Validation of the continuum orthotropic model of tensegrity beam-like and plate-like structures

• Autorzy: Obara P. , Tomasik J.

Identyfikatory

DOI

10.24423/aom.4182

• Języki publikacji: EN

Abstrakty

EN

In this paper, an attempt was made to develop the continuum orthotropic model of tensegrity structures. A basic four-module tensegrity grid built from modified Quadruplex modules was proposed. A procedure called the energy equivalency method was adopted. The basis of this approach is the assumption that the finite element strain energy of a deformed tensegrity truss system contains the same energy as its continuum counterpart. Next, the six-parameter shell theory was used and closed forms for maximum displacements were obtained. Finally, in order to fill the gap in the existing literature, the continuum model was validated – the displacements were compared with displacements obtained from a discrete nonlinear model (the finite element method). The continuum model of tensegrity is a simple tool for analyzing large beam-like structures, plate-like structures and plate strips. It is important in case when discrete modeling becomes too tedious for the analysis. Another point is that many commercial software programs cannot analyze structures characterized by mechanisms. The finding of this work can also be useful for modeling metamaterials whose topology is based on the concept of tensegrity.

Słowa kluczowe

EN

tensegrity; double-layered grid; self-stress; infinitesimal mechanism; continuum orthotropic model; discrete model

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2023
• Tom: Vol. 75, nr 3
• Strony: 249--269
• Opis fizyczny: Bibliogr. 34 poz., rys., tab., wykr.

Twórcy

autor

Obara P.

• Department of Civil Engineering, Kielce University of Technology, Kielce, Tysiaclecia Panstwa Polskiego 7, 25-314 Kielce, Poland

autor

Tomasik J.

• Department of Civil Engineering, Kielce University of Technology, Kielce, Tysiaclecia Panstwa Polskiego 7, 25-314 Kielce, Poland

Bibliografia

• 1. Y. Kono, K.K. Choong, T. Shimada, H. Kunieda, An experimental investigation of a type of double-layer tensegrity grids, Journal of the International Association for Shell and Spatial Structures, 40, 2, 103–111, 1999.
• 2. W. Gilewski, J. Kłosowska, P. Obara, Verification of tensegrity properties of kono structure and blur building, XXV Polish – Russian – Slovak Seminar “Theoretical Foundation of Civil Engineering”, 153, 173–179, 2016.
• 3. L. Crawford, Transgender Architectonics: the Shape of Change in Modernist Space, Routledge, 2015.
• 4. V. Gomez-Jauregui, R. Arias, C. Otero, C. Manchado, Novel technique for obtaining double-layer tensegrity grids, International Journal of Space Structures, 27, 155–166, 2012.
• 5. B.-B. Wang, Cable-strut systems: part I – tensegrity, Journal of Constructional Steel Research, 45, 3, 281–289, 1998.
• 6. P. Obara, J. Tomasik, Parametric analysis of tensegrity plate-like structures: part 2 – quantitative analysis, Applied Sciences, 11, 2, 2021.
• 7. M. Liu, D. Cao, J. Wei, Survey on equivalent continuum modeling for truss structures and their nonlinear dynamics and vibration control, Journal of Vibration Engineering & Technologies, 10, 2, 667–687, 2022.
• 8. A.K. Noor, M.M. Mikulas, Continuum Modeling of Large Lattice Structures: Status and Projections, NASA Technical Paper 2767, 1988.
• 9. A.K. Noor, Continuum modeling for repetitive lattice structures, Applied Mechanics Reviews, 41, 7, 285–296, 1988.
• 10. A. Teughels, G. De Roeck, Continuum models for beam- and platelike lattice structures, IASS-IACM 2000, 4th International Colloquium on Computation of Shell and Spatial Structures, 2000.
• 11. M.P. Nemeth, A Treatise on Equivalent-Plate Stiffnesses for Stiffened Laminated-Composite Plates and Plate-Like Lattices, NASA Technical Paper 2011-216882, 2011.
• 12. K. Kebiche, M.N.K. Aoual, R. Motro, Continuum Models for Systems in a Selfstress State, International Journal of Space Structures, 23, 2, 103–115, 2008.
• 13. K. Yildiz, G.A. Lesieutre, Effective Beam Stiffness Properties of n-Strut Cylindrical Tensegrity Towers, AIAA Journal, 57, 5, 2185–2194, 2019.
• 14. A. Al Sabouni-Zawadzka, W. Gilewski, On Orthotropic Properties of Tensegrity Structures, XXV Polish–Russian–Slovak Seminar Theoretical Foundation of Civil Engineering, 153, 887–894, 2016.
• 15. A. Al Sabouni-Zawadzka, W. Gilewski, Technical Coefficients in Continuum Models of an Anisotropic Tensegrity Module, Procedia Engineering, 111, 871–876, 2015.
• 16. A. Al Sabouni-Zawadzka, J. Kłosowska, P. Obara, W. Gilewski, Continuum model of orthotropic tensegrity Plate-Like structures with Self-Stress included, Engineering Transactions, 64, 501–508, 2016.
• 17. J.O. Dow, Z.W. Su, C.C. Feng, C. Bodley, Equivalent continuum representation of structures composed of repeated elements, AIAA Journal, 23, 10, 1564–1569, 1985.
• 18. A. Libai, J.G. Simmonds [eds.], The Nonlinear Theory of Elastic Shells. One Spatial Dimension, Academic Press, 1988.
• 19. J. Chróscielewski, J. Makowski, W. Pietraszkiewicz, Statics and Dynamics of Multifold Shell: Nonlinear Theory and Finite Element Method, IPPT PAN, Warsaw, 2004 [in Polish].
• 20. S. Burzynski, J. Chróscielewski, K. Daszkiewicz, W. Witkowski, Geometrically nonlinear FEM analysis of FGM shells based on neutral physical surface approach in 6-parameter shell theory, Composites Part B: Engineering, 107, 203–213, 2016.
• 21. J. Chróscielewski, I. Kreja, A. Sabik, W. Witkowski, Modeling of composite shells in 6–parameter nonlinear theory with drilling degree of freedom, Mechanics of Advanced Materials and Structures, 18, 6, 403–419, 2011.
• 22. S. Burzynski, J. Chróscielewski, W. Witkowski, Geometrically nonlinear FEM analysis of 6-parameter resultant shell theory based on 2-D Cosserat constitutive model, ZAMM – Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 96, 2, 191–204, 2016.
• 23. W. Pietraszkiewicz, The resultant linear six-field theory of elastic shells: what it brings to the classical linear shell models?, ZAMM – Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 96, 8, 899–915, 2016.
• 24. W. Witkowski, Synthesis of Formulation of Nonlinear Mechanics of Shells Undergoing Finite Rotations in The Context of FEM, Gdansk University of Technology Publishing House, Gdansk, 2011.
• 25. P. Obara, Application of linear six-parameter shell theory to the analysis of orthotropic tensegrity plate-like structures, Journal of Theoretical and Applied Mechanics, 57, 167–178, 2019.
• 26. P. Obara, Analysis of orthotropic tensegrity plate strips using a continuum twodimensional model, MATEC Web Conference, 262, 2019.
• 27. W. Gilewski, J. Kłosowska, P. Obara, Application of singular value decomposition for qualitative analysis of truss and tensegrity structures, Acta Scientiarum Polonorum Hortorum Cultus, 14, 3, 14, 2015.
• 28. P. Obara, J. Tomasik, Parametric Analysis of tensegrity plate-like structures: part 1 – qualitative analysis, Applied Sciences, 10, 20, 2020.
• 29. K.-J. Bathe, Finite Element Procedures in Engineering Analysis, Prentice-Hall, New Jersey, 1982.
• 30. O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu (ed.), The Finite Element Method: Its Basis and Fundamentals, Butterworth-Heinemann, Oxford, 2013.
• 31. P. Chadwick, M. Vianello, S.C. Cowin, A new proof that the number of linear elastic symmetries is eight, The Jean-Paul Boehler Memorial Volume, 49, 11, 2471–2492, 2001.
• 32. J. Szmelter, Computer Methods in Mechanics, PanstwoweWydawnictwo Naukowe,Warsaw, 1980 [in Polish].
• 33. G. Rakowski, Z. Kacprzyk, Finite Element Method in Structural Mechanics, Warsaw University of Technology Publishing House, Warsaw, 2016 [in Polish].
• 34. EN 1993-1-11: 2006. Eurocode 3: Design of steel structures – Part 1-11: Design of structures with tension components.