A discrete geometry-based optimization model for coupling topology and nodal coordinates in biorthogonal tensegrity structures

Tensegrity is a lightweight and efficient structural system that intimately combines force and form. Existing optimization models coupling topology and nodal coordinates are limited to the design of smaller-scale structures, which imposes higher demands on the designer’s experience and restricts the development of free-form tensegrity designs. A discrete geometry-based optimization model of biorthogonal tensegrity structure coupling topology and nodal position is proposed in this study. By utilizing graph theory, we unify the design of rectangular, annular, and sector extension structures into a single framework. By discretizing curves and surfaces, the nodal constraints are liberated from explicit mathematical expressions, offering designers the freedom to create tensegrity structures of any shape or even simple sketches. This approach significantly reduces the computational complexity of mixed-integer nonlinear programming models, broadening their application in tensegrity design. Furthermore, equilibrium equations based on the force density method are derived to account for rigid body effects, which extends the applicability of the coupled topology and nodal coordinate optimization model. The numerical examples provided validate the effectiveness of the proposed model.