0
$\begingroup$

I am currently doing some research for my university thesis and I am dealing with plates. Right now I am trying to figure out the potential (strain) energy of a plate under bending.

So basically I found a paper which explains exactly this but the following part is confusing me:

enter image description here

My question is:

Usually the bending strain can be expressed as $\Delta U = \dfrac{1}{2} M \cdot \Delta \Theta$. But from geometry, $\Delta \Theta$ should be: $\dfrac{\Delta x}{R}$. Why does the paper use $\Delta x \cdot R$ instead?

I am very happy for a any help or explanation.

$\endgroup$

1 Answer 1

1
$\begingroup$

The paper has an error. The second derivative of the displacement function is the inverse of the radius curvature, not the curvature itself: $$ \frac{1}{R} = \frac{\partial^2 w}{\partial x^2}. $$ So the final equation is still correct.

$\endgroup$
1
  • $\begingroup$ Ohh yeah that makes sense. I didnt notice that! Thank you very much :) $\endgroup$ Commented May 27, 2020 at 6:11

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.