Buckling of shells- critical buckling mode 1

[futura22]

I hv just run an input file of eigenvalue buckling analysis from abaqus documentation website using ABAQUS CAE. Basically there will be two critical buckling mode of n, circumferential full wave and m, longitudinal half wave corresponds to the model. My question is how i am gonna determine the value of m corresponds to a certain eigenvalue obtained from the analysis?

thanx

 

[SWComposites]

Plot the displacements for the particular mode of interest and count the number of half waves.

 

[futura22]

thanx for d reply...

what do you mean by counting the number of half waves? could you tell me in more detail about that please...thanx

 

[40818]

Well, you could start with 1, then when you see another you move to 2........

Sorry couldn't resist!

 

[salmon2]

Hehe, the FEA won't give you a theoretical equation with the input as a parameter instead of a number.

So with FEA, you have to run the simulations many times with changing the input parameter - the increment has to be small to capture the hot spots.

 

[mtnengr]

The circumferential wave number of Fourier no., n, is different for each shell configuration and boundary condition. That is why several computer programs have been written to assist the analyst. For simply supported shells, the lowest harmonic pattern usually follows a sin function.

The general solution for cylinders the modal pattern is expressed as e-lamdax * (Sin n theta * Cos m pi x/2L + Cos n theta * Sin m pi x/2L). Thus a minimum value of m=1 corresponds to a minimum half wave. But, there are a number of factors that can alter these modal patterns. Foresberg in a 1964(?) AIAAJ paper provides a number of cases for cylinders giving approximate eigenvalues. In a more general presentation, Liessa, presents a number of formulae for a variety of shells of revolution in NASA SP-288 for the vibration of shells.

Buckling eigenvalues are close to the vibration eigenvalue set, but are different. There is an old adage that cylinders prefer diamonds and spheres prefer hexagons. It is best to start with an assumed Fourier wave number and search for the minimum using a range of at least a decade above or below. For each eigensolution, there will be an waveform that corresponds to the minumum. It may not necessarily be m=1.

Bifurcation also requires an understanding of modal coupling with the applied force. Energy can be transferred between adjacent modes that will produce a minimum buckling load differing from either applied and principle responding modes.

Suggest that you examine the literature very carefully before attempting to use a general FEM package without an experience factor assisting your results. The publications and computer programs reported at

HTTP://www.volcano.net/~d.citerley

may be of some benefit.