A Method for Determining the Set of Feasible Prestress Forces for Specified Geometry

Abstract

In the design of tensegrity systems, which are commonly used in large-span structures, the determination of a set of prestress forces is one of the most critical issues. The stability of a tensegrity system depends on a set of prestress forces that ensure the entire structure remains in equilibrium and may need architectural requirements. For a specified geometry, a set of prestress forces that are in equilibrium can be obtained through iteration, and this set of prestress forces is referred to as feasible. This study introduces a novel approach for obtaining a feasible set of prestress forces for desired geometries through nonlinear iteration using the Force Density Method. The proposed method effectively mitigates singularity issues arising from non-invertible force density matrices, thereby enhancing computational robustness and reliability. The methodology is applied to four geometric configurations: a simple model, a Levy dome, and two Geiger domes (with and without inner rings), demonstrating its ability to achieve a set of prestress forces that are consistent with established benchmarks. These results highlight the method's potential as a practical and reliable tool for addressing prestress design challenges in tensegrity structures.