Improved Form-Finding of Tensegrity Structures Using Blocks of Symmetry-Adapted Force Density Matrix
Publication: Journal of Structural Engineering
Volume 144, Issue 10
Abstract
Form-finding analysis is very important for developing innovative tensegrity structures. Nevertheless, it is frequently difficult to determine simultaneously the prestress mode and the exact nodal coordinates for a given geometry. This paper presents an improved symmetry method for analytical form-finding of tensegrity structures. The method is based on group representation theory and the force density method, and requires only the specified symmetry type and connectivity of a structure. The force densities of a -dimensional tensegrity structure can be accurately determined using the zero determinant of small-sized block matrices of a symmetry-adapted force density matrix. The nodal coordinate vectors can be obtained from the null spaces of the blocks through symmetry spaces for rigid-body translations along directions. A number of geometries with cyclic symmetry, dihedral symmetry, or tetrahedral symmetry are investigated. Illustrative examples show that the proposed method allows significant simplification of the form-finding process. The analytical solutions offer all feasible stable or superstable tensegrity structures with expected symmetries. The obtained prestress modes for each independent structural configuration necessarily retain full symmetry.
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Acknowledgments
This work has been supported by the Natural Science Foundation of Jiangsu Province (Grant No. BK20150602), the National Natural Science Foundation of China (Grant Nos. 51508089 and 51578133), and the Priority Academic Program Development of Jiangsu Higher Education Institutions.
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Published In
Journal of Structural Engineering
Volume 144 • Issue 10 • October 2018
Copyright
©2018 American Society of Civil Engineers.
History
Received: Mar 8, 2017
Accepted: Apr 11, 2018
Published online: Jul 13, 2018
Published in print: Oct 1, 2018
Discussion open until: Dec 13, 2018
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