Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I am currently working on a project which is described as the deflection of a circular membrane. What I am trying to model is the deflection of a piece of plastic film (E=200MPa,v=0.5) when placed under pressure. I would like some recomendations on the initial displacement field (w(r)) and the horizontal displacement field (u(r)). Keeping in mind that this membrane is not of a small size, but can vary from 5 cm upto 20 cm in diameter. It has a thinkness of 0.05 mm.

Queit honestly I am not exactly sure what the difference is between theory of using a plate to model this and using a membrane.

I hope to start a discussion this way and receive some input with which I can further my study. Experimental investigation has been completed however the theoretical model is still in progress and I need some help.

I hope to hear more soon! If anything is unclear or I have forgotten something, please let me know.

share|cite|improve this question

If you are talking about small displacements, where $\sin\theta\approx\theta$ is a reasonable approximation for the angle from horizontal, then I suggest looking at the linear model. Start with the one-dimensional case, which is a string suspended between two points, uniform load $p$ force/length, and tension $T$. Then a small piece $\Delta x$ long has vertical force $p\Delta x$ due to the load, and on the left end $T\sin\theta\approx T\tan\theta= T\frac{dw}{dx}$, and same expression with opposite sign on the right end. The vertical force balance is $$ -T\frac{dw}{dx}(x)+T\frac{dw}{dx}(x+\Delta x) = p\Delta x$$ Divide by $\Delta x$ and take the limit to get $$ Tw''=p$$ Once you are ok with this, you can do the membrane version, which requires Green's theorem to work out, but the physical ideas are the same, giving $$\nabla^2 w = p/T$$The difference between membrane and plate is that a membrane does not have any resistance to bending. The linear plate equation involves fourth derivatives.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

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