1.
Introduction
This write up provides an insight into the fundamental difference between geometric non linear FE analysis, linear buckling FE analysis and non linear buckling FE analysis.
2. Linear buckling analysis
3. Geometric non linear analysis
This type of analysis is carried out in a series of load steps (load increments) and the change in stiffness is accounted for (by modifying the element stiffness matrices) following each load increment. Physically, one can imagine the string of a guitar – its stiffness increases when tensioned hence the pitch gets higher.
Precisely speaking, if the displacements of a structure are such that they have an effect on the overall gross behaviour of the structure, geometric non linear analysis becomes inevitable.
Imagine a cantilever beam loaded with a concentrated moment at the free end, what would happen if one increases the magnitude of the moment to a enormously large value? Well, the free end of the cantilever would touch the fixed end making the vertical translation at the free end zero and the rotation at the free end 360 degrees i.e. 2π radians. Such an effect, can never be captured using conventional linear analysis.
4.
Non
linear buckling analysis
This write up provides an insight into the fundamental difference between geometric non linear FE analysis, linear buckling FE analysis and non linear buckling FE analysis.
2. Linear buckling analysis
This
is an eigen value extraction analysis. In practice what you do is; you run a
loaded finite element model which in turn returns a ‘load factor’ for each mode
(i.e., each pattern or deflected shape for failure), showing how much towards
buckling the structure is.
If
the factor is greater than 1, it means the structure is safe (in that mode).
Higher the value, the safer it is. If less than one, it means the structure has
buckled.
The buckling load factor (BLF) is an
indicator of the factor of safety against buckling or the ratio of the buckling loads to the
currently applied loads. Table 1 Interpretation of the Buckling Load Factor
(BLF) illustrates the interpretation of possible BLF values returned by software
simulation. Since buckling often leads to bad or even catastrophic results, you
should utilize a high factor of safety (FOS) for buckling loads. That is, the value
of unity in Table 1 Interpretation of the Buckling Load Factor (BLF) should be replaced
with the FOS value.
3. Geometric non linear analysis
This type of analysis is carried out in a series of load steps (load increments) and the change in stiffness is accounted for (by modifying the element stiffness matrices) following each load increment. Physically, one can imagine the string of a guitar – its stiffness increases when tensioned hence the pitch gets higher.
Precisely speaking, if the displacements of a structure are such that they have an effect on the overall gross behaviour of the structure, geometric non linear analysis becomes inevitable.
Imagine a cantilever beam loaded with a concentrated moment at the free end, what would happen if one increases the magnitude of the moment to a enormously large value? Well, the free end of the cantilever would touch the fixed end making the vertical translation at the free end zero and the rotation at the free end 360 degrees i.e. 2π radians. Such an effect, can never be captured using conventional linear analysis.
4.
Non
linear buckling analysis
This is again, same as the Geometric non-Linear analysis, but the analysis continued not until total load is reached (or the maximum prescribed displacement is reached) but until the structure buckles. This is because elements (like columns, for example) actually lose stiffness when compressed (and likewise gains stiffness if subjected to tension).
As the analysis progresses, at that point when any of (or a couple of) the elements loses stiffness to such an extent that it can no longer support the loads coming on it, the buckling point has been reached, and the analysis ends (actually the FE program aborts – older ones hang!). Then you can see which all failed, and at what load they failed.
In fact a non linear buckling
analysis, becomes useful when you have local non linearity’s like tension only
/ compression only included so that if buckling is due to a non important
member then that mode can be discarded from the stability results.
The above are the simplest and very fundamental definitions.
The above are the simplest and very fundamental definitions.
