Plate Buckling Deflection Function for Rayleigh Ritz Method

[SamNaval]

G'Day Everybody,
I am computing buckling of rectangular(a*b) specially orthotropic composite. The boundary conditions are clamped-clamped at the opposing loaded edges and the other two edges are free (also known as CFCF). After having the boundary conditions and the governing differential equation I to need to assume the deflection of the buckled shape in order to apply Rayleigh Ritz Method. At this point I would like to know if anybody can tell me that the following shape function is correct or not:

w(x,y)=A*(1-cos(2*pi*m*x/a)

,where:
w(x,y): the deflection function in x and y direction
A: is to be determined at afterwards
m: Natural for Buckling

or should be the following, du to the modeshape in y-direction(w=A):

w(x,y)=A*(1-cos(2*pi*m*x/a)*A

I assumed it to be correct but the following calculations where simplified so much that I am not sure anymore.

Further I would like to know how to calculate the amplitude A?

Any help would be greatly appreciated.

Thanks
Sam

 

[rb1957]

1) don't multi-post
2) your second form is the same as the first, except you've got A squared. this'll mess severely with the dimensions of the result ... w() is deflection, units = length; A looks like max deflection, units = length. A^2 has units of length^2.
3) the plate absorbs energy to do the work of deflection. The external work done by the deflection (and the applied load) = the internal strain energy (caused by the deflection).
4) you should be able to find worked examples to guide you.

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