Traversing Singularities in Nonlinear Analyses on Cable Network Structures

Nonlinear analyses of cable network structures using Newton's iteration often encounter difficulties in solving for a singular stiffness matrix stemming from the tension-stabilizing nature and slackening of cables. This paper presents a solution method, called null space projection, to traverse such a singular linear system in Newton's iteration. In the method, the current unbalance of internal and external forces is projected on the null space of the stiffness matrix and the contributions of null space basis for the variable updating are derived such that the total potential energy is reduced. Numerical example shows that the method successfully traverses singular systems in Newton's iteration process and consequently gives the equilibrium state of the structure.