An Investigation on Optimal Initial Self-Stress Design of Tensegrity Grid Structures

다국어 초록 (Multilingual Abstract)

To achieve the optimal feasible force density vector of a given geometry confi guration tensegrity grid structure, an effi cient procedure is presented for optimal initial self-stress design of tensegrity grid structures by consecutively solving two linear homogeneous systems in conjunction with a minimization problem. The nonlinear constrained optimization algorithm, known as the Interior-Point Method (I-PM), is utilized to obtain the minimal solution, leading to a set of force densities which guarantee the non-degeneracy condition of the force density matrix. The evaluation of the eigenvalues of tangent stiff ness matrix is also introduced to check the geometric stability of the tensegrity grid structures. Finally, three numerical examples have been investigated comprehensively to prove the capability of the proposed method in optimal initial self-stress design of tensegrities. Furthermore, division of number of member group has been discussed in detail for the purpose of demonstrating the effi ciency of the proposed method in seeking initial force densities of tensegrity grid structures.

참고문헌 (Reference)

1 Simmel, S. S., "Wireframe and tensegrity DNA nanostructures" 47 (47): 1691-, 2014

2 Guest, S., "The stiffness of prestressed frameworks: A unifying approach" 43 (43): 842-854, 2006

3 Motro, R., "Tensegrity: Structural systems for the future" Kogan Page Science 2003

4 Ingber, D. E., "Tensegrity I Cell structure and hierarchical systems biology" 116 (116): 1157-1173, 2003

5 Pellegrino, S., "Structural computations with the singular value decomposition of the equilibrium matrix" 30 (30): 3025-3035, 1993

6 Fu, F., "Structural behavior and design methods of tensegrity domes" 61 (61): 23-35, 2005

7 Zhang, L. Y., "Stiffness matrix based form-finding method of tensegrity structures" 58 (58): 36-48, 2014

8 Motro, R., "Static and dynamic analysis of tensegrity systems" 1987

9 Murakami, H., "Static and dynamic analyses of tensegrity structures Part II Quasi-static analysis" 38 (38): 3615-3629, 2001

10 Lazopoulos, K. A., "Stability of a tensegrity structure: application to cell mechanics" 75 (75): 289-301, 2006

11 Ohsaki, M., "Stability conditions of prestressed pin-jointed structures" 41 (41): 1109-1117, 2006

12 Quirant, J., "Selfstressed systems comprising elements with unilateral rigidity: Selfstress states, mechanisms and tension setting" 22 (22): 203-214, 2007

13 Sanchez, R., "Selfstress states identification and localization in modular tensegrity grids" 22 : 215-224, 2007

14 이승혜, "Results of Generalized Equilibrium Path from Form-finding of Tensegrity Structure" 한국강구조학회 17 (17): 1225-1231, 2017

15 Meszaros, C., "Regularization techniques in interior point methods" 236 (236): 3704-3709, 2012

16 Wachter, A., "On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming" 106 (106): 25-57, 2006

17 Estrada, G. G., "Numerical form-finding of tensegrity structures" 43 (43): 6855-6868, 2006

18 Vassart, N., "Multiparametered form-finding method: Application to tensegrity systems" 14 (14): 147-154, 1999

19 Skelton, R. E., "Minimum mass design of tensegrity bridges with parametric architecture and multiscale complexity" 58 : 124-132, 2014

20 Pellegrino, S., "Matrix analysis of statically and kinematically indeterminate frameworks" 22 (22): 409-428, 1986

21 Connelly, R., "Mathematics and tensegrity" 86 (86): 142-, 1998

22 Luksan, L., "Interior point methods for large-scale nonlinear programming" 20 (20): 569-582, 2005

23 Albuquerque, J. S., "Interior point SQP strategies for structured process optimization problems" 23 (23): 543-554, 1997

24 Yuan, X. F., "Integral feasible prestress state of cable domes" 81 (81): 2111-2119, 2003

25 Tran, H. C., "Initial self-stress design of tensegrity grid structures" 88 (88): 558-566, 2010

26 Montuori, R., "Globally stable tensegrity compressive structures for arbitrary complexity" 179 : 682-694, 2017

27 Jianguo Cai, "Geometry and Mechanical Behaviour of Radially Retractable Roof Structures During the Movement Process" 한국강구조학회 16 (16): 755-764, 2016

28 Feng, X., "Geometrical nonlinear elasto-plastic analysis of tensegrity systems via the co-rotational method" 79 : 1-11, 2017

29 Kebiche, K., "Geometrical non-linear analysis of tensegrity systems" 21 (21): 864-876, 1999

30 Tran, H. C., "Form-finding of tensegrity structures with multiple states of self-stress" 222 (222): 131-147, 2011

31 Lee, S., "Form-finding of tensegrity structures with arbitrary strut and cable members" 85 (85): 55-62, 2014

32 Cai, J., "Form-finding of tensegrity structures using an optimization method" 104 : 126-132, 2015

33 Yuan, X.-F., "Form-finding of tensegrity structures based on the Levenberg-Marquardt method" 192 : 171-180, 2017

34 Zhang, L., "Form-finding of nonregular tensegrity systems" 132 (132): 1435-1440, 2006

35 Cai, J., "Form-finding method for multi-mode tensegrity structures using extended force density method by grouping elements" 187 : 1-9, 2018

36 Xu, X., "Force Finding of Tensegrity Systems Using Simulated Annealing Algorithm" 136 (136): 1027-1031, 2010

37 Cai, J., "Effects of the prestress levels on the stiffness of prismatic and star-shaped tensegrity structures" 22 (22): 1866-1875, 2017

38 B. Shekastehband, "Determining the Bilateral and Unilateral Mechanisms of Tensegrity Systems" 한국강구조학회 17 (17): 1049-1058, 2017

39 Tran, H. C., "Determination of a unique confi guration of free-form tensegrity structures" 220 (220): 331-348, 2011

40 Rhode, L., "Designing tensegrity modules for pedestrian bridges" 32 (32): 1158-1167, 2009

41 Rhode-Barbarigos, L., "Design of tensegrity structures using parametric analysis and stochastic search" 26 (26): 193-203, 2010

42 Paul, C., "Design and control of tensegrity robots for locomotion" 22 (22): 944-957, 2006

43 Caluwaerts, K., "Design and control of compliant tensegrity robots through simulation and hardware validation" 11 (11): 20140520-, 2014

44 Tibert, A. G., "Deployable tensegrity reflectors for small satellites" 39 (39): 701-709, 2002

45 Rovira, A. G., "Control and simulation of a tensegrity-based mobile robot" 57 (57): 526-535, 2009

46 Tran, H. C., "Advanced form-finding of tensegrity structures" 88 (88): 237-246, 2010

47 Tran, H. C., "Advanced form-finding for cablestrut structures" 47 (47): 1785-1794, 2010

48 Zhang, J. Y., "Adaptive force density method for form-finding problem of tensegrity structures" 43 (43): 5658-5673, 2006

49 Fraternali, F., "A tensegrity approach to the optimal reinforcement of masonry domes and vaults through fiber-reinforced composite materials" 134 : 247-254, 2015

50 Feng, X., "A novel method of determining the sole configuration of tensegrity structures" 69 : 66-78, 2015

51 Koohestani, K., "A new approach to the analytical and numerical form-finding of tensegrity structures" 50 (50): 2995-3007, 2013

52 Carpentieri, G., "A minimal mass deployable structure for solar energy harvesting on water canals" 55 (55): 449-458, 2017