[논문]Force-finding of Tensegrity Structure using Optimization Technique

Lee, Sang Jin

doi:10.5659/aikar.2015.17.1.31

Force-finding of Tensegrity Structure using Optimization Technique 원문보기

Architectural research, v.17 no.1, 2015년, pp.31 - 40

Lee, Sang Jin (ADOPT Research Group, Department of Architectural Engineering, Gyeongsang National University)

Abstract ▼ AI-Helper

A simple force-finding process based on an optimization technique is proposed for tensegrity structures. For this purpose, the inverse problem of form-finding process is formulated. Therefore, the position vector of nodes and element connectivity information are provided as priori. Several benchmark tests are carried out to demonstrate the performance of the present force-finding process. In particular, the force density distributions of simplex tensegrity are thoroughly investigated with the important parameters such as the radius, height and twisting angle of simplex tensegrity. Finally, the force density distribution of arch tensegrity is produced by using the present force-finding process for a future reference solution.

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문제 정의

This study is mainly concerned with the force-finding of tensegrity structure and it is based on the equilibrium of structure. In three-dimensional space, let us consider the free node i which is connected to the nodes j and k as illustrated in Figure 1.

가설 설정

1. Define the problem: The initial configuration of tensegrity structure is defined here. The coordinates of nodal points and connectivity information of the target tensegrity structure is prepared.
2. Prepare optimization data: The sign of internal forces of the tensegrity members is provided as constraint. The linking of design variables (Lee, 2013) is also prepared here.

제안 방법

In this section, numerical test is carried out to investigate the force density distributions of simplex tensegrity with several important parameters such as twisting angle, the radius and height of simplex tensegrity. In the first case, we use the angle θ as a parameter and therefore the shape of simplex tensegrity will be severely twisted when larger value of angle is used.
In this study, we try to find force density of tensegrity with the known geometry. Therefore, the equilibrium equation of (2) is used as the objective function with constraints which force the sign of stresses of cable and strut to negative and positive respectively.
Prior to the investigation on the force density distribution of three-dimensional tensegrity structures, two planar tensegrity modules are tested to demonstrate the capability of proposed force-finding procedure. Then, numerical tests on simplex and arch tensegrity structures are carried out to find out the force density distributions of threedimensional tensegrity. All examples use unit force density as the initial design variables.

대상 데이터

Simplex tensegrity is adopted to investigate the force density distribution of three-dimensional tensegrity by using the present force-finding process. It has six nodes, three struts and nine cables (N6-S3-C9). The geometry of simplex tensegrity is generated by (10).

참고문헌 (15)

Burkhardt, R.W. (2008) A practical guide to tensegrity design, Cambridge.
Connelly, R. (1982) Rigidity and energy. Inventiones Mathematicae, 66, 11-33.

상세보기
Connelly, R. and Back, A. (1998) Mathematics and tensegrity. American Scientist, 86, 142-151.

상세보기
Connelly, R. (1999) Tensegrity structures: Why are they stable? in Rigidity Theory and Applications. Kluwer Academic/Plenum Publishers, 47-54.
Estrada, G.G., Bungartz, H.-J. and Mohrdieck, C. (2006) Numerical form-finding of tensegrity structures. International Journal of Solid and Structures, 43, 209-223.
Hernandez Juan, S. and Mirats Tur, J. M. (2008) Tensegrity frameworks: static analysis review. Mechanism and Machine Theory, 43(7), 859-881.

상세보기
Lee, S.J. (1999) A study on the shape and thickness optimization of shells using CAGD through minimization of strain energy with volume constraint, J. Compu. Struc. Eng. Institute of Korea, 12(4), 551-561.
Lee, S.J. (2012) A form-finding of plannar tensegrity structures, Architectural Research, 14, 143-152.

원문보기 상세보기
Lee, S.J. (2013) A form-finding technique for three-dimensional spatial structures, Architectural Research, 15, 207-214.

원문보기 상세보기
Mitsos, I.S., Guest, S.D., Nhamoinesu, S. and Overend, M. (2012) Investigation of a double-layer tensegrity glazing system. In Proceedings of the IASS Annual Symposium - IASS-APCS 2012.
Motro, R. (2003) Tensegrity: structural systems for the future. Kogan Page Science, London.
Pellegrino, S. (1993) Structural computations with the singular value decomposition of the equilibrium matrix. International Journal of Solid and Structures, 21, 3025-3035.
Schek, H.J. (1974) The force density method for form finding and computation of general networks. Journal of Computer Methods in Applied Mechanics and Engineering, 3, 115-134

상세보기
Schenk, M. (2005) Statically balanced tensegrity Mechnisms: a literature review. Technical Report, TU Delft.
Tibert, A.G. and Pellegrino, S. (2003) Review of form-finding methods for tensegrity structures. International Journal of Space Structures. 18, 209-223.

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Force-finding of Tensegrity Structure using Optimization Technique 원문보기

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Force-finding of Tensegrity Structure using Optimization Technique 원문보기

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