Date of Award

Fall 2007

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mechanical & Aerospace Engineering

Program/Concentration

Mechanical Engineering

Committee Director

Gene J. W. Hou

Committee Member

Sebastian Bawab

Committee Member

Han Bao

Call Number for Print

Special Collections; LD4331.E56 T36 2007

Abstract

The production process and the operational environment of a product usually involve many unpredictable elements, such as the manufacturing tolerance, the service loads, the maintenance schedule, etc. Furthermore, the targeted functionality of a product can also be alternated or enhanced in its service life due to the technology advancement, new demands, or new regulation. It is thus a challenge to a designer to include these uncertainties in the early design stage of a product.

This thesis uses a simple three-bar truss problem as a vehicle to investigate the qualities of the optimal solutions resulted from various stochastic programming formulations. The specific stochastic programming techniques selected in this study include the worst case design, the chance programming, and the design with recourse. The last method has been studied in operations research but seldom used in engineering design.

The three-bar truss problem has three design variables. The structural weight is considered as the design objective, which is related to the production cost. The truss structure is subjected to nine constraints ranging from the yielding to the resonance condition. The direction of the load, which is applied to the tip of the structure, can be varied between -45° to 90°. The worst case design treats the direction of the load as a problem parameter, while the chance programming and the design with recourse treat it as a random variable.

Numerical integration, Monte Carlo simulation, and the optimizer provided by MATLAB code are used in this study. Most of the stochastic programming formulations arrive at the same optimal solution. The thesis is concluded with comments on each of the formulations in respect to the efficiency in computation and the accuracy in representing design consideration.

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DOI

10.25777/wz2x-sx03

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