| The objective of this study is to model the uncertainties inherent in the dynamic response of structures. The main source of uncertainty considered in this work is emphasized in the environmental loading, namely, wind loads, wave loads, and ground motion excitation. A perturbation technique is used to introduce the random nature of each variable in the governing equations of motion. Terms up to and including second order are retained and the resulting coupled equations are used as the basis to address the uncertainties in both material and loading. The structures are discretized using standard finite element methods and standard numerical techniques can be successively applied to obtain solution to the zeroth, first and second order systems of equations. Both uncorrelated and correlated random variables are considered, and in the first case it is possible to reduce the amount of computation required to obtain a solution. The methodology presented can be viewed as an addition procedure that can be used in a complementary fashion to existing finite element codes to address variance of material properties and system loads.; This study examines random wind loading of a concrete exhaust tower, random wave excitation of a steel jacket offshore structure, and the excitation of a building using the recorded acceleration record of an earthquake. Information needed in the solution of these practical problems such as an approach to distinguishing the level of importance of these variables and the influence of the correlation of the random variables will be discussed. To assess the performance of the method, comparison of the predictions model addressing various uncertainties in the problem will be made with deterministic predictions. This comparison reveals that careful choice of random variables involved in the model is crucial to obtain the most accurate prediction of the structural responses. Incomplete problem specifications on the uncertainty in problems and large variances in random data are studied to better understand the limitations of the methodology in the solution of the problems of interest to the science and engineering community. |
