Title: Developments in the theory and applications of the variability response function concept
Description: Uncertainty quantification in Civil Engineering applications is crucial to the decision making process in the analysis, design, and retrofitting of infrastructure. The consensus amongst researchers is that deterministic approaches to problem solving can lead to very misleading results, and the assessment of infrastructure performance needs to be addressed within a probabilistic framework. As a result, there is great demand to identify and acquire probabilistic information about uncertain system parameters which affect the performance of a structure. Unfortunately, it is difficult to obtain a full probabilistic description of uncertain system parameters, specifically their spatial correlation structures. In response to this limitation, researchers have sought a means to circumventing the need for a full probabilistic description of system uncertainties in determining structural response statistics. One approach is the Variability Response Function(VRF) concept, introduced by Shinozuka, which decomposes the variability of a response quantity into a deterministic function that is solely dependent on the deterministic components of the structure and the Spectral Density Function (SDF) of the uncertain system parameters modeled as a homogeneous random field.

The deterministic function is called the VRF and is analogous to the Green's function of a differential equation. This dissertation explores the limits of the applicability of the VRF concept in Structural Mechanics problems. The VRF concept is applied to nonlinear statically determinate and indeterminate beams as well as plane stress structures where the flexibility is considered to be a random field. In the latter part of the dissertation the VRF concept is applied to the problem of stochastic characterization of homogenized effective properties through an equivalent energy based homogenization technique. The final chapter of this dissertation presents a novel methodology to rapidly generate sample microstructures for random two phase materials.