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Cao Jinjun, Zhang Huiting, Zhang Liang, Peng Fujun, Yun Weidong. THEORETICAL PREDICTION AND EXPERIMENTAL VERIFICATION OF WRINKLE AMPLITUDE IN A SQUARE MEMBRANE SUBJECTED TO DIAGONAL TENSION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(5): 1403-1410. DOI: 10.6052/0459-1879-19-109
Citation: Cao Jinjun, Zhang Huiting, Zhang Liang, Peng Fujun, Yun Weidong. THEORETICAL PREDICTION AND EXPERIMENTAL VERIFICATION OF WRINKLE AMPLITUDE IN A SQUARE MEMBRANE SUBJECTED TO DIAGONAL TENSION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(5): 1403-1410. DOI: 10.6052/0459-1879-19-109

THEORETICAL PREDICTION AND EXPERIMENTAL VERIFICATION OF WRINKLE AMPLITUDE IN A SQUARE MEMBRANE SUBJECTED TO DIAGONAL TENSION

  • Received Date: April 26, 2019
  • Flexible membrane structures are widely used in the key parts of aerospace vehicles. Surface flatness is one of the main factors affecting the performances of membrane structures. Wrinkle amplitude is an important factor for evaluating the surface flatness of membrane reflector antennas. Wrinkle amplitude is strongly related with the transverse strain, perpendicular to wrinkling direction. Based on the stability theory of thin plates, a theoretical model is proposed to predict the wrinkle amplitude in a square membrane subjected to diagonal tension. The effect of transverse tensile force on the membrane deformation is taken into account. The displacement perpendicular to wrinkling direction is decomposed into three parts: the transverse displacement induced by Poisson's effect, the wrinkling displacement induced by out-of-plane deformation, and the tensile displacement induced by transverse tensile force. The formulation of wrinkle amplitude is reworked. Based on digital image correlation (DIC) technology, speckle experiment is carried out for a square membrane subjected to diagonal tension. The three-dimensional displacement of square membrane is measured by the binocular vision three-dimensional measurement system. The three-dimensional deformed shapes and wrinkle waveforms of membrane are obtained. We study the nonlinear relationship between wrinkle amplitudes and tensile loads. Compared with an existing model, our model greatly improves the accuracy of prediction to wrinkle amplitude, which is in good agreement with experimental results. The theoretical research presented in this paper can provide valuable guidance for the establishment of a fine numerical model and the implementation of algorithm.
  • [1] 刘惠祥, 何国毅, 王琦 . 蜻蜓滑翔时柔性褶皱前翅气动特性分析. 力学学报, 2019,51(1):94-102
    [1] ( Liu Huixiang, He Guoyi, Wang Qi . Numerical study on the aerodynamic performance of the flexible and corrugated forewing of dragonfly in gilding flight. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(1):94-102 (in Chinese))
    [2] Li B, Cao YP, Feng XQ , et al. Surface wrinkling of mucosa induced by volumetric growth: Theory, simulation and experiment. Journal of Mechanics and Physics of Solids, 2011,59(4):758-774
    [3] Zhang C, Li B, Huang X , et al. Morphomechanics of bacterial biofilms undergoing anisotropic differential growth. Applied Physics Letters, 2016,109:143701
    [4] Peng ZL, Yang YZ, Chen SH . Coupled effects of the temperature and the relative humidity on gecko adhesion. Journal of Physics D : Applied Physics, 2017,50:315402
    [5] 胡海岩 . 太阳帆航天器的关键技术. 深空探测学报, 2016,3(4):334-344
    [5] ( Hu Haiyan . Key technologies of solar sail spacecraft. Journal of Deep Space Exploration, 2016,3(4):334-344 (in Chinese))
    [6] Lian PY, Duan BY, Wang W , et al. A pattern approximation method for distorted reflector antennas using piecewise linear fitting of the exponential error term. IEEE Transactions on Antennas and Propagation, 2015,63(10):4546-4551
    [7] Geppert U, Biering B, Lura F , et al. The 3-step DLR-ESA gossamer road to solar sailing. Advances in Space Research, 2011,48:1695-1701
    [8] 谢超, 严飙, 刘钰 等. 大型星载薄膜天线高精度制造技术研究. 载人航天, 2018,24(1):79-83
    [8] ( Xie Chao, Yan Biao, Liu Yu , et al. High precision manufacturing technology for space-based membrane antennas. Manned Spaceflight, 2018,24(1):79-83 (in Chinese))
    [9] Mansfield EH . Tension field theory a new approach which shows its duality with inextensional theory. Proceedings of the 12th International Congress Applied Mechanics, 1968, 305-320
    [10] Steigmann DJ . Tension field theory. Proceedings of the Royal Society of London Part A, 1990,429(1867):141-173
    [11] 李云良, 田振辉, 谭惠丰 . 基于张力场理论的薄膜褶皱研究评述. 力学与实践, 2008,30(4):8-14
    [11] ( Li Yunliang, Tian Zhenhui, Tan Huifeng . Review of methods of wrinkle studies based on tension field theory. Mechanics in Engineering, 2008,30(4):8-14 (in Chinese))
    [12] Stein M, Hedgepeth JM. Analysis of partly wrinkled membranes. NASA, Tech Note , 1961, D-813
    [13] Pipkin AC . Relaxed energy density for isotropic elastic membranes. IMA Journal of Applied Mathematics, 1986,36:85-99
    [14] Roddeman DG, Drukker J, Oomens CW , et al. The wrinkling of thin membrane part I: Theory. Journal of Applied Mechanics, 1987,54:884-887
    [15] Zhang L, Gao Q, Zhang HW . Analysis of 2-D bimodular materials and wrinkled membranes based on the parametric variational principle and co-rotational approach. International Journal for Numerical Methods in Engineering, 2014,98(10):721-746
    [16] Du ZL, Zhang YP, Zhang WS , et al. A new computational framework for materials with different mechanical responses in tension and compression and its applications. International Journal of Solids and Structures, 2016,100(1):54-73
    [17] Shi JB, Liu ZY, Hong ZY . Multibody dynamic analysis using a rotation-free shell element with corotational frame. Acta Mechanica Sinica, 2018,34(4):769-780
    [18] 冯西桥, 曹艳平, 李博 . 软材料表面失稳力学. 北京: 科学出版社, 2017
    [18] ( Feng Xiqiao, Cao Yanping, Li Bo. Surface Wrinkling Mechanics of Soft Materials. Beijing: Science Press, 2017 (in Chinese))
    [19] 李博 . 软物质材料的表面失稳研究. [博士论文]. 北京:清华大学, 2011: 15-32
    [19] ( Li Bo . Studies on surface instability of soft matters. [PhD Thesis]. Beijing: Tsinghua University, 2011: 15-32 (in Chinese))
    [20] 黄春阳, 唐山, 彭向和 . 超弹性薄膜与可压缩基底双层结构表面失稳分析. 力学学报, 2017,49(4):758-762
    [20] ( Huang Chunyang, Tang Shan, Peng Xianghe . Study of surface instability about hyperelastic films on auxetic substrates under compression. Chinese Journal of Theoretical and Applied Mechanics, 2017,49(4):758-762 (in Chinese))
    [21] Cerda E, Ravi CK, Mahadevan L . Wrinkling of an elastic sheet under tension. Nature, 2002,419:579-580
    [22] Cerda E, Mahadevan L . Geometry and physics of wrinkling. Physical Review Letters, 2003,90(7):1-4
    [23] Wong YW, Pellegrino S . Wrinkled membranes part II: Analytical models. Journal of Mechanics of Materials and Structures, 2006,1(1):24-59
    [24] 王长国 . 空间薄膜结构皱曲行为与特性研究. [博士论文]. 哈尔滨:哈尔滨工业大学, 2007: 85-96
    [24] ( Wang Changguo . Study on wrinkling behavior and characteristic of space membrane. [PhD Thesis]. Harbin: Harbin Institute of Technology, 2007: 85-96 (in Chinese))
    [25] Wang CG, Du XW, Wan ZM . An experimental study on wrinkling behaviors and characteristics of gossamer space structures. Strain, 2007,43:332-339
    [26] Lan L, Wang CG, Tan HF . Experiment and evaluation of wrinkling strain in a corner tensioned square membrane. Acta Mechanica Sinica, 2014,30(3):430-436
    [27] Liu YP, Guo K, Wang CG , et al. Wrinkling and ratcheting of a thin film on cyclically deforming plastic substrate: mechanical instability of the solid-electrolyte interphase in Li-ion batteries. Journal of the Mechanics and Physics of Solids, 2019,123:103-118
    [28] 马瑞, 杨庆山, 王晓峰 . 基于稳定理论的剪切薄膜屈曲分析. 力学学报, 2014,46(1):114-119
    [28] ( Ma Rui, Yang Qingshan, Wang Xiaofeng . Chinese Journal of Theoretical and Applied Mechanics, 2014,46(1):114-119 (in Chinese))
    [29] Yang YF, Dai HH, Xu F , et al. Pattern transitions in a soft cylindrical shell. Physical Review Letters, 2018,120:215503
    [30] Fu C, Wang T, Xu F , et al. A modeling and resolution framework for wrinkling in hyperelastic sheets at finite membrane strain. Journal of the Mechanics and Physics of Solids, 2019,124:446-470
    [31] Taylor M, Bertoldi K, Steigmann DJ . Spatial resolution of wrinkle patterns in thin elastic sheets at finite strain. Journal of the Mechanics and Physics of Solids, 2014,62:163-180
    [32] Taylor M, Davidovitch B, Qiu ZL , et al. A comparative analysis of numerical approaches to the mechanics of elastic sheets. Journal of the Mechanics and Physics of Solids, 2015,79:92-107
    [33] 王长国, 杜星文, 赫晓东 . 空间充气薄膜结构的褶皱分析. 力学学报, 2008,40(3):331-338
    [33] ( Wang Changguo, Du Xingwen, He Xiaodong . Wrinkling analysis of space inflatable membrane structures. Chinese Journal of Theoretical and Applied Mechanics, 2008,40(3):331-338 (in Chinese))
    [34] 徐芝纶. 弹性力学(下册)( 第五版 ) . 北京:高等教育出版社, 2016
    [34] ( Xu Zhilun. Elasticity (Vol. 2) (The fifth edition). Beijing: Higher Education Press, 2016 (in Chinese))
    [35] Calladine CR. Theory of Shell Structures. Cambridge: Cambridge University Press, 1983
    [36] Luo PF, Chao YJ, Sutton MA , et al. Accurate measurement of three-dimensional deformations in deformable and rigid bodies using computer vision. Experimental Mechanics, 1993,33(2):123-132
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