Penny-shaped cracks

Guidera, Joseph Thomas; Lardner, R. W.

doi:10.1007/bf01389258

Cited by 78 publications

(43 citation statements)

References 11 publications

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“…Such problems can be solved exactly, usually by integral-transform techniques and dual integral equations (Sneddon 1966). Thus, w n and f n are related by the explicit formula Guidera & Lardner (1975) give a clear derivation of this result. Substituting for f n from (5.5) into (5.6), we find that…”

Section: One-dimensional Equationsmentioning

confidence: 99%

Radiation of water waves by a heaving submerged horizontal disc

Martin

Farina

1997

J. Fluid Mech.

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A thin rigid plate is submerged beneath the free surface of deep water. The plate performs small-amplitude oscillations. The problem of calculating the radiated waves can be reduced to solving a hypersingular boundary integral equation. In the special case of a horizontal circular plate, this equation can be reduced further to onedimensional Fredholm integral equations of the second kind. If the plate is heaving, the problem becomes axisymmetric, and the resulting integral equation has a very simple structure; it is a generalization of Love's integral equation for the electrostatic field of a parallel-plate capacitor. Numerical solutions of the new integral equation are presented. It is found that the added-mass coefficient becomes negative for a range of frequencies when the disc is sufficiently close to the free surface.

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Section: One-dimensional Equationsmentioning

confidence: 99%

Radiation of water waves by a heaving submerged horizontal disc

Martin

Farina

1997

J. Fluid Mech.

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“…(2) agrees with Eq. (2.9) of [5], if the applied loading is identified with a -7(6(f'))). The solution of (2) is required to satisfy the conditions 6(a) = 0, 6'(0) = 0.…”

Section: Penny-shaped Crack Bridged By Fibres 329mentioning

confidence: 99%

Penny-shaped crack bridged by fibres

Movchan¹,

Willis²

1998

Quart. Appl. Math.

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Abstract.An axi-symmetric problem for a penny-shaped crack bridged by fibres is considered. The study is reduced to the analysis of a hypersingular integral equation with respect to the relative crack-face separation over a circular domain occupied by the crack. The special case of a large crack subjected to Mode-I loading is examined. A matched asymptotic expansions technique is used in order to estimate the stress intensity factor at the crack edge and to evaluate the magnitude of the applied load which provides the critical opening for failure of fibres at the centre of the crack. Introduction.The physical problem that motivated this study relates to a body composed of a brittle matrix (in practice, a ceramic) reinforced by parallel fibres. The matrix contains a circular crack, in a plane normal to the axes of the fibres. The fibres, however, remain intact. They "bridge" the crack and carry some load, thereby increasing the material's resistance to catastrophic failure. The simplest model for this system represents the intact composite as an elastic continuum and the effect of the bridging fibres is taken into account by a continuous distribution of (generally nonlinear) springs, joining opposite points on the crack faces. Application of the model requires two steps: the determination of an appropriate force-separation law that characterizes the restraining tractions provided by the fibres, and stress analysis performed for a crack in a body loaded in some prescribed way at points remote from the crack. In the present paper we deal only with the second step, namely we consider a penny-shaped bridged crack in an elastic infinite body and describe the effect of fibres by introducing restraining tractions that follow either a linear or a quadratic force-separation law.The problem is formulated in terms of a hypersingular integral equation over a domain occupied by the crack. In general, this can be solved numerically [1], [2], In the particular case of a long crack, the governing equation contains a small parameter that multiplies the hypersingular integral, leading to a singular perturbation problem. A method for

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“…In the limit case a/b = a ~ 1, the expression (3) is developed into the known strict solution for a penny-shaped crack [ 10].…”

Section: The Choice Of the Asymptotic Componentmentioning

confidence: 99%

“…The W~Q, component is intended to provide the proper weight function behavior [9,10] when the force application point Q is close to the contour point Q' considered. Then in this (1) with allowance for representation (2).…”

Section: Introductionmentioning

confidence: 99%

Point weight function method application for semi-elliptical mode I cracks

Оrynyak¹,

Borodii²

1995

Int J Fract

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AbstracL The method of the approximate weight function construction for a semi-elliptical crack was suggested. The weight function sought was written as the sum of asymptotic (weight function for an elliptical crack in an infinite body) and correction components. To take into account the influence of a body free surface on the asymptotic component behavior, fictitious forces symmetric with respect to the body free surface were introduced.As an example of the efficiency of the proposed method semi-elliptical axial cracks in pressure vessels were considered. The results of the stress intensity factor prediction are in good agreement with the corresponding results obtained by Raju and Newman. The only exception are the results for the points located near the major ellipse axis. This may be explained by the shortcomings of the employed empirical weight function expression for an elliptical crack in an infinite body.

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Penny-shaped cracks

Cited by 78 publications

References 11 publications

Radiation of water waves by a heaving submerged horizontal disc

Radiation of water waves by a heaving submerged horizontal disc

Penny-shaped crack bridged by fibres

Point weight function method application for semi-elliptical mode I cracks

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