Critical Buckling of Prestress-Stable Tensegrity Structures Solved by Real-Coded Genetic Algorithm

Tensegrity structures are classified as kinematically determinate ones with two subcases and kinematically indeterminate ones with three subcases in view of their respective stability properties. How the stiffness of a tensegrity structure changes as the level of prestress changes is explored for different scenarios using six carefully chosen samples. For a tensegrity structure merely satisfying the prestress-stability condition, a new optimization model is presented to determine its critical buckling state corresponding to zero stiffness. A real-coded genetic algorithm (RCGA) is then developed to solve this problem, featured by the fact that a special sign-control technique is embedded in the fundamental genetic operations, making the individuals generated in each step fall into the admissible region automatically. The stability of the neutral equilibrium state for tensegrity structures violating the prestress-stability condition is also discussed. Several numerical examples are tested to validate the efficiency of the present approach.