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# Frictionless Contact

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## 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
whilst the surface displacements are
from Table 21.3.

*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)

$$u_x = \frac{{(1 - 2v)}}{{2\mu }}\frac{{\partial \varphi }}{{\partial x}};u_y = \frac{{(1 - 2v)}}{{2\mu }}\frac{{\partial \varphi }}{{\partial y}};u_z = \frac{{(1 - v)}}{\mu }\frac{{\partial \varphi }}{{\partial z}};z = 0,$$

(29.2)

## 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