How we can control the crack to propagate along the specified path feasibly?
📝 Abstract
A controllable crack propagation (CCP) strategy is suggested. It is well known that crack always leads the failure by crossing the critical domain in engineering structure. Therefore, the CCP method is proposed to control the crack to propagate along the specified path, which is away from the critical domain. To complete this strategy, two optimization methods are engaged. Firstly, a back propagation neural network (BPNN) assisted particle swarm optimization (PSO) is suggested. In this method, to improve the efficiency of CCP, the BPNN is used to build the metamodel instead of the forward evaluation. Secondly, the popular PSO is used. Considering the optimization iteration is a time consuming process, an efficient reanalysis based extended finite element methods (X-FEM) is used to substitute the complete X-FEM solver to calculate the crack propagation path. Moreover, an adaptive subdomain partition strategy is suggested to improve the fitting accuracy between real crack and specified paths. Several typical numerical examples demonstrate that both optimization methods can carry out the CCP. The selection of them should be determined by the tradeoff between efficiency and accuracy.
💡 Analysis
A controllable crack propagation (CCP) strategy is suggested. It is well known that crack always leads the failure by crossing the critical domain in engineering structure. Therefore, the CCP method is proposed to control the crack to propagate along the specified path, which is away from the critical domain. To complete this strategy, two optimization methods are engaged. Firstly, a back propagation neural network (BPNN) assisted particle swarm optimization (PSO) is suggested. In this method, to improve the efficiency of CCP, the BPNN is used to build the metamodel instead of the forward evaluation. Secondly, the popular PSO is used. Considering the optimization iteration is a time consuming process, an efficient reanalysis based extended finite element methods (X-FEM) is used to substitute the complete X-FEM solver to calculate the crack propagation path. Moreover, an adaptive subdomain partition strategy is suggested to improve the fitting accuracy between real crack and specified paths. Several typical numerical examples demonstrate that both optimization methods can carry out the CCP. The selection of them should be determined by the tradeoff between efficiency and accuracy.
📄 Content
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How we can control the crack to propagate along the specified path feasibly?
Zhenxing Cheng, Hu Wang* State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, P.R. Chin
Abstract A controllable crack propagation (CCP) strategy is suggested. It is well known that crack always leads the failure by crossing the critical domain in engineering structure. Therefore, the CCP method is proposed to control the crack to propagate along the specified path, which is away from the critical domain. To complete this strategy, two optimization methods are engaged. Firstly, a back propagation neural network (BPNN) assisted particle swarm optimization (PSO) is suggested. In this method, to improve the efficiency of CCP, the BPNN is used to build the metamodel instead of the forward evaluation. Secondly, the popular PSO is used. Considering the optimization iteration is a time consuming process, an efficient reanalysis based extended finite element methods (X-FEM) is used to substitute the complete X-FEM solver to calculate the crack propagation path. Moreover, an adaptive subdomain partition strategy is suggested to improve the fitting accuracy between real crack and specified paths. Several typical numerical examples demonstrate that both optimization methods can carry out the CCP. The selection of them should be determined by the tradeoff between efficiency and accuracy. Keywords Crack propagation path, Reanalysis solver, Back propagation neural network, Particle swarm optimization, Extended finite element method 1 Introduction Generally, the internal crack propagation is a critical issue in the engineering practice due to its deep effect on the quality and stability of engineering structures. Therefore, predicting the path of crack propagation is significant for guaranteeing the safety or reliability of engineering structures. There are many numerical methods of simulating crack propagation. Such as finite element method (FEM) (Bouchard et al., 2003; Branco et al., 2015), extended finite element method (X-FEM) (Belytschko et al., 2009; Zeng et al., 2016), edge-based finite element method (ES-FEM) (G. R. Liu et al., 2011; Nguyen-Xuan et al., 2013), meshless method (Gu et al., 2011; Tanaka et al., 2015), and so on. The X-FEM might be the most popular method for crack propagation simulation due to its superiority of modeling both strong and weak discontinuities. Belytschko and Black proposed the initial idea of X-FEM at 1999 with minimal re-mesh (Belytschko et al., 1999). Then, Moës el al. (Belytschko et al., 2001) and Dolbow et al. (Dolbow et al., 1999) adopted the Heaviside function to enrichment function and 3D static crack was modeled by Sukumar et al. (Sukumar et al., 2000). Sequentially, the level set methods (LSMs) were applied to X-FEM which could easily track both the crack position and tips (Stolarska et al., 2001). Moreover, the X-FEM has much more applications (Ahmed et al., 2012; Areias et al., 2005; Belytschko et al., 2003; Chessa et al., 2002; Huynh et al., 2009; J.-H. Song et al., 2006; Sukumar et al., 2001; Zhuang et al., 2011; Zilian et al., 2008). More details of the development of X-FEM can be found in the literature (Abdelaziz et al., 2008; Belytschko et al., 2009; Fries et al., 2010). It is well known that the internal crack propagation always leads the failure of engineering structure by crossing the critical domain of the structure. Therefore, if the crack doesn’t cross the critical domain, the failure will not happen. Therefore, a controllable crack propagation method is proposed to control the crack propagation path and lead it propagate along the pre- defined path, so that the critical domain should not be crossed by the crack and the failure will not happen. In
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this study, the particle swarm optimization (PSO) method is used to obtain the suitable variables of design and the artificial neural network is used to improve the efficiency of PSO. The PSO proposed by Kennedy and Eberhart is a popular metaheuristic algorithm which inspired by the social behavior of bird flocking (Kennedy et al., 1995). Later Kennedy and Eberhart suggested a developed version of PSO for discrete optimization (Kennedy et al., 1997). Shi and Eberhart improved the PSO by inertia weight (Shi et al., 1998). Recently, PSO has been applied to many fields, such as structural optimization (Vagelis et al., 2011), dynamic finite element model updating (Shabbir et al., 2015), vehicle engineering (Battaïa et al., 2013), artificial neural network (Chatterjee et al., 2016; W. Sun et al., 2016) and so on (Amini et al., 2013; Amiri et al., 2012; Delice et al., 2014). Much more studies on PSO can be found in the literature (Eberhart et al., 2001; Ma et al., 2015; Poli et al., 2007; Tyagi et al., 2011). Considering the optimization iteration is a time consuming process, an eff
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