Introduction to Elasticity/Distributed force on half plane

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

Distributed force on a half plane
  • 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 .