Algorithm Implementation of the Continuation Method for Solving a Static Equilibrium Problem of a Tensegrity Structure

Abstract

Tensegrity structures are used in fields like architecture, engineering and biomedicine, and have new rising applications in robotics. The static analysis of these structures might be performed for the initial configuration of the structure in absence of external forces. This analysis leads to a set of equations generated from the Newtonian mechanic or the virtual work principle. Because this initial configuration of the structure is important, if different configurations can be found, it will lead to new applications and uses. There are numerical methods that search all the possible solutions in polynomial systems, one of them is the continuation method, that has been used in different fields such as biology and specially in robotics. In this work, two planar tensegrity structures are chosen to perform an analysis of static equilibrium using the virtual work principle, then a polynomial system is generated and solved with a computational implementation of the continuation method. The objective is to find different sets of solutions that might lead to new configurations of the tensegrity structures.