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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
A Constrained Optimization Approach for Form-Finding of Tensegrity Structures and their Static-Load Deflection Properties
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, "A Constrained Optimization Approach for Form-Finding of Tensegrity Structures and their Static-Load Deflection Properties", 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 188, 2011. doi:10.4203/ccp.96.188
Keywords: tensegrity structures, form-finding, constrained optimization, nullspace methods, static deflection.
A new method for form-finding of tensegrity structures using a constrained optimization approach is presented in this paper. The information obtained from the four fundamental spaces of their equilibrium matrices is useful in designing optimal tensegrity structures. In particular, they have been used in conjunction with the constrained optimization approach for form-finding of tensegrity structures. The technique involves dividing the form-finding task into two as follows: obtaining the optimal vector of tension coefficients for the given configuration and determining the nodal coordinates for the optimal set of tension coefficients. This new method offers control of member forces and lengths into the form-finding process while the following assumptions are made: i) members are connected at the nodes in pin-jointed manner; ii) the cables are in tension at all times and can be elastic and, or inflexible; likewise, the bars are in compression at all times and the possibility of buckling is ignored; iii) the influence of external force fields are neglected; iv) the structure is only loaded at the nodes. Moreover, it has been demonstrated with examples that the new method can be used for tensegrity structures with a complex connectivity of members.
Furthermore, the mass and the stiffness matrices and the dynamic equations of motion of a discretized structure were used to obtain the pseudo-static deflection equation. The deflection equation allows the study of nodal displacements of a two-stage tensegrity structure for the various point loads as the level of structural prestress was varied. It was revealed that the nodal displacements of the structures reduce nonlinearly for a given set of static loads making controller design particularly challenging from a control engineering perspective. Near future work will focus on the dynamics and control design algorithms of tensegrity structures modelled as multibody systems for specific engineering applications.
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