Numerical solution of singular integral equations

Erdoğan, F.; Gupta, G. D.; Cook, T. S.

doi:10.1007/978-94-017-2260-5_7

Cited by 677 publications

(470 citation statements)

References 11 publications

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“…For the numerical solution of the SIE in (68), the Gauss-Chebyshev quadrature developed by Erdogan and Gupta (1972) is used. After the appropriate normalization over the interval   1 , 1  , the integral equation takes the discretized form…”

Section: The Corrective Solutionmentioning

confidence: 99%

Distributed dislocation approach for cracks in couple-stress elasticity: shear modes

Gourgiotis

Georgiadis

Defect and Material Mechanics

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Section: The Corrective Solutionmentioning

confidence: 99%

Distributed dislocation approach for cracks in couple-stress elasticity: shear modes

Gourgiotis

Georgiadis

Defect and Material Mechanics

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“…The relation between the applied load and the contact length, b can be found by applying equilibrium condition [46]. Thus, using Eq.…”

Section: Integral Equation Of the Problemmentioning

confidence: 99%

“…By defining the complex potential [13,45,46]: (20) From Muskhelishvili [13] and by using the complex function theory, the dominant part of the integral equation can be written as (21) The index of the integral equation for the semi-circular punch is defined by: …”

Section: On the Solution Of Integral Equationsmentioning

confidence: 99%

Analytical solution of the frictional contact problem of asemi-circular punch sliding over a homogeneous orthotropic half-plane

Küçüksucu

Güler

2016

Hittite J. Sci. Eng.

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C ontact mechanics problems in isotropic materials gained a great deal of interest and commonly investigated throughout the twentieth century. Orthotropic materials have been utilized both in structural design and engineering applications such as ceramic matrix composites [1]. These materials gained popularity in the last two decades and mainly projected to be used in the aerospace industry as fiber metal laminates in the structure of aircrafts and in the components of gas turbine engines [2]. For example, Tyrannohex is a high strength ceramic material containing properties of other orthotropic materials and it is utilized in the gas turbine components [3].The studies in the theory of contact mechanics dates back to Lord Kelvin [4] who solved the problem of a force applied at a point in an isotropic infinite medium using Green's functions [5]. Then Lamé [6] further improved Lord Kelvin 's solution with superimposed stresses in a spherical container. Boussinesq [7], provided the solution of a normal force applied to the boundary of an isotropic semi-infinite solid using Green's functions and Kelvin's method. Almost at the same time Hertz [8] solved the problem involving contact between two elastic bodies with curved surfaces and postulated his famous assumptions about contact mechanics. Cerruti [9]

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“…More detailed information on the PE model can be found in Guo & Noda (2007). By using the method given by Erdogan & Gupta (1972) for solving the singular integral equations, equation (3.24) can be transformed into the following form:…”

Section: (B) Combination Of the Piecewise-exponential Model And The Smentioning

confidence: 99%

“…where More details can be founded in Erdogan & Gupta (1972). From equations (3.23) and (3.25), the unknowns w(r l ) can be solved.…”

Section: (B) Combination Of the Piecewise-exponential Model And The Smentioning

confidence: 99%

A fracture mechanics model for a crack problem of functionally graded materials with stochastic mechanical properties

2012

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This study aimed to develop a method to build a 'bridge' between the macro fracture mechanics model and stochastic micromechanics-based properties so that the macro fracture mechanics model can be expanded to the fracture mechanics problem of functionally graded materials (FGMs) with stochastic mechanical properties. An analytical fracture mechanics model is developed to predict the stress intensity factors (SIFs) in FGMs with stochastic uncertainties in phase volume fractions. Considering the stochastic description of the phase volume fractions, a micromechanics-based method is developed to derive the explicit probabilistic characteristics of the effective properties of the FGMs so that the stochastic mechanical properties can be combined with the macro fracture mechanics model. A thought for choosing the samples efficiently is proposed so that the stable probabilistic characteristic of SIFs can be obtained with a very small sample size. The probability density function of SIFs can be determined by developing a histogram from the generated samples. The present method may provide a thought to establish an analytical model for the crack problems of FGMs with stochastic properties.

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Numerical solution of singular integral equations

Cited by 677 publications

References 11 publications

Distributed dislocation approach for cracks in couple-stress elasticity: shear modes

Distributed dislocation approach for cracks in couple-stress elasticity: shear modes

Analytical solution of the frictional contact problem of asemi-circular punch sliding over a homogeneous orthotropic half-plane

A fracture mechanics model for a crack problem of functionally graded materials with stochastic mechanical properties

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