Determination of stress intensity factors of 2D fracture mechanics problems through a new semi‐analytical method

Khaji, N.; Yazdani, Mahmoud

doi:10.1111/ffe.12375

Cited by 6 publications

(10 citation statements)

References 44 publications

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“…The principle emphasis is put on the significant features that are remarkably modified compared with other researches of the authors. An in‐depth account of formulation of the method can be found in Khaji and Khodakarami and Khaji and Yazdani …”

Section: Basics Of the Semianalytical Methodsmentioning

confidence: 99%

“…Hereafter, the dominant features of this approach are investigated to simulate for fracture mechanics problems. Detailed formulation related to extraction of SIFs may be found in Khaji and Yazdani . The following subsections are devoted for implementation of fracture mechanics issues in the presented semianalytical method.…”

Section: Use Of the Semianalytical Methods In Fracture Analysismentioning

confidence: 99%

“…It is possible to calculate the SIFs with regard to displacement and/or stress solutions. The current semianalytical method uses the displacement solution . The following equations are employed to calculate SIFs for modes I and II.…”

Section: Use Of the Semianalytical Methods In Fracture Analysismentioning

confidence: 99%

“…Recently, Khaji et al proposed another semianalytical method in which merely the problem boundaries are meshed by applying specific subparametric elements along with higher‐order Chebyshev mapping functions. Using the weighted residual method and applying Clenshaw‐Curtis quadrature results in diagonal Euler's differential equations.…”

Section: Introductionmentioning

confidence: 99%

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Development of a new semianalytical approach for 2D analysis of crack propagation problems

Yazdani

Khaji

2018

Fatigue Fract Eng Mat Struct

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This study offers novel progresses for a semianalytical method to simulate 2D propagation of cracks based on linear elastic fracture mechanics. For this purpose, a new algorithm is proposed on the basis of the linear elastic fracture mechanics for crack propagation in single‐mode and mixed mode. Herein, discretization is only performed on the boundaries of the problem by using specific subparametric elements and higher‐order Chebyshev polynomials as mapping functions. Implementing the weighted residual method and by taking Clenshaw‐Curtis numerical quadrature, diagonal Euler's differential equations are obtained. Consequently, once the local coordinate origin is assumed at the tip of the crack, the stress intensity factors can be derived directly. In accordance with the rate of maximum energy release as a propagation criterion and by proposing a new quasi‐automatic remeshing procedure based on domain division, the crack propagation is applied here. Based on the new presented algorithm, application of the new semianalytical method to crack propagation analysis is more flexible and efficient. By taking this advantage, relatively coarse and simple discretization compared with other computational methods may be used. By modelling 4 benchmark problems with a few numbers of degrees of freedom, the validity and accuracy of the current method is illustrated. Results show that the presented algorithm is applicable for efficient and precise prediction of crack trajectories.

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Section: Basics Of the Semianalytical Methodsmentioning

confidence: 99%

Section: Use Of the Semianalytical Methods In Fracture Analysismentioning

confidence: 99%

Section: Use Of the Semianalytical Methods In Fracture Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Development of a new semianalytical approach for 2D analysis of crack propagation problems

Yazdani

Khaji

2018

Fatigue Fract Eng Mat Struct

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“…Recently, the WFM was used and further developed to analyse the SIFs, PZSs, CODs and residual strengths for collinear cracks in finite and infinite sheets. [25][26][27][28] For complex component, advanced semi-analytical [29][30][31] and numerical method such as the dual boundary element method 32 and the finite element alternating method 33 were developed and used to analyse the crack growth behaviour of MSD. However, there is very limited solution to multiple cracks emanating from numerous holes 34 due to its complexity.…”

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confidence: 99%

Weight function, stress intensity factor and crack opening displacement solutions to periodic collinear edge hole cracks

2017

Fatigue Fract Eng Mat Struct

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Periodic collinear edge hole cracks and arbitrary small cracks emanating from collinear holes, which are two typical multiple site damages occurred in the aircraft structures, are studied by using the weigh function method. An explicit closed form weight function for periodic edge hole cracks in an infinite sheet is obtained and further used to calculate the stress intensity factor and crack opening displacement for various loading cases. Compared to finite element method, the present weight function is accurate and highly efficient. The interactions of the holes and cracks on the stress intensity factor and crack opening displacement are quantitatively determined by using the present weight function. An approximate weight function method is also proposed for arbitrary small cracks emanating from multiple collinear holes. This method is very useful for calculating the stress intensity factor for arbitrary small cracks.

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Complex Fourier‐based stress intensity factor analysis of plane elasticity using boundary element theories

Aghamolaei

Hamzehei‐Javaran

Shojaee

2021

Numerical Meth Engineering

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In this article, the boundary element method is implemented for solving linear elastic fracture mechanics problems, using new complex Fourier shape functions which include constant and linear complex Fourier shape functions. They, unlike the classic Lagrange shape functions, can satisfy the exponential and trigonometric function fields in addition to the polynomial ones. Six numerical examples are provided to investigate the new shape functions and also, the stress intensity factors (SIF) are calculated for each so that the accuracy of the present study is illustrated. The results are compared with those obtained by classic Lagrange ones and the existing methods.

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Determination of stress intensity factors of 2D fracture mechanics problems through a new semi‐analytical method

Cited by 6 publications

References 44 publications

Development of a new semianalytical approach for 2D analysis of crack propagation problems

Development of a new semianalytical approach for 2D analysis of crack propagation problems

Weight function, stress intensity factor and crack opening displacement solutions to periodic collinear edge hole cracks

Complex Fourier‐based stress intensity factor analysis of plane elasticity using boundary element theories

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