Derive Euler–Bernoulli equation from Navier-Cauchy equations

jef445

Hello

Is it possible to derive the Euler–Bernoulli equation:
$$\frac{d^2}{dx^2} \left(EI \frac{d^2w}{dx^2} \right) = q$$
from Navier-Cauchy equations:
$$\left( \lambda + \mu \right)\nabla\left(\nabla \cdot \textbf{u} \right) + \mu \nabla^2\textbf{u} + \textbf{F} = 0$$

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.

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Greg Bernhardt

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