A generalized normal flow method with online step controls for pushover analysis of nonlinear softening structures

This paper introduces a robust path-following method for pushover analysis of softening structures due to geometric and/or material nonlinearities. The proposed method is a generalized form of the conventional normal flow method (NFM) that provides dimensional consistency in the correction iterations and improves the convergence properties of the algorithm. The generalized NFM is further enhanced by two online step control processes, namely, the Convex Step-size Control (CSC) process and the Hyper-Plane Step Control (HPSC) process. The CSC process introduces a set of inequality constraints on the step size to form a convex solution space and (i) enhance the convergence properties of the algorithm by preventing overshooting in highly nonlinear areas, and (ii) improve robustness of the path-tracing process by controlling the resolution of the traced equilibrium path (or spacing/distance between successive equilibrium points) making it unlikely to miss (highly nonlinear) sections of the path. The HPSC process introduces a hyper-plane boundary in the solution space to prevent backward path-tracing. The performance of the proposed generalized NFM with the CSC and HPSC processes is validated through examples with structures exhibiting snap-back and snap-through response due to geometric and material nonlinearities. The proposed method is also compared with existing path-following methods typically used for the pushover analysis of nonlinear structures.