Elasticity pp 449-457 | Cite as

Frictionless Contact

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


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
$$\sigma _{zz} = - \frac{{\partial ^2 \varphi }}{{\partial z^2 }};\sigma _{zx} = \sigma _{zy} = 0;z = 0,$$
whilst the surface displacements are
$$u_x = \frac{{(1 - 2v)}}{{2\mu }}\frac{{\partial \varphi }}{{\partial x}};u_y = \frac{{(1 - 2v)}}{{2\mu }}\frac{{\partial \varphi }}{{\partial y}};u_z = \frac{{(1 - v)}}{\mu }\frac{{\partial \varphi }}{{\partial z}};z = 0,$$
from Table 21.3.


Contact Area Stress Intensity Factor Contact Problem Surface Displacement Frictionless Contact 
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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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