Reliability of inelastic wind excited structures by dynamic shakedown and adaptive fast nonlinear analysis (AFNA)

The ever-growing interest in performance-based wind engineering has created a need for assessment frameworks that can efficiently deal with inelasticity. The computationally efficient strain-driven dynamic shakedown approach has provided a solution that is not only capable of identifying failure mechanisms that are potentially critical during extreme winds, e.g., low cycle fatigue and ratcheting, but also allows direct estimation of inelastic deformations. This approach, however, can only solve problems at dynamic shakedown, i.e., with limited nonlinearity, and is not capable of providing response time histories. To address these limitations, this paper presents an efficient framework for reliability assessment of inelastic structures at dynamic shakedown and beyond. To this end, a novel step-by-step integration algorithm is developed for rapid response time history analysis within the setting of dynamic shakedown. The method is based on advancing fast nonlinear analysis through introducing schemes for enabling at each time step the adaptive selection of the step size, number of modes to be included, and number of potentially nonlinear elements. Inelasticity is modeled as distributed at the level of the stress resultants through a return mapping scheme based on the Haar–Kàrmàn principle, therefore enabling the integrated estimation of the state of dynamic shakedown. The scheme is seen to preserve the efficiency of recently developed strain-driven dynamic shakedown algorithms while providing a full range of response time histories at and beyond the state of dynamic shakedown. To enable reliability analysis, the scheme is embedded in a general uncertainty propagation framework.