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Damage Identification of Truss Structures Based on Force Method

Published online by Cambridge University Press:  23 March 2015

Nam-Il Kim
Affiliation:
Department of Architectural Engineering, Sejong University, 98 Kunja Dong, Kwangjin Ku, Seoul 143-747, Korea
Seunghye Lee
Affiliation:
Department of Architectural Engineering, Sejong University, 98 Kunja Dong, Kwangjin Ku, Seoul 143-747, Korea
Namshik Ahn
Affiliation:
Department of Architectural Engineering, Sejong University, 98 Kunja Dong, Kwangjin Ku, Seoul 143-747, Korea
Jaehong Lee*
Affiliation:
Department of Architectural Engineering, Sejong University, 98 Kunja Dong, Kwangjin Ku, Seoul 143-747, Korea
*
*Corresponding author. Email: [email protected] (Jaehong Lee)
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Abstract

An computationally efficient damage identification technique for the planar and space truss structures is presented based on the force method and the micro genetic algorithm. For this purpose, the general equilibrium equations and the kinematic relations in which the reaction forces and the displacements at nodes are take into account, respectively, are formulated. The compatibility equations in terms of forces are explicitly presented using the singular value decomposition (SVD) technique. Then governing equations with unknown reaction forces and initial elongations are derived. Next, the micro genetic algorithm (MGA) is used to properly identify the site and extent of multiple damage cases in truss structures. In order to verify the accuracy and the superiority of the proposed damage detection technique, the numerical solutions are presented for the planar and space truss models. The numerical results indicate that the combination of the force method and the MGA can provide a reliable tool to accurately and efficiently identify the multiple damages of the truss structures.

Type
Research Article
Copyright
Copyright © Global-Science Press 2015 

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References

[1]Sedaghati, R. and Esmailzadeh, E., Optimum design of structures with stress and displacement constraints using the force method, Int. J. Mech. Sci., 45 (2003), pp. 13691389.CrossRefGoogle Scholar
[2]Farshi, B. and Alinia-Ziazi, A., Sizing optimization of truss structures by method of centers and force formulation, Int. J. Solids Struct., 47 (2010), pp. 25082524.CrossRefGoogle Scholar
[3]Kaveh, A., Optimal Structural Analysis, 2nd edn Chichester, John Wiley, Uk, 2006.Google Scholar
[4]Kaveh, A. and Kalatjari, V., Genetic algorithm for discrete-sizing optimal design of trusses using the force method, Int. J. Numer. Meth. Eng., 55 (2002), pp. 5572.Google Scholar
[5]Patnaik, S. N. and Hopkins, D. A., Optimality of a fully stressed design, Comput. Method Appl. M., 165 (1998), pp. 215221.CrossRefGoogle Scholar
[6]Kaveh, A., and Koohestani, K., Efficient finite element analysis by graph-theoretical force method; triangular and rectangular plate bending elements, Finite Elem. Anal. Des., 44 (2008), pp. 646654.CrossRefGoogle Scholar
[7]Henderson, J. C De C., Topological aspects of structural analysis, Aircraft Eng., 32 (1960), pp. 137141.Google Scholar
[8]Henderson, J. C De C. and Maunder, E. A. W., A problem in applied topology: on the selection of cycles for the flexibility analysis of skeletal structures, J. Inst. Math. Appl., 5 (1969), pp. 254269.Google Scholar
[9]Maunder, E. A. W., Topological and Linear Analysis of Skeletal Structures, Ph.D. thesis, Imperial College, London, 1971.Google Scholar
[10]Kaveh, A., Application of Topology and Matroid Theory to the Analysis of Structures, Ph.D. thesis, Imperial College, London, 1974.Google Scholar
[11]Robinson, J., Integrated Theory of Finite Element Methods, Wiley, New York, 1973.Google Scholar
[12]Kaneko, I., Lawo, M. and Thierauf, G., On computational procedures for the force methods, Int. J. Numer. Methods Eng., 18 (1982), pp. 14691495.Google Scholar
[13]Soyer, E. and Topcu, A., Sparse self-stress matrices for the finite element force method, Int. J. Numer. Methods Eng., 50 (2001), pp. 21752194.Google Scholar
[14]Coleman, T. F. and Pothen, A., The null space problem I; complexity, Siam J. Alg. Disc. Meth., 7 (1986), pp. 527537.CrossRefGoogle Scholar
[15]Coleman, T. F. and Pothen, A., The null space problem II; algorithms, Siam J. Alg. Disc. Meth., 8 (1987), pp. 544561.Google Scholar
[16]Pothen, A., Sparse null basis computation in structural optimization, Numer. Math., 55 (1989), pp. 501519.CrossRefGoogle Scholar
[17]Gilbert, J. R. and Heath, M. T., Computing a sparse basis for the null space, Siam J. Alg. Disc. Meth., 8 (1987), pp. 446459.Google Scholar
[18]Patnaik, S. N., Integrated force method versus the standard force method, Comput. Struct., 22 (1986), pp. 151164.Google Scholar
[19]Patnaik, S. N., The variational formulation of the integrated force method, Aiaa J., 24 (1986), pp. 129137.Google Scholar
[20]Villalba, J. D. and Laier, J. E., Localising and quantifying damage by means of a multi-chromosome genetic algorithm, Adv. Eng. Softw., 50 (2012), pp. 150157.Google Scholar
[21]Friswell, M. I., Penny, J. E. T. and Garvey, S. D., A combined genetic and eigensensitivity algorithm for the location of damage in structures, Comput. Struct., 69 (1998), pp. 548556.CrossRefGoogle Scholar
[22]He, R. S. and Hwang, S. F., Damage detection by a hybrid real-parameter genetic algorithm under the assistance of grey relation analysis, Eng. Appl. Artif. Intel., 20 (2007), pp. 980992.Google Scholar
[23]Koh, B. H. and Dyke, S. J., Structural health monitoring for flexible bridge structures using correlation and sensitivity of modal data, Comput. Struct., 85 (2007), pp. 117130.CrossRefGoogle Scholar
[24]Gomes, H. M. and Silva, N. R. S., Some comparisons for damage detection on structures using genetic algorithms and modal sensitivity method, Appl. Math. Model., 32 (2008), pp. 22162232.Google Scholar
[25]Moslem, K. and Nafaspour, R., Structural damage detection by genetic algorithms, Aiaa J., 40 (2002), pp. 13951401.Google Scholar
[26]Rao, M. Ananda, Srinivas, J. and Murthy, B. S. N., Damage detection in vibrating bodies using genetic algorithms, Comput. Struct., 82 (2004), pp. 963968.Google Scholar
[27]Mares, C. and Surace, C., An application of genetic algorithms to identify damage in elastic structures, J. Sound Vib., 195 (1996), pp. 195215.Google Scholar
[28]Schek, H. J., The force density method for form finding and computation of general networks, Com-put. Methods Appl. Mech. Eng., 3 (1974), pp. 115134.Google Scholar
[29]Tran, H. C. and Lee, J., Advanced form-finding of tensegrity structures, Comput. Struct., 88 (2010), pp. 237246.Google Scholar
[30]Livesley, R. K., Matrix Methods of Structural Analysis, 2nd Edn. Pergamon Press, Oxford, 1975.Google Scholar
[31]Pellegrino, S., Structural computations with the singular value decomposition of the equilibrium matrix, Int. J. Solids Struct., 30 (1993), pp. 30253035.Google Scholar
[32]Darwin, C., The Origin of Species, Signet Classic ed., Penguin Books led., 2003.Google Scholar
[33]Goldberg, D. E., Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, 1989.Google Scholar
[34]Krishnakumar, K., Micro-genetic algorithms for stationary and non-stationary function optimization, Proc. Spie Intell. Control Adaptive Syst., 1196 (1989), pp. 282296.Google Scholar
[35]Carroll, D. L., Genetic algorithms and optimizing chemical oxygen-iodine lasers, Dev. Theor. Appl. Mech., 18 (1996), pp. 411424.Google Scholar
[36]Chen, T. Y. and Chen, C. J., Improvements of simple genetic algorithm in structural design, Int. J. Numer. Meth. Eng., 40 (1997), pp. 13231334.Google Scholar