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Mathematical Problems in Engineering
Volume 2013, Article ID 524562, 10 pages
Research Article

Homotopy Iteration Algorithm for Crack Parameters Identification with Composite Element Method

Department of Applied Mechanics, Sun Yat-sen University, Guangzhou, Guangdong 510006, China

Received 19 July 2013; Revised 12 October 2013; Accepted 12 October 2013

Academic Editor: Timon Rabczuk

Copyright © 2013 Ling Huang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An approach based on homotopy iteration algorithm is proposed to identify the crack parameters in beam structures. In the forward problem, a fully open crack model with the composite element method is employed for the vibration analysis. The dynamic responses of the cracked beam in time domain are obtained from the Newmark direct integration method. In the inverse analysis, an identification approach based on homotopy iteration algorithm is studied to identify the location and the depth of a cracked beam. The identification equation is derived by minimizing the error between the calculated acceleration response and the simulated measured one. Newton iterative method with the homotopy equation is employed to track the correct path and improve the convergence of the crack parameters. Two numerical examples are conducted to illustrate the correctness and efficiency of the proposed method. And the effects of the influencing parameters, such as measurement time duration, measurement points, division of the homotopy parameter and measurement noise, are studied.