Finding member connectivities and nodal positions of tensegrity structures based on force density method and mixed integer nonlinear programming. (1st July 2018) - Xu, Xian; Wang, Yafeng; Luo, Yaozhi
Highlights: Member connectivities, nodal positions and force densities are simultaneously used as design variables. The proposed model can be degenerated into single force/form/member connectivities-finding model. Nodal coordinates of the final tensegrity structure can be controlled flexibly. Lengths and force densities of members can be optimized simultaneously. Abstract: An optimization approach based on force density method and mixed integer nonlinear programming is proposed for optimization of tensegrity structures on member connectivities and nodal positions. The member connectivities, nodal coordinates and force densities are simultaneously used as design variables and the number of nodes is the only necessary parameter needed to be given in advance. The proposed approach possesses a general-purpose formulation which can be degenerated into both conversional form-finding formulation and previous member connectivities-finding formulation. Various properties such as the number of cables, nodal coordinates and evenness of member internal forces can be controlled and optimized by introducing appropriate constraints and objective functions. Numerical examples are carried out to verify the proposed approach and illustrate that not only classical tensegrity systems but also novel tensegrity systems can be obtained by the proposed approach.