A mixed boundary value problem in orthotropic strip containing a crack

Yusufoğlu, Elçin; Turhan, İlkem

doi:10.1016/j.jfranklin.2012.09.001

Cited by 20 publications

(16 citation statements)

References 22 publications

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“…The same problem has been solved by Iterative method and Gauss Chebyshev Quadrature in the previous studies [11,12] and the results for the normalized SIF values are compared with [13].…”

Section: Discussionmentioning

confidence: 99%

“…According to the analogy in [11,12], considering kinematic equations, equilibrium equations, Hooke's law, Airy function and using the Fourier transform technique and Eqs. (1), the following system of singular integral equation is obtained:…”

Section: Solution Of Mixed Boundary Value Problem Corresponding To N-mentioning

confidence: 99%

“…Numerical examples for first and second kind singular integral equations are included. An orthotropic strip problem weakened by a crack is handled in the studies of Yusufoğlu and Turhan [11,12]. A singular integral equation is induced by the equations of elasticity theory and Fourier transform of Airy's stress function.…”

Section: Introductionmentioning

confidence: 99%

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A Quadrature Approach for N-Collinear Crack Problem in an Orthotropic Strip

Yusufoğlu¹,

Çetinkaya²

2017

JMSS

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This study presents the determination of the stress intensity factors (SIFs) at the edges of the cracks in an elastic strip weakened by N-collinear cracks. The problem of an orthotropic elastic strip is reduced to a system of Cauchy type singular integral equations. The system of singular integral equations is approached by a Quadrature technique. Under two different loading conditions, the results are obtained for the different cases of crack numbers. The resistance of the strip is examined by considering the orthotropic properties of the strip material. Finally, the crack interactions are clarified during the analysis.

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“…The same problem has been solved by Iterative method and Gauss Chebyshev Quadrature in the previous studies [11,12] and the results for the normalized SIF values are compared with [13].…”

Section: Discussionmentioning

confidence: 99%

Section: Solution Of Mixed Boundary Value Problem Corresponding To N-mentioning

confidence: 99%

See 1 more Smart Citation

A Quadrature Approach for N-Collinear Crack Problem in an Orthotropic Strip

Yusufoğlu¹,

Çetinkaya²

2017

JMSS

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“…For some real-world problems and engineering applications involving the strip conditions similar to the ones considered in the present study , we refer the reader to the works [6,15,29,31,33].…”

Section: Introductionmentioning

confidence: 99%

A New Kind of Nonlocal-integral Fractional Boundary Value Problems

Ahmad

Ntouyas

2015

Bull. Malays. Math. Sci. Soc.

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In this paper, we discuss a new class of nonlocal boundary value problems of fractional differential equations and inclusions with a new integral boundary condition. This new boundary condition states that the value of the unknown function at an arbitrary (local) point ξ is proportional to the contribution due to a sub-strip of arbitrary length (1 − η), that is, x(ξ ) = a 1 η x(s)ds, where 0 < ξ < η < 1 and a is constant of proportionality. The existence of solutions for the given problems is shown by means of contraction mapping principle, a fixed point theorem due to O'Regan and nonlinear alternative for multivalued maps. The results are well illustrated with the aid of examples.

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“…In the problem (1), we have introduced Riemann-Liouville type multistrip integral boundary conditions which can be interpreted as the controller at the right-end of the interval under consideration is influenced by a discrete distribution of finite many nonintersecting sensors (strips) of arbitrary length expressed in terms of Riemann-Liouville type integral boundary conditions. For some engineering applications of strip conditions, see ( [26][27][28][29][30][31][32]).…”

Section: Introductionmentioning

confidence: 99%