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Engineering | Finite Element Analysis | Stress

Value Design

Consulting

Buckling is a critical state of stress and deformation, at which a slight disturbance causes a gross additional deformation, or perhaps a total structural failure of the part. Structural behaviour of the part near or beyond buckling is not evident from the normal arguments of static's. Buckling failures do not depend on the strength of the material, but are a function of the component dimensions & modulus of elasticity. Therefore, materials with a high strength will buckle just as quickly as low strength ones.

If a structure has one or more dimensions that are small relative to the others (slender or thin-walled), and is subject to compressive loads, then a buckling analysis may be necessary. From an FE analysis point of view, a buckling analysis is used to find the lowest multiplication factor for the load that will make a structure buckle. The result of such an analysis is a number of buckling load factors (BLF). The first BLF (the lowest factor) is always the one of interest. If it is less than unity, then buckling will occur due to the load being applied to the structure. The analysis is also used to find the shape of the buckled structure and a fully worked example is included in our Finite Element Course.

Evaluating Linear Instabilities

From a formal point of view, buckling is an eigenvalue problem that is a function of the material & geometric stiffness matrices. Consequently, there will be a number of buckling modes and corresponding mode shapes. As with a frequency analysis, eigenvalue extraction may be carried out using a number of available methods, the best choice depends on the form of the equations being solved. The main methods are the power, subspace, LR, QR, Givens, Householder & Lanczos methods. An important note is that the eigenvalue method does not take into account of any initial imperfections in the structure and so the results rarely correspond with practical tests. Eigenvalue solutions usually over estimate the buckling load and give no information about the post-buckling state of the structure. Sudden buckling simply does not occur in the real world.

So how should we know if a linear buckling analysis is sufficient ?? Carry out both a linear static analysis and a linear (eigenvalue) buckling analysis. If the max stress is significantly less than yield, and the buckling load factor is greater than 1.0, then buckling will probably not occur. If however the BLF is less than 1.0, then the buckling analysis will be linear provided that the max stress is far below yield. In all other cases, a non-linear buckling analysis should be carried out. If the component is critical to the safe operation of a system, full displacement analyses should be carried out.