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Elasticity pp 449-457 | Cite as

Frictionless Contact

  • J. R. Barber
Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 172)

Abstract

As we noted in §21.5.1, Green and Zerna’s Solution F is ideally suited to the solution of frictionless contact problems for the half-space, since it identically satisfies the condition that the shear tractions be zero at the surface z=0. In fact the surface tractions for this solution take the form
$$\sigma _{zz} = - \frac{{\partial ^2 \varphi }}{{\partial z^2 }};\sigma _{zx} = \sigma _{zy} = 0;z = 0,$$
(29.1)
whilst the surface displacements are
$$u_x = \frac{{(1 - 2v)}}{{2\mu }}\frac{{\partial \varphi }}{{\partial x}};u_y = \frac{{(1 - 2v)}}{{2\mu }}\frac{{\partial \varphi }}{{\partial y}};u_z = \frac{{(1 - v)}}{\mu }\frac{{\partial \varphi }}{{\partial z}};z = 0,$$
(29.2)
from Table 21.3.

Keywords

Contact Area Stress Intensity Factor Contact Problem Surface Displacement Frictionless Contact 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of Mechanical Engineering and Applied MechanicsUniversity of MichiganAnn ArborUSA

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