The finite element discretized symplectic method for interface cracks

Zhou, Zhenhuan; Leung, A.Y.T.; Xü, Xinsheng

doi:10.1016/j.compositesb.2013.10.041

Cited by 15 publications

(3 citation statements)

References 26 publications

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“…In region-wise approach, delaminated segment is divided into sub-laminates and the continuity conditions are imposed at the junctions of delaminated segments and the healthy segment. In layerwise theories, delamination can be modeled by introducing discontinuity functions in the displacement fields or by adding an additional embedded layer at the place of delamination [28,29,5]. Delamination models can also be regrouped into free-mode delamination models and constrained-mode delamination models [28].…”

Section: Introductionmentioning

confidence: 99%

Finite element analysis of free vibration of the delaminated composite plate with variable kinematic multilayered plate elements

Kumar

Cinefra

Carrera

et al. 2014

Composites Part B: Engineering

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Section: Introductionmentioning

confidence: 99%

Finite element analysis of free vibration of the delaminated composite plate with variable kinematic multilayered plate elements

Kumar

Cinefra

Carrera

et al. 2014

Composites Part B: Engineering

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“…The approach based on Hamiltonian system has shown great superiority in revealing the structure of solutions and their physical essence as well as predicting the accurate local behavior which is usually covered up by the Saint-Venant principle in the traditional elasticity analysis [16]. Furthermore, the symplectic approach as a rational and a unified manner has been widely applied to various problems in many various branches of applied mechanics [17][18][19][20][21][22][23]. In the numerical calculation, Zhao and Chen [24] reconstructed the symplectic expansion formula in the state space formalism to avoid matrix singularity and achieved the stability of numerical calculation.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solutions for Functionally Graded Beams under Arbitrary Distributed Loads via the Symplectic Approach

Zhao

Gan

2014

Advances in Mechanical Engineering

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A novel symplectic approach is employed in the analysis of homogenous and functionally graded beams subjected to arbitrary tractions on the lateral surfaces. Two models of functionally graded beams are heterogeneous in the sense that the material properties are exponential functions of the length and thickness, respectively. Within the symplectic framework, the method of separation of variables alone with the eigenfunction expansion technique is adopted to obtain the exact analysis of displacement and stress fields. The complete solutions include homogenous solutions with coefficients to be determined by two end boundary conditions and particular solutions satisfying the lateral boundary conditions. Two examples are presented for functionally graded beams to demonstrate the effects of material inhomogeneity. The efficiency and accuracy of the symplectic analysis are shown through numerical results.

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“…However, the complexity of analytical solutions even for simple cases requires the modelling of mechanical behavior of this problem using effective numerical methods. Several investigations have been developed in this domain, via the boundary element method (BEM) (Lee and Choi, 1988;Yuuki and Xu, 1994;Miyazaki et al, 1993), finite element method (FEM) (Ikeda et al, 2006), element free Galerkin method (EFGM) (Pant et al, 2011), extended finite element method (XFEM) (Nagashima et al, 2003;Liu et al, 2004;Belytschko and Gracie, 2007) and other methods (Zhou et al, 2013(Zhou et al, , 2014An et al, 2013). Recently, a large field was opened by Hughes et al (2005) offering the possibility of introducing computer aided design (CAD) tools in the analysis methods using the isoparametric concept.…”

Section: Introductionmentioning

confidence: 99%

Crack analysis in bimaterial interfaces using T-spline based XIGA

Habib

Belaidi

2017

jtam

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Analysis-suitable T-splines are used for the modeling and analyzing of cracks in bimaterial interfaces within the framework of an extended isogeometric analysis (XIGA). The crack tip enrichment functions of bimaterial interface cracks are implemented to reproduce singular fields, and the signed distance functions are used to treat the crack face and the interface in the models. A compatible local refinement algorithm is applied to refine location of the crack and the interface, which helps one to avoid produce excessive propagation of control points. The mixed mode stress intensity factors (SIFs) which are evaluated by the interaction integral (M-integral) are used as analysis parameters. Numerical simulations are performed to analyze the problem and to examine the efficiency of the proposed method. The obtained results are compared with other available results.

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The finite element discretized symplectic method for interface cracks

Cited by 15 publications

References 26 publications

Finite element analysis of free vibration of the delaminated composite plate with variable kinematic multilayered plate elements

Finite element analysis of free vibration of the delaminated composite plate with variable kinematic multilayered plate elements

Analytical Solutions for Functionally Graded Beams under Arbitrary Distributed Loads via the Symplectic Approach

Crack analysis in bimaterial interfaces using T-spline based XIGA

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