Probabilistic Response Predictions using Few Nonlinear Finite Element Analyses

Abstract

This paper combines second-moment statistics with exact and efficiently calculated finite element response sensitivities. The objective is to gain insights from a single, or a few, nonlinear static or dynamic finite element analyses. Three contributions are included. First, the Bouc-Wen material model that is most recently implemented in OpenSees is amended with the algorithmically consistent tangent that is required for correct response sensitivity calculations. Second, the direct differentiation method is implemented for that model. Third, the response sensitivities are transformed into a standardized parameter space; thereafter, points along that vector are transformed back to the original parameter space in order to provide probabilistic insights into the response and the relative importance of correlated input parameters.