# Introduction to Elasticity/Distributed force on half plane

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## Distributed force on a half-plane[edit | edit source]

- Applied load is per unit length in the direction.
- We already know the stresses and displacements due to a concentrated force. The stresses and displacements due to the distributed load can be found by
*superposition*. - The Flamant solution is used as a Green's function, i.e., the distributed load is taken as the limit of a set of point loads of magnitude .

At the point

As , is unbounded. However, if we are interested in regions far from , we can apply the distributed force as a statically equivalent concentrated force and get displacements using the concentrated force solution.

The avoid the above issue, contact problems are often formulated in
terms of the *displacement gradient*

If the point is inside , then the integral is taken to be the sum of the integrals to the left and right of .