Crack growth adaptive XIGA simulation in isotropic and orthotropic materials

Gu, Jiming; Yu, Tiantang; Lich, Le Van; Tanaka, Satoyuki; Yuan, Hongting; Bui, Tinh Quoc

doi:10.1016/j.cma.2020.113016

Cited by 40 publications

(12 citation statements)

References 63 publications

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“…For elements without any enriched control point, the numerical integration is conducted with (p + 1) × (q + 1) integral points, where p and q are the order of LR NURBS basis function in the ξ and η directions, respectively. For elements containing the material interface, the sub-triangle scheme [36] is used, and seven integration points are applied in each sub-triangle element.…”

Section: Xiga For Steady-state Heat Transfer In Heterogeneous Mediamentioning

confidence: 99%

“…Later, they presented a multi-patch isogeometric large deformation thin shell formulation based on RTH splines, and developed a stress recovery technique to drive the adaptive h-refinement procedure [33]. Recently, we proposed the adaptive LR B-splines based XIGA and successfully simulated inclusions [34], holes [35], and cracks [36][37][38]. Yang et al [39] developed an adaptive XIGA based on the PHT-splines for cracked thin plates and shells.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive Extended Isogeometric Analysis for Steady-State Heat Transfer in Heterogeneous Media

Fang¹,

Yu²,

Yang³

2021

Computer Modeling in Engineering &Amp; Sciences

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Steady-state heat transfer problems in heterogeneous solid are simulated by developing an adaptive extended isogeometric analysis (XIGA) method based on locally refined non-uniforms rational B-splines (LR NURBS). In the XIGA, the LR NURBS, which have a simple local refinement algorithm and good description ability for complex geometries, are employed to represent the geometry and discretize the field variables; and some special enrichment functions are introduced into the approximation of temperature field, thus the computational mesh is independent of the material interfaces, which are described with the level set method. Similar to the approximation of temperature field, a temperature gradient recovery technique for heterogeneous media is proposed, and based on the Zienkiewicz-Zhu recovery technique a posteriori error estimator is defined to automatically identify the locally refined regions. The convergence and performance properties of the developed method are verified by using three numerical examples. The numerical results show that (1) The convergence speed of the adaptive local refinement is faster than that of the uniform global refinement; (2) The convergence rate of the high-order basis functions is faster than that of the low-order basis functions; and (3) The existing inclusions change the local distributions of the temperature, and the extreme values of the temperature gradients take place around the inclusion interfaces.

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Section: Xiga For Steady-state Heat Transfer In Heterogeneous Mediamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Adaptive Extended Isogeometric Analysis for Steady-State Heat Transfer in Heterogeneous Media

Fang¹,

Yu²,

Yang³

2021

Computer Modeling in Engineering &Amp; Sciences

Self Cite

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“…Analysis, semi-analysis (Wei et al, 2016), and experimental methods are limited to a few simple structural geometries and loads. Therefore, numerical methods always serve as the mainstream method for crack analysis, which include the finite element method (FEM) (Barsoum, 1976(Barsoum, , 1977, the meshfree/meshless method (Belytschko et al, 1994;Fleming et al, 1997;Rao and Rahman, 2000;Zi et al, 2007;Rabczuk et al, 2010;Zhuang et al, 2011;Zhuang et al, 2012), the extended finite element method (XFEM) (Belytschko and Black, 1999;Daux et al, 2000;Kang et al, 2017), isogeometric analysis (IGA) (De Luycker et al, 2011;Bui, 2015;Ghorashi et al, 2012;Yin et al, 2019;Gu et al, 2020), to name just a few.…”

Section: Introductionmentioning

confidence: 99%

A linear smoothed meshfree method with intrinsic enrichment functions for 2D crack analysis

Ban

Zhang

et al. 2022

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PurposeThis article aims to develop an accurate and efficient meshfree Galerkin method based on the strain smoothing technique for linear elastic continuous and fracture problems.Design/methodology/approachThis paper proposed a generalized linear smoothed meshfree method (LSMM), in which the compatible strain is reconstructed by the linear smoothed strains. Based on the idea of the weighted residual method and employing three linearly independent weight functions, the linear smoothed strains can be created easily in a smoothing domain. Using various types of basic functions, LSMM can solve the linear elastic continuous and fracture problems in a unified way.FindingsOn the one hand, the LSMM inherits the properties of high efficiency and stability from the stabilized conforming nodal integration (SCNI). On the other hand, the LSMM is more accurate than the SCNI, because it can produce continuous strains instead of the piece-wise strains obtained by SCNI. Those excellent performances ensure that the LSMM has the capability to precisely track the crack propagation problems. Several numerical examples are investigated to verify the accurate, convergence rate and robustness of the present LSMM.Originality/valueThis study provides an accurate and efficient meshfree method for simulating crack growth.

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“…This saves time that goes into defining the mesh and prevents geometric errors in the analysis. Further, XIGA has been extended for crack growth analysis of isotropic and orthogonal materials [50][51] and cortical bone fracture modelling [52]. However, it also requires different enrichment functions to model different material problems similar to XFEM.…”

Section: Introductionmentioning

confidence: 99%

Smoothed floating node method for modelling 2D arbitrary crack propagation problems

Singh

Kumar

Chen

2022

Theoretical and Applied Fracture Mechanics

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Crack growth adaptive XIGA simulation in isotropic and orthotropic materials

Cited by 40 publications

References 63 publications

Adaptive Extended Isogeometric Analysis for Steady-State Heat Transfer in Heterogeneous Media

Adaptive Extended Isogeometric Analysis for Steady-State Heat Transfer in Heterogeneous Media

A linear smoothed meshfree method with intrinsic enrichment functions for 2D crack analysis

Smoothed floating node method for modelling 2D arbitrary crack propagation problems

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