Edge-crack diagnosis using improved two-dimensional cracked finite element and micro genetic algorithm
Keywords:
cracked finite element, micro genetic algorithm, user element, ABAQUS, natural frequency, crack diagnosisAbstract
In this paper, a crack diagnosis method based on an improved two-dimensional (2-D) finite element (FE) with an embedded edge crack, and micro genetic algorithm (μ-GA) is proposed. The crack is not physically modelled within the element, but instead, its influence on the local flexibility of the structure is accounted for by the reduction of the element stiffness as a function of the crack length. The components of the stiffness matrix for the cracked element are determined from the Castigliano’s first principle. The element was implemented in the commercial FE code ABAQUS as a user element subroutine. The accuracy of the proposed improved cracked element is verified by comparing the predicted first natural frequency with the available experimental data. Subsequently, a methodology to detect the crack location and size in conjunction with the proposed improved cracked element is formulated as an optimisation problem, and μ-GA is used to find the optimal location and depth by minimising the cost function based on the difference of measured and calculated natural frequencies. The proposed crack detection procedure using the improved 2-D FE with an embedded edge crack, and μ-GA is validated using the available experimental and FE modal analysis data reported in the existing literature. The predicted crack locations and crack sizes demonstrate that this approach is capable of detecting small crack location and depth with small errors.
Downloads
References
ABAQUS. (2004). Documentation (Version 6.5). Pawtucket, RI: Hibbit, Karlson & Sorensen.
Amstutz, S., Horchani, I., & Masmoudi, M. (2005). Crack detection by the topological gradient
method. Control and Cybernetics, 34, 81–101.
Cakoni, F., & Colton, D. (2003). The linear sampling method for cracks. Inverse Problems, 19,
–295.
Carroll, D. L. (1996). Genetic algorithms and optimizing chemical oxygen-iodine lasers. In H.
Wilson, R. Batra, C. Bert, A. Davis, R. Schapery, D. Stewart, & F. Swinson (Eds.),
Developments in theoretical and applied mechanics (Vol. XVIII, pp. 411–424). Tuscaloosa,
Alabama, USA: School of Engineering, The University of Alabama.
Chaudhari, T. D., & Maiti, S. K. (2000). A study of vibration of geometrically segmented beams
with and without crack. International Journal of Solids and Structures, 37, 761–779.
Chinchalkar, S. (2001). Determination of crack location in beams using natural frequencies.
Journal of Sound and Vibration, 247, 417–429.
Chondros, T. G., Dimarogonas, A. D., & Yao, J. (1998). A continuous cracked beam vibration
theory. Journal of Sound and Vibration, 215, 17–34.
Chondros, T. G., Dimarogonas, A. D., & Yao, J. (2001). Vibration of a beam with a breathing
crack. Journal of Sound and Vibration, 239, 57–67.
Chou, J. H., & Ghaboussi, J. (2001). Genetic algorithm in structural damage detection. Computers
and Structures, 79, 1335–1353.
Dado, M. H. (1997). A comprehensive crack identification algorithm for beam under different
end conditions. Applied Mechanics, 51, 381–398.
Doebling, S. W., Farrar, C. R., Prime, M. B., & Shevitz, D. W. (1996). Damage identification
and health monitoring of structural and mechanical systems from changes in their vibration
characteristics: A literature review, (Technical, Report LA13070MS). Los Alamos, NM: Los
Alamos National Laboratory.
Friswell, M. I., Penny, J. E. T., & Garvey, S. D. (1998). A combined genetic and eigensensitivity
algorithm for the location of damage in structures. Computers and Structures, 69, 547–556.
Garreau, S., Guillaume, P., & Masmoudi, M. (2000). The topological asymptotic for PDE
systems: The elasticity case. SIAM Journal on Control and Optimization, 39, 1756–1778.Gawronski, W., & Sawicki, J. T. (2000). Structural damage detection using modal norms. Journal
of Sound and Vibration, 229, 194–198.
Goldberg, D. E. (1989). Genetic algorithms in search, optimization, and machine learning.
Reading, MA: Addison-Wesley.
Goldberg, D. E. (1989). Sizing populations for serial and parallel genetic algorithms. In Proceeding
rd International Conference on Genetic Algorithms and Their Applications (pp. 70–79).
Fairfax, Virginia, USA: George Mason University.
Gondhalekar, S. (1992). Development of a software tool for crack propagation analysis in two
dimensional layered structures (MS thesis). Kansas State University.
Gounaris, G. D., Papadopoulos, C. A., & Dimarogonas, A. D. (1996). Crack identification in
beams by coupled response measurements. Computers and Structures, 58, 299–305.
Harrison, C., & Butler, R. (2001). Locating delaminations in composite beams using gradient
techniques and a genetic algorithm. American Institute of Aeronautics and Astronautics
Journal, 39, 1383–1389.
Haupt, R. L., & Haupt, S. E. (2004). Practical genetic algorithms (2nd ed.). Hoboken, New
Jersey: John Wiley & Sons, Inc.
Hu, N., Wang, X., Fukunaga, H., Yao, Z. H., Zhang, H. X., & Wu, Z. S. (2001). Damage assessment
of structures using modal test data. International Journal of Solids and Structures, 38,
–3126.
James, M. A., & Swenson, D. V. (1999). A software framework for two dimensional mixed
mode-I/II elastic-plastic fracture. In K. J. Miller & D. L. McDowell (Eds.), Mixed-mode crack
behavior, ASTM STP 1359 (pp. 111–126). West Conshohocken, PA: American Society for
Testing and Materials.
Kosmatka, J. B., & Ricles, J. M. (1999). Damage detection in structures by modal vibration
characterization. Journal of Structural Engineering, 125, 1384–1392.
Krawczuk, M. (2002). Application of spectral beam finite element with a crack iterative search
technique for damage detection. Finite Elements in Analysis and Design, 38, 537–548.
Krawczuk, M., Palacz, M., & Ostachowicz, W. (2003). The dynamic analysis of a cracked
Timoshenko beam by the spectral element method. Journal of Sound and Vibration, 264,
–1153.
Krishnakumar, K. (1989). Micro-genetic algorithms for stationary and nonstationary function
optimization. SPIE, Intelligent Control and Adaptive Systems, 1196, 282–296.
Law, S. S., Chan, T. H., & Wu, D. (2001). Efficient numerical modal for the damage detection of
large scale structure. Engineering Structures, 23, 436–451.
Lee, J. (2009). Identification of multiple cracks in a beam using vibration amplitudes. Journal of
Sound and Vibration, 3206, 205–212.
Lee, J., Kim, S-.M., Park, H-.S., & Woo, B-.H. (2005). Optimum design of cold-formed steel
channel beams using micro genetic algorithm. Computers and Structures, 27, 17–24.
Lele, S. P., & Maiti, S. K. (2002). Modelling of transverse vibration of short beams for crack
detection and measurement of crack extension. Journal of Sound and Vibration, 257,
–583.
Li, B., Chen, X., Ma, J., & He, Z. (2005). Detection of crack location and size in structures using
wavelet finite element methods. Journal of Sound and Vibration, 285, 767–782.
Liang, R. Y., Choy, F. K., & Hu, J. (1991). Detection of cracks in beam structures using
measurements of natural frequencies. Journal of the Franklin Institute, 328, 505–518.
Liang, R. Y., & Hu, J. (1993). An integrated approach to detection of cracks using vibration
characteristics. Journal of the Franklin Institute, 330, 841–853.
Mahmoud, M. A., Abu Zaid, M., & Al Harashani, S. (1999). Numerical frequency analysis of
uniform beams with a transverse crack. Communications in Numerical Methods in
Engineering, 15, 709–715.
Mares, C., & Surace, C. (1996). An application of genetic algorithms to identify damage in elastic
structures. Journal of Sound and Vibration, 195, 195–215.
Messina, A., Williams, E. J., & Contursi, T. (1998). Structural damage detection by a sensitivity
and statistical-based method. Journal of Sound and Vibration, 216, 791–808.
Mitchell, M. (1996). An introduction to genetic algorithms. Cambridge, Massachusetts, USA:
MIT Press.Montalvao, D., Maia, N. M. M., & Ribeiro, A. M. R. (2006). A review of vibration-based
structural health monitoring with special emphasis on composite materials. The Shock and
Vibration Digest, 38, 295–324.
Morassi, A. (2001). Identification of a crack in a rod based on changes in a pair of natural
frequencies. Journal of Sound and Vibration, 242, 577–596.
Nandwana, B. P., & Maiti, S. K. (1997a). Detection of the location and size of a crack in stepped
cantilever beams based on measurements of natural frequencies. Journal of Sound and
Vibration, 203, 435–446.
Nandwana, B. P., & Maiti, S. K. (1997b). Modelling of vibration of beam in presence of inclined
edge or internal crack for its possible detection based on frequency measurements. Engineering
Fracture Mechanics, 58, 193–205.
Narkis, Y. (1994). Identification of crack location in vibrating simply supported beams. Journal of
Sound and Vibration, 172, 549–558.
Nikolakopoulos, P. G., Katsareas, D. E., & Papadopoulos, C. A. (1997). Crack identification in
frame structures. Computers and Structures, 64, 389–406.
Osyczka, A., & Kundu, S. (1996). A modified distance method for multicriteria optimization,
using genetic algorithms. Computers & Industrial Engineering, 30, 871–882.
Owolabi, G., Swamidas, A., & Seshadri, R. (2003). Crack detection in beams using changes in
frequencies and amplitudes of frequency response functions. Journal of Sound and Vibration,
, 1–22.
Papadopoulos, C. A., & Dimarogonas, A. D. (1987). Coupled longitudinal and bending vibrations
of a rotating shaft with an open crack. Journal of Sound and Vibration, 117, 81–93.
Patil, D. P., & Maiti, S. K. (2003). Detection of multiple cracks using frequency measurements.
Engineering Fracture Mechanics, 70, 1553–1572.
Patil, D. P., & Maiti, S. K. (2005). Experimental verification of a method of detection of multiple
cracks in beams based on frequency measurements. Journal of Sound and Vibration, 281,
–451.
Peimani, M., Vakil-Baghmisheh, M. T., Sadeghi, M., & Ettefagh, M. M. (2005). Locating damage
in beam like structures with neural networks. In Proceedings of Intelligent Systems, CIS2005,
Tehran, p. 54.
Pezeshk, S., Camp, C. V., & Chen, D. (2000). Design of nonlinear framed structures using
genetic optimization. Journal of Structural Engineering, 126, 382–388.
Potirniche, G. P., Hearndon, J., Daniewicz, S. R., Parker, D., Cuevas, P., Wang, P. T., & Horstemeyer,
M. F. (2008). A two-dimensional damaged finite element for fracture applications.
Engineering Fracture Mechanics, 75, 3895–3908.
Ratcliffe, C. P. (2000). Frequency and curvature based experimental method for locating damage
in structures. Journal of Vibration and Acoustics, 122, 324–329.
Rus, G., Lee, S. Y., Chang, S. Y., & Wooh, S. C. (2006). Optimized damage detection of steel
plates from noisy impact test. International Journal for Numerical Methods in Engineering,
, 707–727.
Rus, G., Lee, S. Y., & Gallego, R. (2005). Defect identification in laminated composite structures
by BEM from incomplete static data. International Journal of Solids and Structures, 42,
–1758.
Sahin, M., & Shenoi, R. A. (2003). Quantification and localization of damage in beam-like structures
by using artificial neural networks with experimental validation. Engineering Structures,
, 1785–1802.
Sahoo, B., & Maity, D. (2007). Damage assessment of structures using hybrid neurogenetic
algorithm. Applied Soft Computing, 7, 89–104.
Salawu, O. S. (1997). Detection of structural damage through changes in frequency: A review.
Engineering Structures, 19, 718–723.
Shifrin, E. I., & Ruotolo, R. (1999). Natural frequencies of a beam with an arbitrary number of
cracks. Journal of Sound and Vibration, 222, 409–423.
Silva, J. M., & Gomes, A. J. L. (1990). Experimental dynamic analysis of cracked free–free
beams. Experimental Mechanics, 30, 20–25.
Sohn, H., Farrar, C., Hemez, F., Shunk, D., Stinemates, D., & Nadler, B. (2003). A review of
structural health monitoring literature: 1996–2001 (Technical, Report LA13976MS). Los
Alamos, NM: Los Alamos National Laboratory.Tada, H., Paris, P. C., & Irwin, G. R. (2000). The stress analysis of cracks handbook (3rd ed.).
New York, NY: ASME Press.
Vestroni, F., & Capecchi, D. (2000). Damage detection in beam structures based on frequency
measurements. Journal of Engineering Mechanics, 126, 761–768.
Wawrzynek, P. A., and Ingraffea, A. R. (1994). FRANC2D: Two-dimensional crack propagation
simulator, Version 2.7 User’s Guide, NASA CR 4572.
Wawrzynek, P. A., & Ingraffea, A. R. (1987). Interactive finite element analysis of fracture
processes: An integrated approach. Theoretical and Applied Fracture Mechanics, 8, 137–150.
Wendtland, D. (1972). Änderung der biegeegenfrequenzen einer idealisierten Schaufel durch Risse
(PhD Dissertation). University of Karlsruhe.
Xia, Y., and Hao, H. (2001). A genetic algorithm for structural damage detection based on
vibration data. In Proceedings of 19th International Modal Analysis Conferences. Kissimmee,
FL, pp. 1381–1387.
