Cruciform crack in an orthotropic elastic plane
01 Feb 1992-International Journal of Fracture (Kluwer Academic Publishers)-Vol. 53, Iss: 4, pp 387-397
TL;DR: In this paper, the problems of determining the stress and displacement fields in an infinite orthotropic plane containing a cruciform crack 387-1, y=0 and 387-2, x=0 when (I) the shape of the crack is prescribed and (II) the cracks are opened by given normal pressures, are reduced to mixed boundary value problems for the quarter plane.
Abstract: The problems of determining the stress and displacement fields in an infinite orthotropic plane containing a cruciform crack 387-1, y=0 and 387-2, x=0 when (I) the shape of the crack is prescribed and (II) the cracks are opened by given normal pressures, are reduced to mixed boundary value problems for the quarter plane. Using integral transform techniques, a closed form solution is obtained for problem I, whereas the solution of problem II has been reduced to solving a Fredholm integral equation of second kind with non-singular kernel. Numerical calculation of the stress intensity factor and crack energy in the case of a linear loading function for various crack lengths are presented for problem II, using the values of material constants for a Boron-Epoxy composite.
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TL;DR: In this paper, the bending of a rectangular plate having moment singularities at the ends of a partial internal line support is analyzed in terms of dual-series equations, and a finite Hankel integral transform is applied to reduce the dual series equations to a Fredholm integral equation.
Abstract: Two cases of a rectangular plate having moment singularities at the ends of a partial internal line support are analytically investigated. The bending of the plate by uniform loading is formulated in terms of dual-series equations. Application of the finite Hankel integral transform reduces the dual-series equations to a Fredholm integral equation of the second kind that can be solved by standard techniques. Numerical results are given for the deflections and bending moments along the line outside of an internal line support and the change in strain energy due to the presence of a partial support.
5 citations
TL;DR: In this article, dual-series equations are applied to the problem of rectangular plates having at least two parallel simply supported edges and a partial internal line support located at the centre where the length of internal line supports can be varied symmetrically, loaded with a uniformly distributed load.
Abstract: The paper deals with the application of dual-series equations to the problem of rectangular plates having at least two parallel simply supported edges and a partial internal line support located at the centre where the length of internal line support can be varied symmetrically, loaded with a uniformly distributed load. By choosing the proper flnite Hankel transform, the dual-series equations can be reduced to the form of a Fredholm integral equation which can be solved conveniently by using standard techniques. The solutions of integral equation and the deformations for each case of the plates are given and discussed in details.
5 citations
Cites methods from "Cruciform crack in an orthotropic e..."
...Based on this integral transform technique, there are many applications in various fields of problem which can be seen continually in Gradwell and Iyer [37] and Tsai [38] for contact problems, De and Patra [39], Fildis and Yahsi [40], and Wang et al.[41] for crack problems....
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...Based on this integral transform technique, there are many applications in various fields of problem which can be seen continually in Gradwell and Iyer [37] and Tsai [38] for contact problems, De and Patra [39], Fildis and Yahsi [40], and Wang et al....
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TL;DR: In this paper, the authors examined the loss of contact between a square plate and the unilateral supports under uniformly distributed load and showed that the losses of contact decrease with the increasing Poisson's ratio.
Abstract: This paper examines the loss of contact between a square plate and the unilateral supports under uniformly distributed load. Since the plate is rested on the unilateral supports, it will have the regions of lost contact between a plate and the supports due to the absence of restraining corner force at the plate corners. This leads to the mixed boundary conditions and these conditions are then written in the form of dual-series equations which can further be reduced to a Fredholm integral equation by taking advantage of finite Hankel transform technique. Numerical results are given for the deflections of free edge and deflections along the middle line of the plate with deferent values of the Poisson’s ratio. In addition, the deflection surface is also presented. From the investigation, it can be indicated that the loss of contact is decreased upon the increasing Poisson’s ratio.
3 citations
Cites methods from "Cruciform crack in an orthotropic e..."
...This type of integral transform has been widely used to analytical study the problems in elasticity theory or in mathematical physics which can be found in the scattering technical literature [21-25]....
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References
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TL;DR: In this article, it was shown that the problem of determining the crack energy and the stress intensity factor for a cruciform crack deformed by internal pressure can be reduced to that of solving an infinite system of simultaneous linear algebraic equations.
46 citations
38 citations
TL;DR: In this article, the problem of determining the stress and displacement fields in an orthotropic elastic strip containing a Griffith crack situated symmetrically and oriented in a direction normal to the edges of the strip is considered.
35 citations
TL;DR: In this paper, the Fourier transform was used to solve the equilibrium equations expressed in terms of displacements for the strip with a crack parallel to the edges. But the Fouriers transform was not applied to the case of the plane strain.
22 citations