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PROCEEDINGS OF THE THIRTEENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING
Edited by: B.H.V. Topping and Y. Tsompanakis
Design of Tensegrity Structures: The Kinematic Method with Forces in Structural Members
M. Abdulkareem1, M. Mahfouf1 and D. Theilliol2
1Department of Automatic Control and Systems Engineering, The University of Sheffield, United Kingdom
M. Abdulkareem, M. Mahfouf, D. Theilliol, "Design of Tensegrity Structures: The Kinematic Method with Forces in Structural Members", in B.H.V. Topping, Y. Tsompanakis, (Editors), "Proceedings of the Thirteenth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 189, 2011. doi:10.4203/ccp.96.189
Keywords: tensegrity structures, form-finding, kinematic methods, tension coefficients, member forces, nonlinear optimization, pre-stress.
A basic issue in the design of tensegrity structures, similar to other internally prestressed stable structures, is in the selection and definition of their optimal structural forms: a process called form-finding  . Various methods have been proposed for form-finding; one of these is the kinematic form-finding method which obtains a tensegrity structure by geometric considerations alone. The well-known advantage of the kinematic form-finding method is that it allows the control of lengths of structural members and, as such, though the principle is structurally correct, the stability of the structure is not guaranteed . In addition, it is thought that it is only applicable to systems with a few structural members supposedly arising from the large constraints that would be required for larger systems. In this paper, we have not only established a relationship between the kinematic form-finding method and the forces in structural members with guaranteed stability of the resulting structure, but we have also shown a simple way to alleviate the problem of handling large constraints by writing them in a simpler forms for symmetric and practical structures. It can be seen that the kinematic method assumes that the magnitudes of tension coefficients in all cables and bars are equal, thus, the possibility that an optimal set of tension coefficients exists for a given structural configuration is ignored. Also an approach is shown using nonlinear constrained optimization for obtaining the optimal tension coefficient for a given configuration, which can be used with the kinematic form-finding methods for tensegrity structures. The use of the new approach is described using a class 2 tensegrity configuration given in  that can be used, for example, as a shelter on a disaster site for a temporary hospital or housing.
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