• Structural Engineering and Mechanics
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• v.48 no.2
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• pp.241-255
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• 2013

The receding contact problem for two elastic layers whose elastic constants and heights are different supported by two elastic quarter planes is considered. The lower layer is supported by two elastic quarter planes and the upper elastic layer is subjected to symmetrical distributed load whose heights are 2a on its top surface. It is assumed that the contact between all surfaces is frictionless and the effect of gravity force is neglected. The problem is formulated and solved by using Theory of Elasticity and Integral Transform Technique. The problem is reduced to a system of singular integral equations in which contact pressures are the unknown functions by using integral transform technique and boundary conditions of the problem. Stresses and displacements are expressed depending on the contact pressures using Fourier and Mellin formula technique. The singular integral equation is solved numerically by using Gauss-Jacobi integration formulation. Numerical results are obtained for various dimensionless quantities for the contact pressures and the contact areas are presented in graphics and tables.

• Structural Engineering and Mechanics
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• v.18 no.4
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• pp.441-459
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• 2004

This paper explores the potential use of neural networks (NNs) in the field of contact mechanics. A neural network model is developed for predicting, with sufficient approximation, the contact lengths between the elastic layer and two elastic circular punches. A backpropagation neural network of three layers is employed. First contact problem is solved according to the theory of elasticity with integral transformation technique, and then the results are used to train the neural network. The effectiveness of different neural network configurations is investigated. Effect of parameters such as load factor, elastic punch radii and flexibilities that influence the contact lengths is also explored. The results of the theoretical solution and the outputs generated from the neural network are compared. Results indicate that NN predicted the contact length with high accuracy. It is also demonstrated that NN is an excellent method that can reduce time consumed.

• Tribology and Lubricants
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• v.24 no.2
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• pp.90-95
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• 2008

An elastic-plastic contact analysis is developed using a semi-analytical method. The elastic contact is solved within a Hertz theorem. The reciprocal theorem with initial strains is then introduced, to express the surface geometry as a function of contact stress and plastic strains. The irreversible nature of plasticity leads to an incremental formulation of the elastic-plastic contact problem, and an algorithm to solve this problem is set up. Closed form expression, which give residual stresses and surface displacements from plastic strains, are obtained by integration of the reciprocal theorem. The distribution of contact stress, residual stress and plastic strain are obtained by the changed surface geometry.

• Journal of the Korean Geotechnical Society
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• v.23 no.3
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• pp.77-88
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• 2007

A micromechanics-based model to simulate the elastic and elastic-plastic behavior of granular soils is developed. The model accounts for the fabric anisotropy represented by the statistical parameter of the spatial distribution of contact normals, the evolution of fabric anisotropy as a function of stress ratio, the continuous change of the co-ordination number relating to the void ratio, and the elastic and elastic-plastic microscopic contact stiffness. Using the experimental data for metallic materials, the elastic-plastic contact stiffness is derived as a power function of the normal contact force as well as the contact force initiating the yielding of contact bodies. To quantitatively assess microscopic model parameters, approximate solutions of cross-anisotropic elastic moduli are derived in terms of the micromechanical parameters.

• Structural Engineering and Mechanics
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• v.21 no.2
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• pp.205-220
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• 2005

This paper presents the possibilities of adapting artificial neural networks (ANNs) to predict the dimensionless parameters related to the maximum contact pressures of an elasticity problem. The plane symmetric double receding contact problem for a rigid stamp and two elastic strips having different elastic constants and heights is considered. The external load is applied to the upper elastic strip by means of a rigid stamp and the lower elastic strip is bonded to a rigid support. The problem is solved under the assumptions that the contact between two elastic strips also between the rigid stamp and the upper elastic strip are frictionless, the effect of gravity force is neglected and only compressive normal tractions can be transmitted through the interfaces. A three layered ANN with backpropagation (BP) algorithm is utilized for prediction of the dimensionless parameters related to the maximum contact pressures. Training and testing patterns are formed by using the theory of elasticity with integral transformation technique. ANN predictions and theoretical solutions are compared and seen that ANN predictions are quite close to the theoretical solutions. It is demonstrated that ANNs is a suitable numerical tool and if properly used, can reduce time consumed.

• Structural Engineering and Mechanics
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• v.25 no.4
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• pp.383-403
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• 2007

The contact problem for an elastic layer resting on an elastic half plane is considered according to the theory of elasticity with integral transformation technique. External loads P and Q are transmitted to the layer by means of two dissimilar rigid flat punches. Widths of punches are different and the thickness of the layer is h. All surfaces are frictionless and it is assumed that the layer is subjected to uniform vertical body force due to effect of gravity. The contact along the interface between elastic layer and half plane will be continuous, if the value of load factor, ${\lambda}$, is less than a critical value, ${\lambda}_{cr}$. However, if tensile tractions are not allowed on the interface, for ${\lambda}$ > ${\lambda}_{cr}$ the layer separates from the interface along a certain finite region. First the continuous contact problem is reduced to singular integral equations and solved numerically using appropriate Gauss-Chebyshev integration formulas. Initial separation loads, ${\lambda}_{cr}$, initial separation points, $x_{cr}$, are determined. Also the required distance between the punches to avoid any separation between the punches and the layer is studied and the limit distance between punches that ends interaction of punches, is investigated. Then discontinuous contact problem is formulated in terms of singular integral equations. The numerical results for initial and end points of the separation region, displacements of the region and the contact stress distribution along the interface between elastic layer and half plane is determined for various dimensionless quantities.

• Journal of Mechanical Science and Technology
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• v.17 no.12
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• pp.1928-1937
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• 2003

Effect of elastic modulus mismatch on the contact crack initiation is investigated to find major parameters in designing desirable surface-coated system. Silicon nitride coated soft materials with various elastic modulus mismatch, E$\_$c//E$\_$s/＝1.06∼356 are prepared for the analysis. Hertzian contact test is conducted for producing contact cracks and the acoustic emission detecting technique for measuring the critical load of crack initiation. The implication is that coating thickness and material strength are controllable parameters to prevent the initiation of contact cracks resulted from the elastic modulus mismatch in the hard ceramic coating layer on the soft materials.

• Structural Engineering and Mechanics
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• v.37 no.3
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• pp.285-296
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• 2011

The plane crack-contact problem for an infinite elastic layer with two symmetric rectangular rigid stamps on its upper and lower surfaces is considered. The elastic layer having an internal crack parallel to its surfaces is subjected to two concentrated loads p on its upper and lower surfaces trough the rigid rectangular stamps and a pair of uniform compressive stress $p_0$ along the crack surface. It is assumed that the contact between the elastic layer and the rigid stamps is frictionless and the effect of the gravity force is neglected. The problem is reduced to a system of singular integral equations in which the derivative of the crack surface displacement and the contact pressures are unknown functions. The system of singular integral equations is solved numerically by making use of an appropriate Gauss-Chebyshev integration formula. Numerical results for stress-intensity factor, critical load factor, $\mathcal{Q}_c$, causing initial closure of the crack tip, the crack surface displacements and the contact stress distribution are presented and shown graphically for various dimensionless quantities.

• Structural Engineering and Mechanics
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• v.15 no.3
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• pp.331-344
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• 2003

The plane contact problem for two infinite elastic layers whose elastic constants and heights are different is considered. The layers lying on a Winkler foundation are acted upon by symmetrical distributed loads whose lengths are 2a applied to the upper layer and uniform vertical body forces due to the effect of gravity in the layers. It is assumed that the contact between two elastic layers is frictionless and that only compressive normal tractions can be transmitted through the interface. The contact along the interface will be continuous if the value of the load factor, ${\lambda}$, is less than a critical value. However, interface separation takes place if it exceeds this critical value. First, the problem of continuous contact is solved and the value of the critical load factor, ${\lambda}_{cr}$, is determined. Then, the discontinuous contact problem is formulated in terms of a singular integral equation. Numerical solutions for contact stress distribution, the size of the separation areas, critical load factor and separation distance, and vertical displacement in the separation zone are given for various dimensionless quantities and distributed loads.

• Structural Engineering and Mechanics
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• v.72 no.6
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• pp.775-783
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• 2019

The present study deals with the numerical analysis of the symmetric contact problem of two bonded layers resting on an elastic half plane compressed with a rigid punch. In this context, Finite Element Method (FEM) based software called ANSYS and ABAQUS are used. It is assumed that the elastic layers have different elastic constants and heights and the external load is applied to the upper elastic layer by means of a rigid stamp. The problem is solved under the assumptions that the contact between two elastic layers, and between the rigid stamp are frictionless, the effect of gravity force is neglected. To validate the constructed model and obtained results a comparison is performed with the analytical results in literature. The numerical results for normal stresses and shear stresses are obtained for various parameters of load, material and geometry and are tabulated and illustrated.