Flamant Solution

The Flamant solution provides expressions for the stresses and displacements in a linear elastic wedge loaded by point forces at its sharp end. This solution was developed by A. Flamant in 1892 by modifying the three-dimensional solution of Boussinesq.

The stresses predicted by the Flamant solution are (in polar coordinates)

$\begin{align} \sigma_{rr} & = \frac{2C_1\cos\theta}{r} + \frac{2C_3\sin\theta}{r} \\ \sigma_{r\theta} & = 0 \\ \sigma_{\theta\theta} & = 0 \end{align}$

where are constants that are determined from the boundary conditions and the geometry of the wedge (i.e., the angles ) and satisfy

$\begin{align} F_1 & + 2\int_{\alpha}^{\beta} (C_1\cos\theta + C_3\sin\theta)~\cos\theta~ d\theta = 0 \\ F_2 & + 2\int_{\alpha}^{\beta} (C_1\cos\theta + C_3\sin\theta)~\sin\theta~ d\theta = 0 \end{align}$

where are the applied forces.

The wedge problem is self-similar and has no inherent length scale. Also, all quantities can be expressed in the separated-variable form . The stresses vary as .

Read more about Flamant Solution: Forces Acting On A Half-plane, Derivation of Flamant Solution

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