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Solution of some Engineering Partial Differential Equations Governed by the Minimal of a Functional by Global Optimization Method

Published online by Cambridge University Press:  01 May 2013

Y. M. Cheng ,
D. Z. Li ,
N. Li ,
Y. Y Lee  and
S. K. Au
Y. M. Cheng*
Affiliation:
Department of Civil and Environmental Engineering, Hong Kong Polytechnic University, Hong Kong
D. Z. Li
Affiliation:
Department of Civil and Environmental Engineering, Hong Kong Polytechnic University, Hong Kong
N. Li
Affiliation:
Department of Civil and Environmental Engineering, Hong Kong Polytechnic University, Hong Kong
Y. Y Lee
Affiliation:
Department of Civil and Architectural Engineering, City University of Hong Kong
S. K. Au
Affiliation:
Wong and Cheng, Hong Kong
*
*Corresponding author ([email protected])
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Abstract

Many engineering problems are governed by partial differential equations which can be solved by analytical as well as numerical methods, and examples include the plasticity problem of a geotechnical system, seepage problem and elasticity problem. Although the governing differential equations can be solved by either iterative finite difference method or finite element, there are however limitations to these methods in some special cases which will be discussed in the present paper. The solutions of these governing differential equations can all be viewed as the stationary value of a functional. Using an approximate solution as the initial solution, the stationary value of the functional can be obtained easily by modern global optimization method. Through the comparisons between analytical solutions and fine mesh finite element analysis, the use of global optimization method will be demonstrated to be equivalent to the solutions of the governing partial differential equations. The use of global optimization method can be an alternative to the finite difference/ finite element method in solving an engineering problem, and it is particularly attractive when an approximate solution is available or can be estimated easily.

Keywords

Differential equationUltimate limit stateOptimization methodVariational principle
Type
Articles
Information
Journal of Mechanics , Volume 29 , Issue 3 , September 2013 , pp. 507 - 516
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2013 

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References

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