Journal of Korean Society of Steel Construction (한국강구조학회 논문집)

Korean Society of Steel Construction (한국강구조학회)
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Form-finding of Tensegrity Systems by using Frequency Constraints

진동수 목적함수를 이용한 텐세그리티 시스템의 형상탐색기법

  • Lee, Seung Hye (Department of Architectural Engineering, Sejong University) ;
  • Lee, Jae Hong (Department of Architectural Engineering, Sejong University) ;
  • Kang, Joo Won (School of Architecture, Yeungnam University)
  • Received : 2016.04.20
  • Accepted : 2016.08.07
  • Published : 2016.10.27
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Abstract

In this study, a form-finding method of tensegrity systems by using the force density method combined with the stiffness matrix method was presented. Numerous studies have been made on form-finding methods of the tensegrity systems. However, these methods are limited in the tensegrity systems with multiple null space of the equilibrium matrix. The proposed method can uniquely define a single integral feasible set of force densities for the structures. In order to draw maximum natural frequency that can lead a maximum stiffness of the tensegrity systems, a constrained maximization problem is formulated in the genetic algorithm. Several numerical examples are presented to prove dfficiency in searching for self-equilibrium congifurations of tensegrity systems with multiple self-stress states. A good performance of the proposed method has been shown in the results.

본 연구에서는 내력밀도법과 강성행렬법을 결합한 방법을 사용한 텐세그리티 시스템의 형상탐색기법을 제안하였다. 텐세그리티 시스템의 형상탐색 기법에 대한 연구는 많은 연구자들에 의해 계속되어왔으나 그 기법들은 복수의 자기응력 상태를 갖는 시스템의 경우 한계가 있다. 제안 기법을 사용하면 복수의 자기응력상태를 갖는 텐세그리티 구조물에 대한 최적의 내력밀도 값을 결정할 수 있다. 텐세그리티 시스템의 최대 강성 값을 유도하기 위해 구조물의 고유진동수 값을 최대로 이끌어 내는 목적함수를 설정한 유전 알고리즘을 사용하였다. 다수의 평형상태를 갖는 텐세그리티 시스템의 자기평형 형태를 얻을 수 있는 본 기법에 대한 효율성을 입증하기 위해 수치해석 예제를 수행하였으며 이를 통해 만족하는 결과 값을 얻을 수 있었다.

Keywords

References

  1. Raj, R.P. and Guest, S.D. (2006) Using Symmetry for Tensegrity Form-Finding. JOURNAL-INTERNATIONAL ASSOCIATION FOR SHELL AND SPATIAL STRUCTURES, p.152, p.245.
  2. Pugh, A. (1976) An Introduction to Tensegrity. Univ of California Press.
  3. Tibert, A.G. and Pellegrino, S. (2011) Review of Form-Finding Methods for Tensegrity Structures. International Journal of Space Structures, Vol.26, No.3, pp.241-255. https://doi.org/10.1260/0266-3511.26.3.241
  4. Schenk, M. (2005) Statically Balanced Tensegrity Mechanisms. A Literature Review. Department of BioMechanical Engineering. Delft University of Technology.
  5. Schek, H.J. (1974) The Force Density Method for Form Finding and Computation of General Networks. Computer Methods in Applied Mechanics and Engineering, Vol.3, No.1, pp.115-134. https://doi.org/10.1016/0045-7825(74)90045-0
  6. Linkwitz, I.K. and Schek, H.J. (1971) Einige Bemerkungen Zur Berechnung von Vorgespannten Seilnetzkonstruktionen. Ingenieur-Archiv, Vol.40, No.3, pp.145-158. https://doi.org/10.1007/BF00532146
  7. Vassart, N. and Motro, R. (1999) Multiparametered Formfinding Method: Application to Tensegrity Systems. International Journal of Space Structures, Vol.14, No.2, pp.147-154. https://doi.org/10.1260/0266351991494768
  8. Masic, M., Skelton, R.E., and Gill, P.E. (2005) Algebraic Tensegrity Form-Finding. International Journal of Solids and Structures, Vol.42, No.16, pp.4833-4858. https://doi.org/10.1016/j.ijsolstr.2005.01.014
  9. Zhang, J.Y. and Ohsaki, M. (2006) Adaptive Force Density Method for Form-Finding Problem of Tensegrity Structures. International Journal of Solids and Structures, Vol.43, No.18, pp.5658-5673. https://doi.org/10.1016/j.ijsolstr.2005.10.011
  10. Estrada, G.G., Bungartz, H.J., and Mohrdieck, C. (2006) Numerical Form-Finding of Tensegrity Structures. International Journal of Solids and Structures, Vol.43, No.22, pp.6855-6868. https://doi.org/10.1016/j.ijsolstr.2006.02.012
  11. 정우성, 이재홍(2011) 특이값 분해로 정식화 된 새로운 하중법을 이용한 입체 텐세그리티 형상 탐색, 한국강구조학회 2011년도 학술발표대회 논문집, 한국강구조학회, pp.175-176. (Chung, W.S. and Lee, J.H. (2011) Form-finding of Multi-stage Tesegrity Structures by using Singular Value Decomposition, Proc. of the 22nd Annual Conf, KSSC, pp.175-176 (in Korean).)
  12. 우병현, 이재홍(2012) 멀티스테이지 텐세그리티 구조물의 비선형 해석, 한국강구조학회 2012년도 학술발표대회 논문집, 한국강구조학회, pp.45-46. (Woo, B.H. and Lee, J.H. (2012) Nonlinear Analysis of Multistage Tensegrity Structure, Proc. of the 23rd Annual Conf, KSSC, pp.45-46 (in Korean).)
  13. 이승혜, 이재홍(2013) 유전자 알고리즘을 이용한 다중 자기응력 상태 텐세그리티 시스템의 형상탐색, 한국강구조학회 2013년도 학술발표대회 논문집, 한국강구조학회, pp.1-2. (Lee, S.H. and Lee, J.H. (2013) Form-finding of Tensegrity Systems with Multiple States of Self-stress Using Genetic Algorith, Proc. of the 24th Annual Conf, KSSC, pp.1-2 (in Korean).)
  14. Shon, S.D. and Lee, S.J. (2011) Optimum Structural Design of Sinusoidal Corrugated web Beam using Real-Valued Genetic Algorithm, Magazine of the Korean Society of Steel Construction, KSSC. Vol.23, No.5, pp.581-593.
  15. Choi, S.H. (2006) Optimization of Direct Design System of Semi-Rigid Steel Frames using Advanced Analysis and Genetic Algorithm, Magazine of the Korean Society of Steel Construction, KSSC. Vol.18, No.6, 707-715.
  16. Tran, H.C. and Lee, J. (2010) Advanced Orm-Finding of Tensegrity Structures. Computers & Structures, Vol.88, No.3, pp.237-246. https://doi.org/10.1016/j.compstruc.2009.10.006
  17. Connelly, R. and Terrell, M. (1995) Globally Rigid Symmetric Tensegrities. Structural Topology 1995 num 21.
  18. Pellegrino, S. and Calladine, C.R. (1986). Matrix Analysis of Statically and Kinematically Indeterminate Frameworks. International Journal of Solids and Structures, Vol.22, No.4, pp.409-428. https://doi.org/10.1016/0020-7683(86)90014-4
  19. Pellegrino, S. (1993) Structural Computations with the Singular Value Decomposition of the Equilibrium Matrix. International Journal of Solids and Structures, Vol.30, No.21, pp.3025-3035. https://doi.org/10.1016/0020-7683(93)90210-X
  20. Guest, S. (2006) The Stiffness of Prestressed Frameworks: a Unifying Approach. International Journal of Solids and Structures, Vol.43, No.3, pp.842-854. https://doi.org/10.1016/j.ijsolstr.2005.03.008
  21. Kebiche, K., Kazi-Aoual, M.N., and Motro, R. (1999) Geometrical Non-Linear Analysis of Tensegrity Systems. Engineering Structures, Vol.21, No.9, pp.864-876. https://doi.org/10.1016/S0141-0296(98)00014-5
  22. Holland, J.H. (1975) Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. U Michigan Press.
  23. Tran, H.C. and Lee, J. (2011) Form-Finding of Tensegrity Structures with Multiple States of Self-Stress. Acta Mechanica, Vol.222, No.1-2, pp.131-147. https://doi.org/10.1007/s00707-011-0524-9
  24. Estrada, G.G., Bungartz, H.J., and Mohrdieck, C. (2006) Numerical Form-Finding of Tensegrity Structures. International Journal of Solids and Structures, Vol.43, No.22, pp.6855-6868. https://doi.org/10.1016/j.ijsolstr.2006.02.012

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