A dynamic XFEM formulation for crack identification
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A dynamic XFEM formulation for crack identification Chao Zhang . Cuixia Wang . Tom Lahmer . Pengfei He . Timon Rabczuk
Received: 1 April 2015 / Accepted: 20 May 2015 Ó Springer Science+Business Media Dordrecht 2015
Abstract Nelder–Mead (NM) and Quasi-Newton (QN) optimization methods are used for the numerical solution of crack identification problems in elastodynamics. Fracture is modeled by the eXtended Finite Element Method. The Newmark-b method with Rayleigh damping is employed for the time integration. The effects of various dynamical test loads on the crack identification are investigated. For a timeharmonic excitation with a single frequency and a short-duration signal measured along part of the C. Zhang C. Wang T. Lahmer T. Rabczuk (&) Institute of Structural Mechanics, Bauhaus-Universita¨t Weimar, 99423 Weimar, Germany e-mail: [email protected] C. Wang e-mail: [email protected] T. Lahmer e-mail: [email protected] C. Zhang (&) College of Water Resources and Architectural Engineering, Northwest A&F University, Yangling 712100, People’s Republic of China e-mail: [email protected] P. He Department of Aerospace Engineering, Tongji University, Shanghai 200092, People’s Republic of China e-mail: [email protected] T. Rabczuk School of Civil, Environmental and Architectural Engineering, Korea University, Seoul, Korea
external boundary, the crack is detected through the solution of an inverse time-dependent problem. Compared to the static load, we show that the dynamic loads are more effective for crack detection problems. Moreover, we tested different dynamic loads and find that NM method works more efficient under the harmonic load than the pounding load while the QN method achieves almost the same results for both load types. Keywords XFEM Nelder–Mead method Quasi-Newton method Crack identification Inverse analysis
1 Introduction Identification of flaws in structures is a critical element in the management of maintenance and quality assurance processes in engineering. Non-destructive testing (NDT) techniques based on a wide range of physical principles have been developed and are used in common practice for structural health monitoring. However, basic NDT techniques are usually limited in their ability to provide the accurate information on locations, dimensions and shapes of flaws, which is important in applications, such as health monitoring in aircrafts. One alternative to extract additional information from the results of NDT is to append it with a computational model that provides detailed analysis of the physical process involved and enables the accurate
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identification of the flaw parameters (Stavroulakis 2000). The mathematical problem of identifying flaws from measurement data is an inverse problem and is often ill-posed (Liu and Han 2004; Kirsch 2011). Inverse analysis is a common approach to identify the flaws. Scattering data are obtained by simulating many candidate flaws. Each simulation involves the solution of a forw
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