Continuous and discontinuous contact problems for strips on an elastic semi-infinite plane

Çakiroğlu, Adnan; Cakiroglu, Fevzi L.

doi:10.1016/0020-7225(91)90080-m

Cited by 15 publications

(6 citation statements)

References 9 publications

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“…To solve the system of integral equations, it is found to be more convenient to assume that (26c) as well as (26a) and (26b) has an index +1 [29]; consequently, the function ( ) ( = 1, . .…”

Section: Case Of Discontinuous Contactmentioning

confidence: 99%

“…The contact problem for an elastic layer has attracted considerable attention in the past because of its possible application to a variety of structures of practical interest. The layer usually rests on a foundation which may be either elastic or rigid and the body force due to gravity may be neglected or effect of gravity may be taken into account [28][29][30][31][32][33][34][35]. Studies regarding the frictionless contact along the interface may be found in [2][3][4][5][6][7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

“…When the magnitude of the compressive external load exceeds a certain value, a separation will take place between the layer and the foundation. The length of separation region along the interface is unknown, and the problem becomes a discontinuous contact problem [28][29][30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

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Contact Problem for an Elastic Layer on an Elastic Half Plane Loaded by Means of Three Rigid Flat Punches

Özşahin

Taskıner

2013

Mathematical Problems in Engineering

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The frictionless contact problem for an elastic layer resting on an elastic half plane is considered. The problem is solved by using the theory of elasticity and integral transformation technique. The compressive loadsPandQ(per unit thickness in direction) are applied to the layer through three rigid flat punches. The elastic layer is also subjected to uniform vertical body force due to effect of gravity. The contact along the interface between elastic layer and half plane is continuous, if the value of the load factor,λ, is less than a critical value, . In this case, initial separation loads, and initial separation points, are determined. Also the required distance between the punches to avoid any separation between the punches and the elastic layer is studied and the limit distance between punches that ends interaction of punches is investigated for various dimensionless quantities. However, if tensile tractions are not allowed on the interface, for the layer separates from the interface along a certain finite region. Numerical results for distance determining the separation area, vertical displacement in the separation zone, contact stress distribution along the interface between elastic layer and half plane are given for this discontinuous contact case.

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Section: Case Of Discontinuous Contactmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Contact Problem for an Elastic Layer on an Elastic Half Plane Loaded by Means of Three Rigid Flat Punches

Özşahin

Taskıner

2013

Mathematical Problems in Engineering

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“…Civelek and Erdogan [1] offered a solution to the frictionless contact problem for an elastic layer under gravity while continuous and discontinuous contact problems for a layer on an elastic semi‐infinite plane were investigated by Çakıroğlu and Çakıroğlu [2]. Çakıroğlu et al.…”

Section: Introductionmentioning

confidence: 99%

“…Some examples of contact mechanic studies in which the effect of body forces are taken into account are presented below. Civelek and Erdogan [1] offered a solution to the frictionless contact problem for an elastic layer under gravity while continuous and discontinuous contact problems for a layer on an elastic semi-infinite plane were investigated by Çakıroğlu and Çakıroğlu [2]. Çakıroğlu et al [3] conducted a study focusing on the continuous and discontinuous contact problems of two elastic layers resting on an elastic half-plane and Birinci and Erdöl [4] studied the frictionless contact problem for two elastic layers supported by a Winkler foundation, while Özşahin [5] studied the frictionless contact problem for a layer on an elastic half-plane loaded by means of two dissimilar rigid punches.…”

Section: Introductionmentioning

confidence: 99%

Continuous and discontinuous contact problem of a functionally graded orthotropic layer indented by a rigid cylindrical punch: Analytical and finite element approaches

Karabulut

Çömez

2023

Z Angew Math Mech

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In this study, the continuous and discontinuous contact problems of a functionally graded (FG) orthotropic layer lying on a homogeneous and isotropic layer were investigated. The orthotropic layer was indented by a rigid cylindrical punch which was subjected to a concentrated normal force, and a homogeneous isotropic layer was firmly attached to a rigid substrate. For the analytical solution, the general expressions for the stresses and displacements were obtained in the presence of body forces by using elasticity theory and Fourier integral transforms. The continuous and discontinuous contact problems were reduced to the singular integral equations by means of boundary conditions. The system of the singular integral equations was solved using the Gauss-Chebyshev integration formula. Then, the finite element solution of the two cases was also performed. Analytical results and numerical results (FEM) for critical load, initial separation distance, separation region in discontinuous contact, contact lengths under the punch, and contact stress distributions between the layer-punch and layer-layer were obtained for the dimensionless quantities.

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The contact problem of a functionally graded layer under the effect of gravity

et al. 2023

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This paper considers the continuous and discontinuous contact problems of a functionally graded (FG) layer under the effect of gravity. A finite distributed load is applied to the beam from the top and the beam is placed to the top of a rigid foundation. It is assumed that the shear modulus and mass density of the beam vary exponentially whereas Poisson's ratio remains constant. The problem is solved for both continuous and discontinuous cases. In each case, the governing equations and boundary conditions of the problem are reduced to an integral equation by the help of Fourier integral transform. In the continuous contact, the integral equation solved analytically and critical load that causes initial separation between the layer and the rigid foundation, separation distance and contact pressures are investigated for various non‐homogeneity parameters that presents the change in the shear modulus and density and loadings. The singular integral equation in case of discontinuous contact is numerically solved by using corresponding Gauss–Chebyshev quadrature and an iterative scheme. The effect of non‐homogeneity parameters and loading on the separation distance between the layer and the foundation and contact pressures are analyzed. All the results are shown in tables and figures. It is seen that increasing stiffness and decreasing density at the top of the layer reduce maximum pressures but increase separation distances. This study aims to fill the deficiency in the mechanical behavior of the coatings under gravity.

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Continuous and discontinuous contact problems for strips on an elastic semi-infinite plane

Cited by 15 publications

References 9 publications

Contact Problem for an Elastic Layer on an Elastic Half Plane Loaded by Means of Three Rigid Flat Punches

Contact Problem for an Elastic Layer on an Elastic Half Plane Loaded by Means of Three Rigid Flat Punches

Continuous and discontinuous contact problem of a functionally graded orthotropic layer indented by a rigid cylindrical punch: Analytical and finite element approaches

The contact problem of a functionally graded layer under the effect of gravity

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