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Input 4th order biharmonic PDE of thin plate flexure into COMSOL

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Dear All,

I am new to COMSOL. I am now using COMSOL to model the thin plate flexure. The problem is that I do not know how to input the 4th order biharmonic PDE of thin plate flexure into COMSOL.

The 1D equation is:

∇^4 w+ (ρ/D)*w=q/D or

(∂^4 w)/(∂x^4 )+(ρ/D)*w=q in 1D or

(∂^4 w)/(∂x^4 )+(∂^4 w)/(∂x^2 ∂y^2 )+(∂^4 w)/(∂y^4 )+(ρ/D)*w=q in 3D.

the boundary conditions are w = 0 at all vertical boundaries for the square plate.

I got some information from the forum that I need to convert the 4th order PDE to systems of 2nd order PDE, i.e.,

∇^2 w = u;

∇^2 u =q - (ρ/D)*w;

So then I added 2 PDEs with coefficient form under the same model, BUT I do not know how to couple these two equations and what need to be done for the boundary settings and model coupling?

I attach here the COMSOL model I did, which has many problems.

If any of you can give me some advice on how to proceed this model, I would greatly appreciate your help.


Thank you very much,
Steve


0 Replies Last Post Dec 2, 2011, 4:44 p.m. EST
COMSOL Moderator

Hello Steve Shi

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