- 270
[18]   XIONG C, LEI Y, YAO X Dynamic experimental study of deployable composite structure[J]. Applied Composite Materials, 2011, 18 (5): 439- 448
doi: 10.1007/s10443-010-9174-7
[19]   ZHANG Z, WU H, YE G, et al Experimental study on bistable behaviour of anti-symmetric laminated cylindrical shells in thermal environments[J]. Composite Structures, 2016, 144: 24- 32
doi: 10.1016/j.compstruct.2016.02.062
[20]   ZHANG Z, WU H, YE G, et al Systematic experimental and numerical study of bistable snap processes for anti-symmetric cylindrical shells[J]. Composite Structures, 2014, 112: 368- 377
doi: 10.1016/j.compstruct.2014.02.030
[21]   LEI Y M, YAO X F Experimental study of bistable behaviors of deployable composite structure[J]. Journal of Reinforced Plastics and Composites, 2010, 29 (6): 865- 873
doi: 10.1177/0731684408100738
[22]   刘东新, 刘伟. 复合材料力学基础[M]. 西安: 西北工业大学出版社, 2010.
[23]   SCHLECHT M, SCHULTE K Advanced calculation of the room-temperature shapes of unsymmetric laminates[J]. Journal of Composite Materials, 1999, 33 (16): 1472- 1490
doi: 10.1177/002199839903301601
[24]   ARRIETA A F, KUDER I K, WAEBER T, et al Variable stiffness characteristics of embeddable multi-stable composites[J]. Composites Science and Technology, 2014, 97: 12- 18
doi: 10.1016/j.compscitech.2014.03.017
[25]   HALDAR A, REINOSO J, JANSEN E, et al Thermally induced multistable configurations of variable stiffness composite plates: Semi-analytical and finite element investigation[J]. Composite Structures, 2018, 183: 161- 175
doi: 10.1016/j.compstruct.2017.02.014
[1] Guo-hui SHEN,Yu-nan BAO,Yong GUO,Gang SONG,Yi-wen WANG. Along-line wind loads and distribution patterns of transmission lines[J]. Journal of ZheJiang University (Engineering Science), 2020, 54(9): 1658-1665.
[2] Kai-jun LOU,Feng YU,Tang-dai XIA,Jian MA. Stability analysis of diaphragm wall retained structure in clay[J]. Journal of ZheJiang University (Engineering Science), 2020, 54(9): 1697-1705.
[3] Yong CHEN,Yong-quan LI,Chong-lei XIE,Kuang-liang QIAN,Ye-sheng ZHANG,Peng-yun CHENG,Xuan-zuo YE. Pushover test study of masonry structure restrained by steel-tube-bundle shear walls[J]. Journal of ZheJiang University (Engineering Science), 2020, 54(3): 499-511.
[4] Li-guo WANG,Xu-dong SHAO,Jun-hui CAO,Yu-bao CHEN,Guang HE,Yang WANG. Performance of steel-ultrathin UHPC composite bridge deck based on ultra-short headed studs[J]. Journal of ZheJiang University (Engineering Science), 2020, 54(10): 2027-2037.
[5] Shui-guang TONG,Jia-zhi MIAO,Zhe-ming TONG,Shun HE,Shu-feng XIANG,Xiang-hui SHUAI. Finite element analysis and optimization for static and dynamic characteristics of diesel forklift frame[J]. Journal of ZheJiang University (Engineering Science), 2019, 53(9): 1637-1646.
[6] Shao-heng HE,Tang-dai XIA,Lian-xiang LI,Bing-qi YU,Ze-yong LIU. Influence of groundwater seepage on deformation of foundation pits with suspended impervious curtains[J]. Journal of ZheJiang University (Engineering Science), 2019, 53(4): 713-723.
[7] Wen-qiang DAI,Xu ZHENG,Zhi-yong HAO,Yi QIU. Prediction of high-speed train interior noise using energy finite element analysis[J]. Journal of ZheJiang University (Engineering Science), 2019, 53(12): 2396-2403.
[8] XIA Yong-qiang, XIAO Nan. Initial rotational stiffness formula of semi-rigid joint with T-stub in beam-to-column connection[J]. Journal of ZheJiang University (Engineering Science), 2018, 52(10): 1935-1942.
[9] WANG Xing, XU Wu, ZHANG Xiao-jing, ZHANG Li-na, HU Ben-run. Numerical prediction and experimental verification of fatigue life of TC4 plate strengthened by cold expansion[J]. Journal of ZheJiang University (Engineering Science), 2017, 51(8): 1610-1618.
[10] JIANG Nan, CHEN Min-you, XU Sheng-you, LAI Wei, GAO Bing. Thermal fatigue of IGBT module considering crack damage[J]. Journal of ZheJiang University (Engineering Science), 2017, 51(4): 825-833.
[11] CHEN Wei gang, DENG Hua,BAI Guangbo,DONG Shi lin, ZHU Zhong yi. Load bearing behavior of bearing joint of flat aluminum alloy lattice structures[J]. Journal of ZheJiang University (Engineering Science), 2016, 50(5): 831-840.
[12] HE Zhi ming, ZHANG Xiao jing, LIU Tian qi, YANG Shu xun. Numerical simulation of whole process of cold expansion in 300M steel lug[J]. Journal of ZheJiang University (Engineering Science), 2016, 50(4): 783-791.
[13] BI Yun bo, LI Xia, YAN Wei miao, SHEN Li heng, ZHU Yu, FANG Wei. Pressure force optimization of press foot device for orbital drilling process[J]. Journal of ZheJiang University (Engineering Science), 2016, 50(1): 102-110.
[14] WANG Jiao-jiao, SHI Yong-jiu, WANG Yuan-qing, PAN Peng, MAKINO Toshio, QI Xue. Experimental study on low yield point steel LYP100 under cyclic loading[J]. Journal of ZheJiang University (Engineering Science), 2015, 49(8): 1401-1409.
[15] ZHAO Qiong, TONG Shui-guang, ZHONG Wei, GE Jun-xu. Optimal design of luffing mechanism of portal crane based on genetic algorithm and finite element analysis[J]. Journal of ZheJiang University (Engineering Science), 2015, 49(5): 880-886.