Date of Award

12-2015

Document Type

Thesis

Degree Name

Master of Science (MS)

Legacy Department

Mechanical Engineering

Advisor

Fadel, Georges M

Committee Member

Wiecek, Margaret

Committee Member

Thompson, Lonny L

Abstract

The Parametric Programming method is investigated to consider its applicability to structural optimization problems. It is used to solve optimization problems that have design variables as implicit functions of some independent input parameter(s). It provides optimal solutions as a parametric function of the input parameter(s) for the entire parameter space of interest. It does not require the detailed discrete optimizations needed at a large number of parameter values as in traditional non-parametric optimization. Parametric programming is widely used in optimal controls, model predictive control, scheduling, process synthesis and material design under uncertainty due to the above mentioned benefits. Its benefits are however, still unexplored in the field of structural optimization. Parametric programming could for instance, be used to aid designers in identifying and optimizing for uncertain loading conditions in complex systems. The first objective of this thesis is to identify a suitable multi-parametric programming algorithm among the many available ones in the literature to solve structural optimization problems. Once selected, the second goal is to implement the chosen algorithm and solve single parametric and multi-parametric sizing optimization problems, shape optimization problems, and use multi-parametric programming as a multi-objective optimization tool in structural optimization. In this regard, sizing optimization of truss structures and shape optimization of beams for load magnitude and load directions as varying parameters are solved for single and multi-parameter static and/or dynamic load cases. Parametric programming is also used to solve the multi-objective optimization of a honeycomb panel and the results are compared with those from non-parametric optimization conducted using commercial optimization software. Accuracy of results, and computational time are considered. From these studies, inferences are drawn about the issues and benefits of using parametric programming in structural optimization.

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