Introduction to Elasticity/Flamant solution

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The Flamant Solution[edit | edit source]

Elastic wedge loaded by two forces at the tip
  • This problem is also self-similar (no inherent length scale).
  • All quantities can be expressed in the separated-variable form .
  • The stresses vary as (the area of action of the force decreases with increasing ). How about a conical wedge ?

From Michell's solution, pick terms containing in the stresses. Then,

Therefore, from Tables,

From traction BCs, . From equilibrium,

After algebra,

Special Case : , [edit | edit source]

The displacements are

where

and