Optimal self-stress determination of tensegrity structures

•A new method is introduced for self-stress determination of tensegrity structures.•Unlike traditional methods, this method does not require member grouping.•This method is efficient for large-scale and irregular tensegrity structures.•A derivative-free stochastic algorithm is used to reduce computational cost. In traditional methods for self-stress determination of a tensegrity structure, member grouping, which highly relies on geometric simplicity of the structure, is a key component. For this reason, these methods are not efficient to handle complex or irregular tensegrity structures. In addition, most of optimization algorithms used in traditional methods are based on gradients. Therefore, exponential increase of computational effort is inevitable for self-stress determination of large-scale tensegrity structures. To resolve those issues, a new method called the stochastic fixed nodal position method is developed for self-stress determination of tensegrity structures. This method utilizes a derivative-free stochastic algorithm in numerical optimization with the starting point being obtained by solving a linear system of equations, so that the computation cost is reduced, and member grouping is no longer required. The proposed method is suitable for large-scale, complex, and irregular tensegrity structures. The proposed method is applied to self-stress determination of a planar tensegrity structure, a spatial four-way tensegrity grid, and an irregular tensegrity structure in the simulation. Results show that the proposed method can handle both regular and irregular tensegrity structures, and has a low computational cost, a super linear rate of convergence, and high accuracy.