CODEWITHSUNDEEP
finite-element-analysisnastran
Jeroen
Jeroen

Reputation: 129

For a buckling analysis, must all forces be multiplied by the resulting eigenvalue, or only the compressive load?

I am trying to do a linear buckling analysis (sol 105) with Nastran on a cylindrical shell structure. My understanding is that the compressive load that I apply to the structure must be multiplied by the resulting eigenvalue to get the buckling load. This gives me results that I expect.

However, now I apply a single perturbation load (SPL), a small transverse force acting midway along the cylinder on a single grid point. My understanding is that the magnitude of the SPL stays the way it is, (Unlike the compressive load where I multiply it with the eigenvalue to obtain buckling load.) The results I obtain are not what I expect, as the buckling load should not reduce so much as the SPL increases, according to the theory on this topic.

I am wondering if anyone knows what I am doing wrong. I feel like my mistake is probably very easy, but I haven't been able to solve it yet. Here is some more information on my implementation:

boundary conditions:

Upvotes: 0

Views: 971

Answers (2)

kcw78
kcw78

Reputation: 8091

There is a way to scale some loads and hold others constant. Create 2 Static Subcases with 2 (different) sets of loads:

  1. Constant loads (that are not scaled, like a preload or internal pressure)
  2. Those that will be scaled by the eigenvalue
  3. Order does not matter

Use the Nastran STATSUB entry to define. It looks like this:

SUBCASE 100
   LOAD = 1  $ Static pre-load
SUBCASE 200
   LOAD = 2  $ Varying buckling load
$ -------------
SUBCASE 1000
  STATSUB(PRELOAD)  = 100
  STATSUB(BUCKLING) = 200
  METHOD =   10

The eigensolution is modified to include influence of static and varying loads.

Upvotes: 2

bp91
bp91

Reputation: 41

I'm not a Nastran user but I've done a lot of buckling analysis with Cast3M software. The linear buckling analysis does not need perturbation loading, but only your main axial loading (F^0). To recap,

  1. Solve the linear problem for axial loading :
    • solve for u^0 : [K] * u^0 = F^0
    • get the linear stresses from the Hooke law : \sigma^0 = D * B * u^0
  2. Solve the eigenvalue buckling problem :
    • [ K + \lambda Kgeo(\sigma^0)] * X = 0

Then, if you want to perform a non-linear (large displacement) post-buckling analysis, it is recommended to introduce a small perturbation which "excites" the buckling mode.

If you introduce the perturbation loading before the linear buckling analysis, maybe Nastran is adding it to F^0 and it is then logical that the result of buckling changes.

Hope this can help you.

Upvotes: 2

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