• Tribology and Lubricants
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• v.31 no.5
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• pp.189-194
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• 2015

This paper focuses on the conformal contact problem. A typical example of conformal contact is the contact between a pin and hole. In particular, this paper focuses on the condition for assuming a contact stress field to be a Hertzian pressure profile by using well-known classical solutions associated with Hertzian contact. Persson first developed the conformal contact analysis method around half a century ago, but there have been no significant improvements since then. The present research also adopted this method, but developed new solutions from the viewpoint of application to structural design. The analysis began with a comparison between Persson°Øs conformal contact stress and the Hertzian stress fields. The next step was to check the differences in the normalized stress values of both. This study used the tolerance for the difference in the peak stresses of Persson°Øs solution and the Hertz solution to validate the Hertzian assumption. This gave the range for the difference in radii of the pin and hole when the contact force and mechanical properties of the material are specified. The results showed that, at a tolerance of 5%, the Hertzian assumption is valid if half of the contact angle is less than 35°ý. In addition, the Hertzian assumption holds even for a relatively long contact length, in contrast to the general incomplete contact problem. This paper discusses these results along with other aspects of the application to the design.

• Structural Engineering and Mechanics
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• v.27 no.5
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• pp.555-574
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• 2007

Static response of an elastic beam on a two-parameter tensionless foundation is investigated by assuming that the beam is symmetrically subjected to a uniformly distributed load and concentrated edge loads. Governing equations of the problem are obtained and solved by pointing out that a concentrated edge foundation reaction in addition to a continuous foundation reaction along the beam axis in the case of complete contact and a discontinuity in the foundation reactions in the case of partial contact come into being as a direct result of the two-parameter foundation model. The numerical solution of the complete contact problem is straightforward. However, it is shown that the problem displays a highly non-linear character when the beam lifts off from the foundation. Numerical treatment of the governing equations is accomplished by adopting an iterative process to establish the contact length. Results are presented in figures to demonstrate the linear and non-linear behavior of the beam-foundation system for various values of the parameters of the problem comparatively.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1992.03a
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• pp.11-26
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• 1992

In this research, a numerical algorithm has been developed, which can be applied to the large deformation and large displacement contact problems between angle change have been proposed considering the change in geometric shape and rate of contact force. A set of linear simultaneous equations is constructed by adding the geometric shape change and contact conditions to the original stiffness matrix. A new method to determine time increment has been proposed based on Euler method, in which the condition to prevent the contact bodies from penetrating and overrunning each other has been taken into consideration. Practical application to contact problem is extrusion in which bodies are sliding along the contact boundary.

• Transactions of Materials Processing
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• v.12 no.1
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• pp.26-33
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• 2003

This paper is concerned with the numerical analysis of frictional contact problems in axisymmetric bodies using the rigid-plastic finite element method. A contact finite element method, based on a penalty function, are derived from variational formulations. The contact boundary condition between two deformable bodies is prescribed by the proposed algorithm. The program which can handle frictional contact problem is developed by using pre-existing rigid-plastic finite element code. Some examples used in this paper illustrate the effectiveness of the proposed formulations and algorithms. Efforts focus on the deformation patterns, contact force, and velocity gradient through the various simulations.

• Structural Engineering and Mechanics
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• v.34 no.3
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• pp.319-334
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• 2010

The dynamic response of a finite Bernoulli-Euler beam resting on a tensionless Pasternak foundation and subjected to a concentrated harmonic load is investigated in this study. This load may be applied at the center of the beam, or it may be offset from the center. Since the elastic foundation is assumed to be tensionless, the beam may lift off the foundation, resulting in contact and non-contact regions in the system. An analytical/numerical solution is obtained from the governing equations of the contact and non-contact regions to determine the coordinates of the lift-off points. Although there is no nonlinear term in the equations, the problem appears to be nonlinear since the contact regions are not known in advance. Due to that nonlinearity, the essentials of the problem (the coordinates of the lift-off points) are calculated numerically using the Newton-Raphson technique. The results, which represent the symmetric and asymmetric responses of the beam, are presented graphically in this work. They illustrate the effects of the forcing frequency and the beam length on the extent of the contact regions and displacements.

• 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.

• Proceedings of the KSME Conference
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• 2001.06a
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• pp.144-150
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• 2001

Considered is non-symmetric contact traction induced by the tilting of a contact body and/or by a far field bulk tensile load to the other body. The problem is under the regime of plane strain. General profile of the contact end is incorporated and partial slip condition is supposed. As an example contact configuration, an indentation of a punch with rounded corners onto a half plane is studied. The variation of the internal stress field due to the tilting and the bulk tension is investigated. An edge crack problem is analyzed to examine the influence of the non-symmetric traction. It is shown that the tilting of a punch does not influence the behaviour of the crack. Rather, the effect of the bulk tension on the cracking behaviour is found considerable.

• Transactions of Materials Processing
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• v.12 no.1
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• pp.34-42
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• 2003

This paper presents a rigid-plastic finite element method to handle the frictional contact problem between two deformable bodies experiencing large deformation. The variational formulation combined with incremental quasi-static model is employed for treating the contact boundary condition. The frictional behavior of the model obeys Coulomb's law of friction. The proposed contact algorithms are classified into two categories, one for searching contacting nodes and the other for calculating contact forces at the contact surface. A slave node and master contact segment are defined using the geometric condition of finite elements on the contact interface. The penalty parameter is used to limit the penetration between contacting bodies, and the finite elements are coupled with contact boundary elements.us gates and cavity thicknesses. Through this study we have observed that the jetting is related to the die swell of material. This means that the jotting is strongly affected by the elastic flow property rather than the viscous flow property in viscoelastic characteristics of molten polymer. Different resins have different elastic properties, and elastic flow behavior depends on the shear rate of flow, i.e. injection speed. Large die swell would eliminate jetting however, the retardation of die swell would stimulate jetting. In the point of mole design, reducing the thickness ratio of cavity to gate can reduce or eliminate jetting regardless of amount of elasticity of polymer melt.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.5
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• pp.439-444
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• 2009

This paper presents an efficient contact detection algorithm for the plane elastostatic contact problem of the boundary element method(BEM). The data structures of the boundary element method are dissected to develop an efficient contact detection algorithm. This algorithm is consists of three parts as global searching, local searching and contact relation setting to reflect the corner node problem. Contact master and slave type elements are used in global searching step and quad-tree is selected as the spatial decomposition method in local searching step. To set up contact relation equations, global contact searching is conducted at node level and local searching is performed at element level. To verify the efficiency of the proposed contact detection algorithm of BEM, numerical example is presented.

• Structural Engineering and Mechanics
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• v.12 no.1
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• pp.17-34
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• 2001

The frictionless contact problem for a layered composite which consists of two elastic layers having different elastic constants and heights resting on two simple supports is considered. The external load is applied to the layered composite through a rigid stamp. For values of the resultant compressive force P acting on the stamp vertically which are less than a critical value $P_{cr}$ and for small flexibility of the layered composite, the continuous contact along the layer - the layer and the stamp - the layered composite is maintained. However, if the flexibility of the layered composite increases and if tensile tractions are not allowed on the interface, for P > $P_{cr}$, a separation may be occurred between the stamp and the layered composite or two elastic layers interface along a certain finite region. The problem is formulated and solved for both cases by using Theory of Elasticity and Integral Transform Technique. Numerical results for $P_{cr}$, separation initiation distance, contact stresses, distances determining the separation area, and the vertical displacement in the separation zone between two elastic layers are given.