Transient response of structures with uncertain structural parameters

Abstract

This paper focuses on the transient dynamic analysis of structures with uncertain structural parameters, subjected to an impact load. The analyzed uncertainty is associated with the Young’s modulus and mass density of the structures and also with the applied impact load. Two methods viz. adaptive Taylor methods and direct optimisation based interval finite element approach are used in the present work to obtain time-history response of the structure with uncertain parameters. In case of first approach, adaptive Taylor series expansion along with gradient method based on computation of time-dependent partial derivatives is used to determine the bounds on the response as a function of time. In case of second approach based on optimisation, these parametric uncertainties are quantified by triangular membership functions based on the fuzzy formalism, and the uncertain transient analysis is performed using the α-sublevel technique. Wilson-θ method is applied to solve the transient response problem at the core of the analysis. In order to solve the sequence of optimisation problems, fmincon optimisation function from the MATLAB optimisation toolbox adapted to multiple output analysis of FE models is developed. The performance and accuracy of this approach is examined by taking up example problems. The present work demonstrates the effectiveness of the direct optimisation approach based fuzzy finite element method and adaptive Taylor methods in evaluating the dynamic response of structures with multiple uncertainties.