Stress analysis of a finite wedge weakened by cavities

Faal, R.T.; Fariborz, S.J.; Daghyani, Hamid Reza

doi:10.1016/j.ijmecsci.2006.08.001

Cited by 18 publications

(10 citation statements)

References 10 publications

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“…This is because the dislocation solution is a Green's function solution of a given crack problem Hills et al (1996). There are limited numbers of investigations on anti-plane elasticity problems in finite domains weakened by defects, including the work by Chang (1985), Ma (1988Ma ( , 1989, Faal et al (2007), Matbuly and Nassar (2009). Chang (1985) and Ma (1988Ma ( , 1989) studied the solution of central crack problem in rectangular sheets.…”

Section: Introductionmentioning

confidence: 99%

“…Chang (1985) and Ma (1988Ma ( , 1989) studied the solution of central crack problem in rectangular sheets. Faal et al (2007) conducted the stress analysis of a finite wedge weakened by arbitrarily shaped cavities. In the study by Matbuly and Nassar (2009), the anti-plane stress analysis of two interfacial cracks located between two dissimilar orthotropic rectangular planes under shear loading was conducted.…”

Section: Introductionmentioning

confidence: 99%

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Anti-Plane stress analysis of orthotropic rectangular planes weakened by multiple defects

Faal

Daliri

Milani

2011

International Journal of Solids and Structures

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a b s t r a c tThe solution of a Volterra type screw dislocation problem in an orthotropic rectangular plane with finite length and width and various boundary conditions is obtained by means of a separation of variables technique. A distributed dislocation method is employed to obtain integral equations of the plane with cracks and cavities under an anti-plane traction. The ensuing equations are of the Cauchy singular type and have been solved numerically. Several examples are presented to demonstrate the applicability of the proposed solution.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Anti-Plane stress analysis of orthotropic rectangular planes weakened by multiple defects

Faal

Daliri

Milani

2011

International Journal of Solids and Structures

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“…In this case the problem reduces to that of two edge-bonded dissimilar materials with an interfacial crack subjected to concentrated anti-plane shear tractions on the crack faces. Faal et al (2007) presented the solution of a Volterra-type screw dislocation in an isotropic finite wedge weakened by multiple cavities under various boundary conditions using the image method. Shahani (2007) extracted closed form solutions for the stress distribution in the isotropic finite wedge under anti-plane deformation.…”

Section: Introductionmentioning

confidence: 99%

Analysis of anisotropic sector with a radial crack under anti-plane shear loading

Shahani

Ghadiri

2010

International Journal of Solids and Structures

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a b s t r a c tIn this paper, the anti-plane shear deformation of an anisotropic sector with a radial crack is investigated. The traction-traction boundary conditions are imposed on the radial edges and the traction-free condition is considered on the circular segment of the sector. A novel mathematical technique is employed for the solution of the problem. This technique consists of the use of some recently proposed finite complex transforms (Shahani, 1999), which have complex analogies to the standard finite Mellin transforms of the first and second kinds. However, it is essential to state the traction-free condition of the crack faces in the form of a singular integral equation which is done in this paper by describing an exact analytical method. The resultant dual integral equations are solved numerically to determine the stress intensity factors at the crack tips. In the special cases, the obtained results coincide with those cited in the literature.

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“…Appling the displacement boundary conditions (5) and continuity equations (7) to W (r, n) in view of (4) gives…”

Section: Application Of Boundary Conditions: Problem (A)mentioning

confidence: 99%

Stress analysis of the cracked and uncracked transversely isotropic sectors with different types of boundary conditions

Faal

Hassani

2012

Mathematics and Mechanics of Solids

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The anti-plane deformation of an uncracked transversely isotropic sector is studied for two different types of boundary conditions. The solution of the problem is accomplished by means of two methods for each boundary condition, namely using the finite Fourier cosine transform and the method of separation of variables. The closed-form solutions are obtained for displacement and stress fields in the whole domain for each kind of boundary conditions. In the special cases, i.e. finite wedges, the results for the stress field show an exact agreement with those in the literature. In the following, the stress analysis of a transversely isotropic sectors weakened by a circular crack as well as radial crack is accomplished. The resultant singular integral equation of the Cauchy type are solved numerically and, finally, the stress intensity factors of the crack tips versus the ratios of the material properties are plotted and discussed.

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Stress analysis of a finite wedge weakened by cavities

Cited by 18 publications

References 10 publications

Anti-Plane stress analysis of orthotropic rectangular planes weakened by multiple defects

Anti-Plane stress analysis of orthotropic rectangular planes weakened by multiple defects

Analysis of anisotropic sector with a radial crack under anti-plane shear loading

Stress analysis of the cracked and uncracked transversely isotropic sectors with different types of boundary conditions

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