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Upper and Lower Bounds of the Solution for the Superelliptical Plates Problem Using Genetic Algorithms

H.W. Tang1, Y.T. Yang1, C.K. Chen1
1 NCKU, Tainan, Taiwan.

Computer Modeling in Engineering & Sciences 2012, 85(3), 193-206. https://doi.org/10.3970/cmes.2012.085.193

Abstract

In this article, a new method combining the Mathematical Programming and the Method of Weighted Residual called MP-MWR is presented. Under the validation of maximum principle, and up on the collocation method, the differential equation can be transferred into a bilateral inequality problem. Applying the genetic algorithms helps to find optimal solutions of upper and lower bounds which satisfy the inequalities. Here, the method is verified by analyzing the deflection of superelliptical clamped plate problem. By using this method, the good approximate solution and its error bounds can be obtained effectively and accurately.

Keywords

Mathematical Programming, Method of Weighted Residuals, collocation method, superelliptical plate, genetic algorithms.

Cite This Article

Tang, H., Yang, Y., Chen, C. (2012). Upper and Lower Bounds of the Solution for the Superelliptical Plates Problem Using Genetic Algorithms. CMES-Computer Modeling in Engineering & Sciences, 85(3), 193–206.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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