Elasticity/Flamant solution

The Flamant Solution

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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 : α = -π, β = 0

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The displacements are

 

where

 

and