Is it possible to derive the Euler–Bernoulli equation:

[tex]\frac{d^2}{dx^2} \left(EI \frac{d^2w}{dx^2} \right) = q [/tex]

from Navier-Cauchy equations:

[tex]\left( \lambda + \mu \right)\nabla\left(\nabla \cdot \textbf{u} \right) + \mu \nabla^2\textbf{u} + \textbf{F} = 0[/tex]

I don't really know where to start because the Navier-Cauchy equations are 3 equations but the Euler–Bernoulli equation is just 1 equation.