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Input 4th order biharmonic PDE of thin plate flexure into COMSOL
Posted Dec 2, 2011, 4:44 p.m. EST Materials, Modeling Tools & Definitions, Parameters, Variables, & Functions, Studies & Solvers, Structural Mechanics Version 4.2 0 Replies
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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
Attachments:
Hello Steve Shi
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