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Buckling Analysis

Buckling

 

Buckling is a sudden failure mode of a structure subjected to a certain load.

For example, a column subjected to high compressive stress might exhibit buckling.

 

The figure below shows the buckling of a plastic bottle pressured evenly from surrounding.

The pressure is even but the deformed shape is asymmetrical.

Equation of Linear Buckling Analysis

At buckling, the stiffness matrix becomes singular and the determinant is zero.

 

Linear stiffness matrix K and nonlinear stiffness matrix KG are given.

The equation is solved to acquire eigenvalues and eigenvectors.

 

λ is the buckling load factor calculated from eigenvalues. The buckling load is the product of the load set on the model and this factor.

Eigenvectors are related to the buckling-mode shape. They can be confirmed by selecting "Displacement [relative value]" as Field.

 

The default number of bucking modes is 1. To change it, go to [High-Level Setting] > activate [Eigenvalue Calculation Setting] dialog box > enter a desired number.

 

Femtet employs linear approach that can solve the buckling load factor and the buckling mode, but cannot solve the behavior before and after the buckling.

 

Important Point

Nonlinear stiffness matrix KG is obtained through large deformation analysis.
This sometimes results in nonconvergence or unlikely solutions.

Reducing the load might solve the problem.

The reduced load will increase the buckling load factor.

For example, if the load is reduced to 1/10, the resulting buckling load factor will be 10 times more.

 

If the buckling load factor is around 1, the calculation is instable and the result is not reliable.

It is recommended to reduce the load in such a case.

 

 

References:

K.J.Bathe "Finite Element Procedures in Engineering Analysis, (1982), Prentice-Hall