Derive Euler–Bernoulli equation from Navier-Cauchy equations

Hello

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.
 
Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Hot Threads

Top