Potential Energy Optimization Approach in the Form-Finding of Tensegrities and Cable–Strut Systems

Abstract

A form-finding process for tensegrities and cable–strut systems is determined as a minimum problem of potential energy that is constructed considering initial estimated pre-stress states. Both the Jacobian and Hessian matrices of a potential energy function are derived explicitly regarding free nodal coordinates. Based on these derivations, both the first-order geodesic dynamic relaxation optimization method and the second-order optimization method of Newton can be applied to solve form-finding problems involving tensegrities and cable–strut structures. It should be noted that both the pre-stress state and the configuration of the systems are adjusted during the optimization process to satisfy self-equilibrium conditions. The geometrical constraints are then included in the proposed work as equality constraint conditions to find the final forms satisfying not only the self-equilibrium states but also the designers’ demands. Two well-known and complex systems are investigated to assess the efficiency of the proposed method, i.e. free-standing truncated icosahedral tensegrity and the Kiewitt Dome.

Keywords:

• Jacobian and Hessian matrices
• geodesic dynamic relaxation method
• Newton method
• free-standing tensegrity
• supported cable–strut systems

Disclosure Statement

No potential conflict of interest was reported by the authors.

Data Availability Statement

The Julia codes used to implement Algorithms 1 to 4 to obtain the results in the manuscript are available from the corresponding author upon reasonable request.

Additional information

Funding

This work was supported by The University of Danang, University of Science and Technology [Code Number of Project: T2023-02-17].