• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.2
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• pp.185-192
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• 1988

Computation of the elasto-plastic solution of ball indentation was carried out by the quadratic programming method. The problem was formulated as an elasto-plastic contact problem under the assumption of small displacement and small deformation and then transformed into a minimization problem. Finite element approximation resulted in a quadratic programming problem. Numerical and experimental study were done with aluminium Al 2024-T351 and commercially pure copper. The computed load-displacement curves were in good agrement with those obtained from experiments. Tabor's relationship for representative strains was also examined. Stress distributions were found to resemble closely those results available in the literature.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.21 no.2
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• pp.232-240
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• 2012

This study proposed efficient method of singular value for inverse problem, linear approximation of contact position and loading in single and double meshing of transmission contact element, using 2-dimension model considered near the tooth by root stress. Determination of root stress is carried out for the gear tooth by finite element method and boundary element method. Boundary element discretization near contact point is carefully performed to keep high computational accuracy. The predicted results of boundary element method are good accordance with that of finite element method.

• Journal of the Korean Mathematical Society
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• v.52 no.6
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• pp.1195-1207
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• 2015

Lagrange multiplier method for solving the contact problem in elasticity is considered. Based on lower semicontinuity of sensitivity functional we prove the convergence of modified dual scheme to corresponding saddle point.

• Tribology and Lubricants
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• v.2 no.2
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• pp.52-58
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• 1986

The contact problem of a rigid smooth plane and computer-slmuiated elastic rough surfaces is studied by divided the sampling intervals into three groups. An iso-parametric element ,is used to calculate the contact pressure-separation relationship accurately. It is obtained that: 1) the more asperity shows the higher contact pressure, 2) the smaller element gives the better results but the effect is negligible.

• Journal of the Korean Society for Railway
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• v.17 no.1
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• pp.14-18
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• 2014

Wheel/rail contact is a significant problem in railway dynamics. In this paper, the wheel/rail contact is examined analytically and numerically as a contact problem between two cylinders where torque and friction have effect. Furthermore, the contact of a real wheel and rail is investigated numerically where the normal and shear force act. This study demonstrates that the wheel/rail contact is a process that generates traction force through creep where rolling and sliding occurs simultaneously depending on the shape of the wheel and rail, and the friction coefficient between them.

• Computers and Concrete
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• v.27 no.3
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• pp.199-210
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• 2021

The aim of this paper was to examine the continuous and discontinuous contact problems between the functionally graded (FG) layer pressed with a uniformly distributed load and homogeneous half plane using an analytical method and FEM. The FG layer is made of non-homogeneous material with an isotropic stress-strain law with exponentially varying properties. It is assumed that the contact at the FG layer-half plane interface is frictionless, and only the normal tractions can be transmitted along the contacted regions. The body force of the FG layer is considered in the study. The FG layer was positioned on the homogeneous half plane without any bonds. Thus, if the external load was smaller than a certain critical value, the contact between the FG layer and half plane would be continuous. However, when the external load exceeded the critical value, there was a separation between the FG layer and half plane on the finite region, as discontinuous contact. Therefore, there have been some steps taken in this study. Firstly, an analytical solution for continuous and discontinuous contact cases of the problem has been realized using the theory of elasticity and Fourier integral transform techniques. Then, the problem modeled and two-dimensional analysis was carried out by using ANSYS package program based on FEM. Numerical results for initial separation distance and contact stress distributions between the FG layer and homogeneous half plane for continuous contact case; the start and end points of separation and contact stress distributions between the FG layer and homogeneous half plane for discontinuous contact case were provided for various dimensionless quantities including material inhomogeneity, distributed load width, the shear module ratio and load factor for both methods. The results obtained using FEM were compared with the results found using analytical formulation. It was found that the results obtained from analytical formulation were in perfect agreement with the FEM study.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.813-823
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• 2021

In this work, we present the classical formulation for the antiplane problem of a eletro-viscoelastic materialswith total sliprate dependent friction and write the corresponding variational formulation. In the second step, we prove that the solution converges to the solution of the corresponding electro-elastic problem as the viscosity converges to zero.

• Structural Engineering and Mechanics
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• v.2 no.3
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• pp.295-309
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• 1994

The present paper concerns the mathematical study and the numerical treatment of the problem of semirigid connections in bolted steel column base plates by taking into account the possibility of appearance of separation phenomena on the contact surface under certain loading conditions. In order to obtain a convenient discrete form to simulate the structural behaviour of a steel column base plate, the continuous contact problem is first formulated as a variational inequality problem or, equivalently, as a quadratic programming problem. By applying an appropriate finite element scheme, the discrete problem is formulated as a quadratic optimization problem which expresses, from the standpoint of Mechanics, the principle of minimum potential energy of the semirigid connection at the state of equilibrium. For the numerical treatment of this problem, two effective and easy-to-use solution strategies based on quadratic optimization algorithms are proposed. This technique is illustrated by means of a numerical application.

• Proceedings of the KSR Conference
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• 2011.10a
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• pp.643-648
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• 2011

Fatigue crack in most rails take place by rolling contact between wheel and rail in railway industry. Therefore, it is critical to understand the rolling contact phenomena, especially for the three-dimensional situation. In this paper the steady-state rolling contact problem of KTX wheel and rail (UIC60) has been studied with three-dimensional finite element analysis. The variation of contact pressure and contact stresses on rolling contact surface were obtained using the finite element method. The three-dimensional distribution of contact stresses on the contact surface are investigated. Results show that the distribution of shear stress and contact stress (von Mises) on the contact surface varies rapidly as a result of the variation of stick-slip region. The contact stress at the leading edge is greater than at the trailing edge because of stick and slip phenomena.

• Tribology and Lubricants
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• v.38 no.3
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• pp.73-83
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• 2022

This paper is concerned with an analysis of a surface edge crack emanated from a sharp contact edge. For a geometrical model, a square wedge is in contact with a half plane whose materials are identical, and a surface perpendicular crack initiated from the contact edge exists in the half plane. To analyze this crack problem, it is necessary to evaluate the stress field on the crack line which are induced by the contact tractions and pseudo-dislocations that simulate the crack, using the Bueckner principle. In this Part I, the stress filed in the half plane due to the contact is re-summarized using an asymptotic analysis method, which has been published before by the author. Further focus is given to the stress field in the half plane due to a pseudo-edge dislocation, which will provide a stress solution due to a crack (i.e. a continuous distribution of edge dislocations) later, using the Burgers vector. Essential result of the present work is the corrective functions which modify the stress field of an infinite domain to apply for the present one which has free surfaces, and thus the infiniteness is no longer preserved. Numerical methods and coordinate normalization are used, which was developed for an edge crack problem, using the Gauss-Jacobi integration formula. The convergence of the corrective functions are investigated here. Features of the corrective functions and their application to a crack problem will be given in Part II.