Restart adaptive pushover analysis (RAPA) of tall structures to collapse by inverse optimization: Monotonic and cyclic loading

A new mixed force/displacement inverse optimization algorithm is proposed for performing non-linear adaptive pushover analysis of structures using advanced finite element methods in order to evaluate the ultimate behaviour of structures to collapse under lateral seismic or wind loads. One of the novel points of the proposed adaptive procedure is that it utilizes the restart capability of the finite element analysis program ABAQUS to apply a target displacement at the roof of the structure and then corrects the initial load profile through optimization to match the load distribution calculated by a frequency analysis. By controlling the roof displacement directly and the load profile indirectly, the algorithm surmounts many of the shortcomings of its predecessors as it accounts for stiffness change, includes higher mode effects and provides the required stability to capture the structural behaviour with emphasis on solving the instabilities of the descending branch, such as abrupt changes on forces caused by material or geometrical failures (fracture, cracking, buckling). The novel adaptive algorithm is developed using MATLAB libraries and its accuracy and robustness is illustrated and verified through two tall slender steel structures (a 20-storey high rise building and a wind turbine supporting structure) which are modelled and analyzed in ABAQUS. The results are compared to those of other conventional methods of pushover analysis and proved to be superior to them. The proposed algorithm was able to trace successfully the descending branch of the pushover curves of both structural models, especially in the case of the wind turbine structure which showed an almost vertical strength drop caused by the sudden onset of local buckling on the tubular steel tower, while all other current force-based methods failed due to convergence issues. Having established accuracy, the method is then tested under cyclic lateral loads. The cyclic pushover analysis was successful in obtaining the hysteretic curve of the wind turbine tower, and in comparison with monotonic pushover analysis, was found to be a superior option for assessing structural ductility and initiation of local bucking under seismic events as it accounts for damage accumulation.