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Mathematical Problems in Engineering
Volume 2015, Article ID 859653, 8 pages
http://dx.doi.org/10.1155/2015/859653
Research Article

Position and Thickness Optimization of Ribs for Ventilation Covering Using the Micro Genetic Algorithm with an Interpolated Smooth Objective Function

1Department of Mechanical Engineering & IEDT, Kyungpook National University, Daegu 702-701, Republic of Korea
2Department of Mechanical Engineering, Graduate School of Kyungpook National University, Daegu 702-701, Republic of Korea

Received 27 February 2015; Revised 17 July 2015; Accepted 26 July 2015

Academic Editor: Alessandro Gasparetto

Copyright © 2015 Young-Doo Kwon et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Structures with supporting ribs are adopted in many fields of engineering. These ribs are attached to the main plate or shell to increase stiffness and reduce the stresses of a structure. Currently, much research in structural optimization has been devoted to size or thickness optimizations. In this study, the discrete positions of the ribs of a structure are optimized in addition to their thicknesses. The objective function, which is the total weight of a structure, is a continuous function with respect to the thickness of the ribs. However, it is a stepwise function of a dimensionless variable, which represents the set of positions of the ribs. Because of this stepwise objective function, the gradient method of optimization is not applicable. Therefore, we applied the micro genetic algorithm (MGA), which does not need derivatives of the objective function. To accelerate the rate of convergence, the stepwise objective function is interpolated to a smooth artificial objective function that does not alter the optimal solution.