ABSTRACT
ABSTRACT: Efficient and accurate analytical tools are needed in earthquake engineering to propagate uncertainties from the seismic input and finite element (FE) model parameters to a probabilistic estimate of the seismic performance through advanced large-scale nonlinear simulations based on the same FE models as those used in deterministic analysis. Sensitivities of the FE response with respect to both model and loading parameters represent an essential ingredient in studying this complex propagation of uncertainties. This chapter presents recent developments in FE response sensitivity analysis based on the Direct Differentiation Method (DDM) for displacement-based, force-based, and three-field mixed finite elements. First-Order SecondMoment (FOSM) approximations of the first-and second-order statistics of the response of structural systems with random/uncertain parameters and subjected to deterministic quasi-static and/or dynamic loads are obtained using DDM-based FE response sensitivities and compared to Monte Carlo simulation results. The probability of a structural response quantity exceeding a specified threshold level is evaluated using the First-Order Reliability Method (FORM) combined with DDM-based FE response sensitivities in the search for the “design point(s)’’ (DPs). Both time-invariant and time-variant problems are considered. The geometry of limit-state surfaces near the DP(s) is explored in subspaces defined by planes of major principal curvatures. This geometry explains the lack of accuracy of FORM-based solutions in some cases and suggests the development of new improved solution strategies, e.g., the Design Point – Response Surface – Simulation (DP-RS-Sim) method. The examples presented in this study include both structural systems and soil-foundation-structure interaction systems and are based on two types of analysis which are used extensively in earthquake engineering, namely pushover analysis and time history analysis.
