Publication Date




Embargo Period


Degree Type


Degree Name

Doctor of Philosophy (PHD)


Mechanical Engineering (Engineering)

Date of Defense


First Committee Member

Singiresu S. Rao

Second Committee Member

Michael R. Swain

Third Committee Member

Ryan L. Karkkainen

Fourth Committee Member

Shihab S. Asfour


Most engineering systems involve several uncertain or imprecise parameters such as geometric dimensions (due to tolerances), material constants such as yield strength, Young’s modulus and Poisson’s ratio and external actions such as gust, earthquake and other dynamic loads. These input uncertainties cause the output or response of the system also to be uncertain. If approximate deterministic values of the basic input parameters are used in the analysis of structural/mechanical systems, the high accuracy and reliability expected of these systems cannot be assured. This indicates that, for more reliable performance and to meet the stringent design requirements of practical systems, the uncertainties of the basic input parameters are to be considered in the analysis. Probabilistic approaches have been used in the past few decades to quantify the uncertainties associated with the structural/mechanical systems in the presence of uncertainties in the basic input parameters. The probabilistic approaches, however, require a knowledge of the probability distributions of the input parameters which are not known in most structural/mechanical systems. Other uncertainty-based methods such as fuzzy or linguistic description-based methods have also been used to model the uncertainties associated with mechanical systems. However, in most practical systems, the uncertain input parameters of the problem are often described in terms of ranges or intervals. The interval analysis has been used by some researchers for the analysis of uncertain systems whose parameters are described as intervals or ranges. Unfortunately, due to the so-called dependency problem, the interval analysis leads to wider ranges than the correct ones and sometimes the resulting system response might also violate the physical laws of the problem. Hence, a modified procedure, such as the truncation-based interval analysis, needs to be used to overcome and control the overestimation caused by the dependency problem when interval analysis is used. In this work, a new interval-based method, termed the universal grey system (number) theory, is presented which leads to more accurate and reasonable bounds on the response quantities of structural/mechanical systems. Specifically, this work presents interval-based uncertainty models for micromechanical properties of composite materials. Modeling and analysis of composite laminates in the presence of uncertainties are also presented. Interval-based uncertainty failure models are developed for the failure assessment of composite materials. A new numerical procedure, termed the universal grey number-based Gaussian elimination method, is developed to find accurate bounds of response quantities of large structures that require the solution of systems of linear interval algebraic equations. A universal grey number-based finite element method is developed for the analysis of laminated beams and plates in the presence of uncertainties. An interval-based optimization technique, termed the universal grey number-based genetic algorithm, is developed for determining the optimum design of uncertain structural/mechanical systems. This work shows that the universal grey system theory predicts realistic and more improved results compared to enumeration method, probabilistic method, interval analysis and truncation-based interval analysis.


Uncertainty; Structural/mechanical systems

Available for download on Friday, June 25, 2021