

Article
Optimum prestress selection for tensegrity structures
Authors: 
Dalil Safaei, S.D., Eriksson, , Tibert, G. 
Document Type: 
Conference 
Pubstate: 
Accepted 
Journal: 
10th WORLD CONGRESS ON COMPUTATIONAL MECHANICS (WCCM 2012) 
Volume: 

Year: 
2012 
AbstractStructures composed of tension elements and compression elements in equilibrium are denoted tensegrity structures. Stability of tensegrity structures is achieved through introducing initial member forces (prestress). The prestress design can be seen consisting of two different stages: (i) find the bases of possible prestress states, and their admissible combinations considering unilateral behavior of the elements and stability of the structure, (ii) finding the prestress magnitude of a compatible prestress state. Once the distribution and intensity of the initial stresses have been chosen, the mechanical behavior of the structure is investigated. So far, no research has been carried out to connect the two steps, i.e. finding a suitable prestress pattern which also considers mechanical properties of the highly prestressed structure without considering external loads e.g. natural frequencies. This paper aims at finding an optimum selfstress state considering prestress magnitude. The prestress problem is on a linear static level where no slackening is allowed. An optimization is performed to find the optimum selfstress state from the selfstress modes obtained by a singular valued decomposition (SVD) of the equilibrium matrix. The objective functions are either the first natural vibration mode or the flexibility of the structure. The flexibility of the structure is obtained by rotation of a small load around each free node and determines the maximum displacement at the same node. Finite element analysis is employed for the linear analysis of the structure and a genetic algorithm for optimization i.e., a nongradient optimization method. The intensity of the prestress is assumed at most 30% of the buckling load of the compression members. The examples considered are a double layer tensegrity grid consisting of 29 independent selfstresses, and tensegrity rings of square, pentagon, and hexagon type with 7, 6, and 6 states of selfstresses, respectively. The method is applicable to complex asymmetric threedimensional structures. The new aspect of this work is a link between the SVD analysis, finite element analysis and genetic algorithm. In addition, this work has a major advantage for design of tensegrity structures, since the magnitude of prestress as well as of the prestress pattern is used to achieve desired properties.

