Linear buckling analysis

Rahul_P1

Hello, I have a similar buckling question. In the results contour plot of the 'Mag' of 'Buckling Mode 1', what exactly do the values represent? That is, what are the color contours representing? I presume the force given (e.g. F=6.183E+03) is the eigenvalue for the whole model.

Thanks,

Rahul_P1

All,

The short answer is that the contour you see is the contour of the normalized values of a particular result of the linear buckling analysis called Eigenvector δm

δm is the associated buckling displacement shape for a particular mode.

Eigenvectors δm are the primary result in a buckling analyses, they are normalized with respect to the maximum vector component, (to put it simply the maximum vector value is taken as 1 and the rest of the values are taken equivalently) using which the mode shape is plotted.

This same mode will also have a particular eigenvalue λm this is called the buckling load factor. Use the following table to interpret the BLF for engineering purposes

we know the applied load of course as referred to in the above table,

How do we obtain these two values λm and δm?

The problem of linear buckling in finite element analysis is solved by first applying a reference level of loading, pref, to the structure. A standard linear static analysis is then carried out to obtain stresses which are needed to form the geometric stiffness matrix KF. The buckling loads are then calculated by solving an eigenvalue problem:

|K + λm KF| δm = 0

Where K is the stiffness matrix of the structure and λm  is the multiplier to the reference load. The solution of the eigenvalue problem generally yields n eigenvalues λm , where n is the number of degrees of freedom (in practice, only a subset of eigenvalues is usually calculated). The vector δm is the eigenvector corresponding to the eigenvalue.

Thanks and regards

Rahul Ponginan