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2D Theory of Shell-like Tensegrity Structures

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Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 110))

Abstract

Six-parameter shell theory is proposed for tensegrity-like structures. Continuum model to describe mechanical properties of tensegrity lattices is based on the equivalence of the strain energy with discrete model. Parametric analysis is presented to describe the influence of geometrical properties and the level of self-equilibrated normal forces to the static response of the structure.

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References

  1. Pietraszkiewicz, W.: Consistent second approximation to the elastic strain energy in a shell. Z Angew Math. Mech. 59, 206–208 (1979)

    Google Scholar 

  2. Pietraszkiewicz, W.: Finite Rotations and Lagrangean Description in the Non-linear Theory of Shells. Polish Scientific Publishers, Warsaw, Poznań (1979)

    Google Scholar 

  3. Pietraszkiewicz, W., Babur, J.: Finite rotations in the description of continuum deformation. Int. J. Eng. Sci. 21, 1097–1115 (1983)

    Article  Google Scholar 

  4. Chróścielewski, J., Makowski, J., Pietraszkiewicz, W.: Nonlinear dynamics of flexible shell structures. Comp. Ass. Mech. Eng. Sci. 9, 341–357 (2002)

    Google Scholar 

  5. Chróścielewski, J., Makowski, J., Pietrasziewicz, W.: Statics and Dynamics of Multifold-shells: Nonlinear Theory and Finite Element Method (in Polish). IFTR Polish Academy of Sciences Press, Warsaw (2004)

    Google Scholar 

  6. Eremeyev, V.A., Pietraszkiewicz, W.: The non-linear theory of elastic shells with phase transition. J. Elast. 74, 67–86 (2004)

    Article  Google Scholar 

  7. Eremeyev, V.A., Pietraszkiewicz, W.: Local symmetry group in the general theory of elastic shells. J. Elast. 85, 125–152 (2006)

    Article  Google Scholar 

  8. Chróścielewski, J., Witkowski, W.: Four-node semi-EAS element in six-field nonlinear theory of shells. Int. J. Numer. Meth. Eng. 68, 1137–1179 (2006)

    Article  Google Scholar 

  9. Panasz, P., Wiśniewski, K.: Nine-node shell elements with 6 dofs/node based on two-level approximation. Finite Elem. Anal. Des. 44, 784–796 (2008)

    Article  Google Scholar 

  10. Gilewski, W.: High-precision finite elements on moderately thick shell theory. Ph.D. dissertation. Warsaw University of Technology (1986)

    Google Scholar 

  11. Gilewski, W., Al Sabouni-Zawadzka, A., Pełczyński, J.: Physical shape functions in 6-parametre shell theory finite elements. In: Pietraszkiewicz, W., Witkowski, W. (Eds.) Shell Structures: Theory and Applications 4. CRC Press, Boca Raton, London, New York, Leiden (2017)

    Chapter  Google Scholar 

  12. Al Sabouni-Zawadzka, A., Kłosowska, J., Obara, P., Gilewski, W.: Continuum model of orthotropic tensegrity plate-like structures with self-stress included. Engng. Trans. 64, 501–508 (2016)

    Google Scholar 

  13. Obara, P., Gilewski, W.: Discrete and equivalent 6-parameter shell approach to simulate mechanical behavior of tensegrity lattices. Solmech 2018, Warsaw, Poland (2018)

    Google Scholar 

  14. Pugh, A.: An Introduction to Tensegrity. University California Press, Berkeley, Los Angeles, London (1976)

    Google Scholar 

  15. Motro, R.: Tensegrity: Structural Systems for the Future. Kogan Page, London (2003)

    Book  Google Scholar 

  16. Skelton, R.E., de Oliveira, M.C.: Tensegrity Systems. Springer, London (2009)

    Google Scholar 

  17. Al Sabouni-Zawadzka, A., Gilewski, W.: Inherent properties of smart tensegrity structures. Appl. Sci. 8, 787-1-14 (2018)

    Article  Google Scholar 

  18. Kasprzak, A., Gilewski, W.: 3D Continuum Model of Tensegrity Modules with the Effect of Self-stress. WCCM XI, ECCM V, Barcelona, Spain (2014)

    Google Scholar 

  19. Pellegrino, S., Calladine, C.R.: Matrix analysis of statically and kinematically indeterminate frameworks. Int. J. Solid Struct. 22, 409–422 (1990)

    Article  Google Scholar 

  20. Lewiński, T.: On algebraic equations of elastic trusses, frames and grillages. J. Theor. Appl. Mech. 39, 307–322 (2001)

    Google Scholar 

  21. Pełczyński, J., Gilewski, W.: An extension of algebraic equations of elastic trusses with self-equilibrated system of forces. ECMM 6, Glasgow, UK (2018)

    Google Scholar 

  22. Green, A.E., Zerna, W.: Theoretical Elasticity. Press, Oxford, UK, Oxford Uni (1968)

    Google Scholar 

  23. Chadwick, P., Vianello, M., Cowin, S.A.: A new proof that the number of linear elastic symmetries is eight. J. Mech. Phys. Solids 49, 2471–2492 (2001)

    Article  Google Scholar 

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Correspondence to Wojciech Gilewski .

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Gilewski, W., Obara, P., Al Sabouni-Zawadzka, A. (2019). 2D Theory of Shell-like Tensegrity Structures. In: Altenbach, H., Chróścielewski, J., Eremeyev, V., Wiśniewski, K. (eds) Recent Developments in the Theory of Shells . Advanced Structured Materials, vol 110. Springer, Cham. https://doi.org/10.1007/978-3-030-17747-8_15

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