Abstract
A continuum model of the orthotropic tensegrity plate-like structures with self-stress included is proposed within the six-parameter flat shell theory. This approach allows to simplify calculations, that is, it is not necessary to describe the whole complex tensegrity cable-strut structure with the use of computational methods. Average displacements, strains and internal forces for orthotropic tensegrity plate-like structures can be determined within the model. The closed form solutions for selected tensegrity plate strips and simply supported rectangular plate with sinusoidal load are presented in the paper. Tensegrity modules, which are based on the four-strut expanded octahedron modules with additional connecting cables are proposed as the examples. Self-stress and some geometrical parameters are introduced for parametric analysis.Keywords:
tensegrity plate-like structure, six-parameter flat shell theoryReferences
[1] Motro R., Tensegrity: structural systems for the future, Kogan Page, London, 2003.
[2] Skelton R.E., de Oliveira M.C., Tensegrity systems, Springer, London, 2009.
[3] Gilewski W., Kłosowska J., Obara P., Applications of tensegrity structures in civil engineering, Procedia Engineering, XXIV Sem. Theoretical Foundation of Civil Engineering, 111: 242–248, 2015. https://doi.org/10.1016/j.proeng.2015.07.084.
[4] Al Sabouni-Zawadzka A., Gilewski W., Technical coefficients for continuum models of orthotropic tensegrity modules, [in:] Advances in Mechanics: Theoretical, Computational and Interdisciplinary Issues, Kleiber M., Burczyński T., Wilde K., Górski J., Winkelmann K., Smakosz Ł. (eds.), CRC Belkema, Taylor & Francis Group, London, pp. 197–200, 2016.
[5] Gilewski W., Kasprzak A., 3D continuum models of tensegrity modules with the effect of self-stress, 11th World Congress on Computational Mechanics, Barcelona, 2014. http://www.wccm-eccm-ecfd2014.org/frontal/Ebook.asp.
[6] Kebiche K., Kazi Aoual M.N., Motro R., Continuum models for systems with a self-stress state, International Journal of Space Structures, 23(2): 103–115, 2008. https://doi.org/10.1260/026635108785260588.
[7] Chróścielewski J. Makowski J., Pietraszkiewicz W., Statics and dynamics of multifold shells [in Polish], IPPT PAN, Warszawa, 2004.
[8] Witkowski W., Synthesis of formulation of nonlinear mechanics of shells undergoing finite rotations in the context of FEM [in Polish], Wydawnictwo Politechniki Gdańskiej, 2011.
[2] Skelton R.E., de Oliveira M.C., Tensegrity systems, Springer, London, 2009.
[3] Gilewski W., Kłosowska J., Obara P., Applications of tensegrity structures in civil engineering, Procedia Engineering, XXIV Sem. Theoretical Foundation of Civil Engineering, 111: 242–248, 2015. https://doi.org/10.1016/j.proeng.2015.07.084.
[4] Al Sabouni-Zawadzka A., Gilewski W., Technical coefficients for continuum models of orthotropic tensegrity modules, [in:] Advances in Mechanics: Theoretical, Computational and Interdisciplinary Issues, Kleiber M., Burczyński T., Wilde K., Górski J., Winkelmann K., Smakosz Ł. (eds.), CRC Belkema, Taylor & Francis Group, London, pp. 197–200, 2016.
[5] Gilewski W., Kasprzak A., 3D continuum models of tensegrity modules with the effect of self-stress, 11th World Congress on Computational Mechanics, Barcelona, 2014. http://www.wccm-eccm-ecfd2014.org/frontal/Ebook.asp.
[6] Kebiche K., Kazi Aoual M.N., Motro R., Continuum models for systems with a self-stress state, International Journal of Space Structures, 23(2): 103–115, 2008. https://doi.org/10.1260/026635108785260588.
[7] Chróścielewski J. Makowski J., Pietraszkiewicz W., Statics and dynamics of multifold shells [in Polish], IPPT PAN, Warszawa, 2004.
[8] Witkowski W., Synthesis of formulation of nonlinear mechanics of shells undergoing finite rotations in the context of FEM [in Polish], Wydawnictwo Politechniki Gdańskiej, 2011.
