This paper is concerned with an internal crack problem in an infinite functionally graded elastic layer. The crack is opened by an internal uniform pressurep0along its surface. The layer surfaces are supposed to be acted on by symmetrically applied concentrated forces of magnitudeP/2with respect to the centre of the crack. The applied concentrated force may be compressive or tensile in nature. Elastic parametersλandμare assumed to vary along the normal to the plane of crack. The problem is solved by using integral transform technique. The solution of the problem has been reduced to the solution of a Cauchy-type singular integral equation, which requires numerical treatment. The stress-intensity factors and the crack opening displacements are determined and the effects of graded parameters on them are shown graphically.
Berinde has shown that Newton's method for a scalar equationf(x)=0converges under some conditions involving onlyfandf′and notf″when a generalized stopping inequality is valid. Later Sen et al. have extended Berinde's theorem to the case where the condition thatf′(x)≠0need not necessarily be true. In this paper we have extended Berinde's theorem to the class ofn-dimensional equations,F(x)=0, whereF:ℝn→ℝn,ℝndenotes then-dimensional Euclidean space. We have also assumed thatF′(x)has an inverse not necessarily at every point in the domain of definition ofF.
This article is concerned with the study of frictionless contact between a rigid punch and a transversely isotropic functionally graded layer. The rigid punch is assumed to be axially symmetric and is supposed to be pressing the layer by an applied concentrated load. The layer is resting on a rigid base and is assumed to be sufficiently thick in comparison with the amount of indentation by the rigid punch. The graded layer is modeled as a non-homogeneous medium. The relationship between the applied load P and the contact area is obtained by solving the mathematically formulated problem through using the Hankel transform of different order. Numerical results have been presented to assess the effects of functional grading of the medium and the applied load on the stress distribution in the layer as well as on the relationship between the applied load and the area of contact.
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