Integral equation and contact problem

Abdou, M. A.; Salama, F. A.

doi:10.1016/s0096-3003(03)00175-9

Cited by 3 publications

(2 citation statements)

References 6 publications

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“…The Gauss quadrature formula [2] can be chosen to evaluate (92). To simplify the development somewhat, but without removing any generality of the result, the interval of integration can be changed from [0, ] S to [ 1,1]   by a suitable transformation…”

Section: The Structure Resolvent and Asymptotic Analysismentioning

confidence: 99%

“…problem in the theory of elasticity that related to the field of problem considered here, Abdou and Salama [1] established and solved the Fredholm integral equation of the second kind with a generalized potential kernel which investigated from the semi-symmetric Hertz problem for two different elastic materials, where the kernel of integral equation can be represented in the nonhomogeneous wave equation form. However, there are more various techniques remained to be discovered in several scientific or technical literatures that can cope with the other types of integral equation solution, but not only for the case of Fredholm-type integral equations.…”

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confidence: 99%

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On a treatment of coupled integral equations in nonlinear unilateral contact problem of plates

Sompornjaroensuk

Kongtong

2013

ams

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Application of finite Hankel integral transforms to the problem of a uniformly loaded unilaterally supported rectangular thin plates, the solution of partial differential equation can then be reduced to two coupled Fredholm integral equations of the second kind that obtained from the coupled dual-series equations of mixed boundary conditions, and also together with two constraint integral equations resulted from both of zero corner force condition and compatibility of edge displacements near each plate corner that loses contact. Owing to the summation of many different infinite series in the kernels and inhomogeneous parts of equations for the requirements of attainable highest accuracy and reducible computational time, the modified mathematical manipulations are improved and required asymptotic expansion for large arguments of the Bessel and Struve functions is treated to accelerate the convergence of series rapidly. The latter is to avoid the undesirable lengthy computer runs in numerical computations. Consequently, this paper is devoted to demonstrate the mathematical description and numerical algorithms in order to solve the system of coupled integral equations.

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Section: The Structure Resolvent and Asymptotic Analysismentioning

confidence: 99%

mentioning

confidence: 99%

On a treatment of coupled integral equations in nonlinear unilateral contact problem of plates

Sompornjaroensuk

Kongtong

2013

ams

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A modified approach to numerical solution of Fredholm integral equations of the second kind

Panda

Martha

Chakrabarti

2015

Applied Mathematics and Computation

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Analysis of Continuous and Discontinuous Cases of a Contact Problem Using Analytical Method and FEM

Birinci

Adıyaman

Yaylacı

et al. 2015

Lat. Am. j. solids struct.

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In this paper, continuous and discontinuous cases of a contact problem for two elastic layers supported by a Winkler foundation are analyzed using both analytical method and finite element method. In the analyses, it is assumed that all surfaces are frictionless, and only compressive normal tractions can be transmitted through the contact areas. Moreover, body forces are taken into consideration only for layers. Firstly, the problem is solved analytically using theory of elasticity and integral transform techniques. Then, the finite element analysis of the problem is carried out using ANSYS software program. Initial separation distances between layers for continuous contact case and the size of the separation areas for discontinuous contact case are obtained for various dimensionless quantities using both solutions. In addition, the normalized contact pressure distributions are calculated for both cases. The analytical results are verified by comparison with finite element results. Finally, conclusions are presented.

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Integral equation and contact problem

Cited by 3 publications

References 6 publications

On a treatment of coupled integral equations in nonlinear unilateral contact problem of plates

On a treatment of coupled integral equations in nonlinear unilateral contact problem of plates

A modified approach to numerical solution of Fredholm integral equations of the second kind

Analysis of Continuous and Discontinuous Cases of a Contact Problem Using Analytical Method and FEM

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