Plate Buckling Deflection Function for Rayleigh Ritz Method

[SamNaval]

G'Day Everybody, I am computing buckling of a rectangular(edges: a*b) specially orthotropic composite plate. 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:
A: is to be determined at afterwards
m: Natural for Buckling

or should be the following, du to the modeshape in y-direction(w(y)=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.
Any help would be greatly appreciated.

Thanks in advance.
Sam

 

[Illmatic1]

myThe second shape function is correct. You need to account for the boundary conditions in both x and y directions. The first shape function only accounts for the boundary conditions in the x direction. The second shape function takes into account the boundary conditions in both x and y directions.