Tensegrity structure optimization for finding stable configurations

Tensegrity structures are prestressed truss-like structures that balance tensile and compressive forces within a network of struts and cables. They have gained significant attention in engineering and architecture due to their favorable attributes, such as deployability, aesthetic appeal, non-linear behavior, tunable stiffness, and minimal material usage. Researchers have focused most of their work on form-finding methods such as force density, adaptive force density, dynamic relaxation, and evolutionary algorithms. In this research work, the objective is to determine bistable/multistable configurations in a class of symmetric tensegrity structures (class-1symmetrical simplex tensegrity). The bistability or multistability of tensegrity structures, which enables seamless transitions between different shapes and states, can provide optimal performance for a variety of tasks. This research explores optimizing potential energy without using any nonlinear incremental finite element like methods. Instead, this study utilizes an existing commercially available minimization function for non-linear optimization to trace the potential energy curve and determine stable configurations. It is found that the transitions in the lower-order tensegrity structures are twinning-like transitions with the abrupt release of strain energy, while higher-order structures tend to exhibit smooth transitions between two different stable configurations with different energy levels.