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CLC number: TU393.3

On-line Access: 2015-09-03

Received: 2015-04-07

Revision Accepted: 2015-07-13

Crosschecked: 2015-08-07

Cited: 0

Clicked: 1146

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Jin-yu Zhou

http://orcid.org/0000-0001-6514-5081

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Journal of Zhejiang University SCIENCE A 2015 Vol.16 No.9 P.737-748

http://doi.org/10.1631/jzus.A1500081


Distributed indeterminacy evaluation of cable-strut structures: formulations and applications


Author(s):  Jin-yu Zhou, Wu-jun Chen, Bing Zhao, Zhen-yu Qiu, Shi-lin Dong

Affiliation(s):  1Space Structures Research Center, Shanghai Jiao Tong University, Shanghai 200240, China; more

Corresponding email(s):   zjysjtu@sjtu.edu.cn

Key Words:  Flexible structures, Cable-strut structures, Distributed indeterminacy, Initial force design, Force finding, Singular value decomposition, Form transforming


Jin-yu Zhou, Wu-jun Chen, Bing Zhao, Zhen-yu Qiu, Shi-lin Dong. Distributed indeterminacy evaluation of cable-strut structures: formulations and applications[J]. Journal of Zhejiang University Science A, 2015, 16(9): 737-748.

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year="2015",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A1500081"
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%A Wu-jun Chen
%A Bing Zhao
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T1 - Distributed indeterminacy evaluation of cable-strut structures: formulations and applications
A1 - Jin-yu Zhou
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Abstract: 
The indeterminacy evaluation is an effective method for system identification; it can predict the mechanical behaviors of flexible structures in the primary design. However, the conventional indeterminacy evaluation based solely on geometry and topology has neglected the influence of material properties on mechanical behavior and the contribution of each component to the total indeterminacy. To address these issues, a distributed indeterminacy evaluation taking account of the effect of component stiffness was carried out with a view to providing reasonable interpretations and feasible applications for two concepts, i.e., the distributed static indeterminacy (DSI) and the distributed kinematic indeterminacy (DKI). A unified method for the DSI is proposed, and a comparative analysis between this and an existing method revealed that the proposed method has a wider range of applicability and is essentially identical in the kinematically determinate case. It can be concluded that since the DSI is representative of symmetric properties, a simple but efficient grouping criterion can be established which can improve the efficiency of the specific force finding method entitled double singular value decomposition (DSVD). On the other side, an evaluable method for the DKI is proposed suggesting that DKI is a useful indicator for the assessment of nodal mobility and can provide a feasible solution to the form transforming study.

This paper presents distributed static/kinematic indeterminacy (DSI/DKI) for cable-strut structures by applying mathematical formulation. Three example problems including Geiger dome, Levy dome and tensegrity are provided to explain the physical aspects of DSI and DKI. The extension of the previously developed DSI concept and introduction of DKI for cable-strut structures is interesting.

索杆结构分布式不定数分析:推导和应用

目的:针对预张力索杆体系,将构件刚度与体系判定相结合,提出分布式静不定和分布式动不定的计算方法,使体系分析从"系统"层面向"构件"层面延伸。
创新点:1. 推导出具有广泛适应性的分布式静不定公式,并证明与原有方法的内在关系。2. 首次提出分布式动不定数学公式。3. 给出分布式不定数的物理意义及潜在的应用。
方法:该方法在平衡矩阵理论基础上,采用奇异值分解法分别求解相互正交的两类单元变形量和两类节点外荷载模态;在排除整体刚体位移模态后,利用该正交性,求解分布式静不定和动 不定。
结论:1. 该方法能克服已有方法中的奇异性问题,具有普遍性,可适用于动定及动不定结构。2. 作为结构双对称性的代表,分布式静不定数可被用作一个简单而有效的分组准则;该准则能提高二次奇异值找力法(DSVD)的效率并能为设计师提供更多的初始预应力设计可能性。3. 揭示分布式静不定与结构重要性及结构敏感性间的关系。4. 分布式动不定数可被用作节点可动性的一个基本指标。

关键词:柔性结构;索杆结构;分布式不定数;初始预应力设计;找力分析;奇异值分解;形状变换

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1]Ashwear, N., Eriksson, A., 2014. Natural frequencies describe the pre-stress in tensegrity structures. Computers & Structures, 138:162-171.

[2]Calladine, C., 1978. Buckminster Fuller’s “tensegrity” structures and Clerk Maxwell’s rules for the construction of stiff frames. International Journal of Solids and Structures, 14(2):161-172.

[3]Calladine, C., Pellegrino, S., 1991. First-order infinitesimal mechanisms. International Journal of Solids and Structures, 27(4):505-515.

[4]Chen, Q., Kou, X.J., 2013. A constraint matrix approach for structural ultimate resistance to access the importance coefficient values of rigid joints. Advances in Structural Engineering, 16(11):1863-1870.

[5]Chen, Q., Kou, X.J., Zhang, Y., 2010. Internal force and deformation matrixes and their applications in load path. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 11(8):563-570.

[6]Chen, W.J., Zhang, S.J., 2006. Deployable Space Structures and Analysis Theory. China Astronautic Publishing House, Beijing, China (in Chinese).

[7]Chen, W.J., Guan, F.L., Dong, S.L., 2000. Dynamic analysis of deployable space truss structures. Chinese Journal of Computational Mechanics, 17:411-416 (in Chinese).

[8]Chen, W.J., Zhou, J.Y., Zhao, J.Z., 2014. Computational methods for the zero-stress state and the pre-stress state of tensile cable-net structures. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 15(10):813-828.

[9]Eriksson, A., Tibert, A.G., 2006. Redundant and force-differentiated systems in engineering and nature. Computer Methods in Applied Mechanics and Engineering, 195(41-43):5437-5453.

[10]Gao, Y., Liu, X.L., 2013. Weighted graph form of structures and its application in robustness analysis. Journal of Shanghai Jiaotong University (Science), 18(2):216-223.

[11]Guest, S., 2006. The stiffness of prestressed frameworks: a unifying approach. International Journal of Solids and Structures, 43(3-4):842-854.

[12]Jiang, M., Kou, X.J., Li, Z.M., 2012. The redundancy matrix of rigid-frame structure and its application. Journal of Donghua University, 29:107-110.

[13]Kou, X.J., Chen, Q., Song, J., 2008. Reliability estimation involving indirect load effects. Proceeding of the 4th Asian-Pacific Symposium, Hong Kong, p.137-140.

[14]Lee, S., Woo, B., Lee, J., 2014. Self-stress design of tensegrity grid structures using genetic algorithm. International Journal of Mechanical Sciences, 79:38-46.

[15]Pai, P.F., 2011. Three kinematic representations for modeling of highly flexible beams and their applications. International Journal of Solids and Structures, 48(19):2764-2777.

[16]Pellegrino, S., 1990. Analysis of prestressed mechanisms. International Journal of Solids and Structures, 26(12):1329-1350.

[17]Pellegrino, S., 1993. Structural computations with the singular value decomposition of the equilibrium matrix. International Journal of Solids and Structures, 30(21):3025-3035.

[18]Pellegrino, S., Calladine, C.R., 1986. Matrix analysis of statically and kinematically indeterminate frameworks. International Journal of Solids and Structures, 22(4):409-428.

[19]Ströbel, D., 1995. Die Anwendung der Ausgleichungsrechnung auf Elastomechanische Systeme. PhD Thesis, Universität Stuttgart, Stuttgart, Germany (in German).

[20]Ströbel, D., Singer, P., 2008. Recent developments in the computational modelling of textile membranes and inflatable structures. In: Oñate, E., Kröplin, B. (Eds.), Textile Composites and Inflatable Structures II. Springer Netherlands, p.253-266.

[21]Sultan, C., 2013. Stiffness formulations and necessary and sufficient conditions for exponential stability of prestressable structures. International Journal of Solids and Structures, 50(14-15):2180-2195.

[22]Tibert, A.G., 2005a. Distributed indeterminacy in frameworks. Proceedings of the 5th International Conference on Computation of Shell and Spatial Structures, Salzburg, Austria.

[23]Tibert, A.G., 2005b. Flexibility evaluation of prestressed kinematically indeterminate frameworks. The 18th Nordic Seminar on Computational Mechanics, Helsinki, Finland.

[24]Tran, H.C., Lee, J., 2010. Initial self-stress design of tensegrity grid structures. Computers & Structures, 88(9-10):558-566.

[25]Tran, H.C., Lee, J., 2013. Form-finding of tensegrity structures using double singular value decomposition. Engineering with Computers, 29(1):71-86.

[26]Tran, H.C., Park, H.S., Lee, J., 2012. A unique feasible mode of prestress design for cable domes. Finite Elements in Analysis and Design, 59:44-54.

[27]Yuan, X.F., Chen, L.M., Dong, S.L., 2007. Prestress design of cable domes with new forms. International Journal of Solids and Structures, 44(9):2773-2782.

[28]Zhang, L.Y., Li, Y., Cao, Y.P., et al., 2013. A unified solution for self-equilibrium and super-stability of rhombic truncated regular polyhedral tensegrities. International Journal of Solids and Structures, 50(1):234-245.

[29]Zhang, L.Y., Li, Y., Cao, Y.P., et al., 2014. Stiffness matrix based form-finding method of tensegrity structures. Engineering Structures, 58:36-48.

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