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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 77
PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON CIVIL AND STRUCTURAL ENGINEERING COMPUTING
Edited by: B.H.V. Topping
Paper 130

Design of Frames using Genetic Algorithms, Force Method and Graph Theory

A. Kaveh and M. Abdie

Department of Civil Engineering, Iran University of Science and Technology, Tehran, Iran
and Building and Housing Research Center, Tehran, Iran

Full Bibliographic Reference for this paper
A. Kaveh, M. Abdie, "Design of Frames using Genetic Algorithms, Force Method and Graph Theory", in B.H.V. Topping, (Editor), "Proceedings of the Ninth International Conference on Civil and Structural Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 130, 2003. doi:10.4203/ccp.77.130
Keywords: genetic algorithm, structural optimization, frames, force method, analysis, cycle basis.

Summary
In optimal design, the members should be proportionally designed to reduce the usage of material and cost of the structure. Optimization can be categorized as sizing optimization, shape optimization, topology optimization and layout optimization. Methods for optimization are classified as mathematical programming methods and heuristic search approaches. The latter may employ neural networks, simulated annealing or genetic algorithms.

In this paper sizing optimization of frames employing Genetic algorithm (GA) is studied. In the process of optimal design, analysis should be performed several times. Here, the force method is employed for the analysis. The advantage of using this method lies in the fact that the matrices corresponding to the particular and complementary solutions ( $ \mathbf{B}_0$ and $ \mathbf{B}_1$ matrices) are formed independently of the mechanical properties of members. These matrices are constructed using concepts from graph theory. $ \mathbf{B}_0$ is formed using a shortest route tree having minimum number of non-zero entries. $ \mathbf{B}_1$ is formed on a suboptimal cycle basis leading to highly sparse flexibility matrix [1,2]. These matrices are employed several times in the process of a sequential analyses, where the number of equations solved is the same as the degree of static indeterminacy in place of the total degrees of freedom, thus increasing the speed of optimization.

Early papers on structural optimization using GA are due to Goldberg and Samtani [3], Jenkins [4], Adeli and Cheng [5], Rajeev and Krishnamoorthy [6], Erbatur et al [7], Kameshki and Saka [8] and Kaveh and Kalatjari [9,10]. Many others have published papers improving the results and increasing the speed of GA in the last decade. Here, some of the features of the method of Reference [7] is extended for optimal design of frames.

In this paper, three different fitness functions are used and it is shown that the fitness function of type I has a better convergence rate. The use of different crossovers is also examined.

Though the examples are chosen from planar frames, however, the present method can equally be applied to space frames. In this method, the matrices B0, $ \mathbf{B}_1$ and $ \mathbf{F}_m$ can be modified to make the method applicable to any other space structures.

In the example presented, increasing the population size reduces the number of iteration cycles required for convergence, and vice versa.

References
1
Kaveh A., Structural Mechanics: Graph and Matrix Methods, Research Studies Press (John Wiley), 2nd edition, 1995.
2
Kaveh, A., Optimal Structural Analysis, Research Studies Press (John Wiley), UK, 1997.
3
Goldberg, D.E., Samtani, M.P., "Engineering Optimization via Genetic Algorithm, Electronic Computation", ASCE, New York, 1986, pp 471- 476.
4
Jenkins, W.M., "Towards structural optimization via the Genetic algorithm", Computers and Structures, 40(1991)1321-1327. doi:10.1016/0045-7949(91)90402-8
5
Adeli, H and Cheng, N.T., "Integrated genetic algorithm for optimization of space structures", Journal of Aerospace Engineering, ASCE, 6(1993)315-328. doi:10.1061/(ASCE)0893-1321(1993)6:4(315)
6
Rajeev, S., Krishnamoorthy, C.S., "Discrete optimization of structures using Genetic algorithms", Journal of Structural Engineering, ASCE, 118(1992) 1233-1250. doi:10.1061/(ASCE)0733-9445(1992)118:5(1233)
7
Erbatur, F., Hasançebi, O., Tütünçü, I., Kiliç, H., "Optimal design of planar and space structures with Genetic algorithms", Computers and Structures, 75(2000)209-224. doi:10.1016/S0045-7949(99)00084-X
8
Kameshki, E.S. and Saka, M.P., "Optimum design of nonlinear steel frames with semi-rigid connections using a genetic algorithm", Computers and Structures, 79(2001)1593-1604. doi:10.1016/S0045-7949(01)00035-9
9
Kaveh A. and Kalatjari V., "Genetic algorithm for discrete-sizing optimal design of trusses using the force method", International Journal for Numerical Methods in Engineering, 55(2002)55-72. doi:10.1002/nme.483
10
Kaveh A. and Kalatjari V., "Topology optimization of trusses by the force method and Genetic algorithm", International Journal of Numerical Method in Engineering, No. 4, 58(2003) to appear. doi:10.1002/nme.800

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