Optimum pre-stress selection for tensegrity structures

Authors: Dalil Safaei, S.D., Eriksson,  , Tibert, G.
Document Type: Conference
Pubstate: Accepted
Year: 2012


Structures composed of tension elements and compression elements in equilibrium are denoted tensegrity structures. Stability of tensegrity structures is achieved through introducing initial member forces (pre-stress). The pre-stress design can be seen consisting of two different stages: (i) find the bases of possible pre-stress states, and their admissible combinations considering unilateral behavior of the elements and stability of the structure, (ii) finding the pre-stress magnitude of a compatible pre-stress 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 pre-stress pattern which also considers mechanical properties of the highly pre-stressed structure without considering external loads e.g. natural frequencies. This paper aims at finding an optimum self-stress state considering pre-stress magnitude. The pre-stress problem is on a linear static level where no slackening is allowed. An optimization is performed to find the optimum self-stress state from the self-stress 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 non-gradient optimization method. The intensity of the pre-stress 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 self-stresses, and tensegrity rings of square, pentagon, and hexagon type with 7, 6, and 6 states of self-stresses, respectively. The method is applicable to complex asymmetric three-dimensional 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 pre-stress as well as of the pre-stress pattern is used to achieve desired properties.