Morphology Of Tensegrity Structures Based On Equilibrium Matrix Theory

As a new type of spatial tensile structures, tensegrity system consists of continuous cables and interval struts, which reflects the basic rule of "continuous tension and isolated compression" in the universe. Nowadays, tensegrity system is becoming one of the leading-edge research topics of spatial structures, and it has drawn widely attention from researchers around the world. Based on the previous studies, this paper has carried out an intensive study and investigation towards a few key problems in tensegrity system. Also, analytic and numerical methods including equilibrium matrix theory, singular value decomposition (SVD) as well as fish-swarm algorithm etc. have been used in this paper.The main aspects of the work in this paper are as followed:1. The equilibrium matrix theory, singular value decomposition (SVD) and criteria for the geometrical stability of tensegrity system are introduced. Besides, equilibrium matrix of spatial bar elements is deduced, and singular value decomposition is used in this problem. Several numerical examples are presented and compared to previous papers, which shows the efficiently of the SVD.2. To solve the problem of the structures’ geometrical stability and initial prestress, a new mathematical optimization model, which considering uniformity as well as the tension-compression condition of elements prestress at the same time, is proposed in this paper.3. A new intelligent algorithm-the fish-swarm algorithm is used to solve the proposed optimization model. Also, several numerical examples are presented, which as a result show that the proposed optimization model can solve the force-finding problem of any multi-states of self-stress tensegrity system accurately and effectively.4. Based on the equilibrium matrix theory and proposed optimization model, the author wrote a MATLAB program, which is used in all the numerical examples in this paper. At last the codes of the program corresponding to two examples are given.Numerical examples prove that the theory and program proposed is correct, and the algorithm is effective, which can be a theory basis of morphology study of tensegrity system. Moreover, the conclusions and problems that deserve further study are summarized at the end the paper.