Analytical solution of the peak bending moment of an M boom for membrane deployable structures

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:206

Article

Yang, Hui¹  Guo, Hongwei²  Wang, Yan¹  Feng, Jian¹  Tian, Dake³ 

[1] Anhui Univ, Coll Elect Engn & Automat, Hefei 230601, Peoples R China

[2] Harbin Inst Technol, State Key Lab Robot & Syst, Harbin 150001, Peoples R China

[3] Shenyang Jianzhu Univ, Sch Mech Engn, Shenyang 110168, Peoples R China

关键词: Self-deployable structure;    Thin-walled boom;    Nonlinear deformation;    Analytical solution;    Experiment;   

DOI  :  10.1016/j.ijsolstr.2020.09.005

来源: Elsevier

【 摘 要 】

A deployable M cross section thin-walled boom (M boom) can be flattened and coiled elastically around a hub; and can then be self-deployed by releasing the stored strain energy. The M boom has been proposed as the key member of membrane deployable structures. First, the covariant base vectors of geometrical relation of the single type I tape spring were analyzed by establishing three coordinate systems. Second, the constitutive relation between stress and strain was expressed according to the Kirchhoff-Love hypothesis. Third, the equilibrium and controlling equations of the single tape spring were modeled based on Calladine shell theory. Fourthly, the total strain energy model of the single type I tape spring was built by integration. Fifth, the strain energy of the M boom was modeled by the sum of the strain energies of the six tape springs. Then, the strain energies of the single type II and III tape springs were analyzed. The sum of the strain energies of the six tape springs equals the total strain energy of the M boom. The bending moment model was established based on the minimum potential energy principle. The experimental equipment and four M boom samples were processed. The bending force value of the M booms was tested 20 times. Then, the average peak bending moment was calculated. The relative error between the theoretical and experimental results of the peak bending moment does not exceed 6.5% verifying the accuracy of the theoretical model. (C) 2020 Published by Elsevier Ltd.

【 授权许可】

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