Your approach shows a very good solution.

Regards,

Henrik

5. Add a Stationary study for calculating the deformed geometry, deselect the Solid Mechanics interface.

6. Select ‘Variables not solved for’ and choose to take data from Study 1.

7. Add a Stationary study, select ‘Geometric nonlinearity’ and deselect the Deformed Geometry interface

8. Select ‘Variables not solved for’ and choose to take data from Study 2.

9. Select ‘Auxiliary sweep’ and enter an appropriate range for the load parameter.

Regards,

Benedikt

I will outline a procedure below (assuming that a 2D Solid Mechanics interface is used):

1. Run the buckling analysis in the Solid Mechanics with the default displacement degrees of freedom (u,v)

2. Check the maximum displacement of the arbitrarily scaled mode. Lets assume that you think that 1/400 of that value would form a good imperfection.

3. Add a Deformed Geometry interface.

4. Add a Prescribed Mesh Displacement (domain level). Select all domains, and enter ‘u/400′ and ‘v/400′ as the displacements.

5. Add another Solid Mechanics interface. As a default it has degrees of freedom (u2,v2).

6. Use the same boundary conditions as in the linearized buckling study. Enter the load as depending on some parameter ‘para’.

7. Add a Stationary study, and select ‘Geometric nonlinearity’.

8. Deselect the first Solid Mechanics interface in the new study so that only the two new interfaces are solved for.

9. Select ‘Variables not solved for’ and choose to take data from Study 1.

10 Select ‘Auxiliary sweep’ and enter an appropriate range for the load parameter.

Regards,

Henrik

Thanks for the overview of different ways to treat the buckling problem. I have done a linear static analysis followed by a linear buckling analysis. How would I proceed to use the buckling shape as an initial imperfection for a geometrically nonlinear analysis? I can use the buckling solution as initial value, but it has to be scaled, since the buckling shape has an arbitrary magnitude. However, I could not find a way to do this.

Benedikt

]]>Here are the expressions you asked for, ready for Copy-Paste.

Solid 3D:

-(solid2.SX*test(0.5*(uX^2+vX^2+wX^2))+2*solid2.SXY*test(0.5*(uX*uY+vX*vY+wX*wY))+2*solid2.SXZ*test(0.5*(uX*uZ+vX*vZ+wX*wZ))+solid2.SY*test(0.5*(uY^2+vY^2+wY^2))+2*solid2.SYZ*test(0.5*(uY*uZ+vY*vZ+wY*wZ))+solid2.SZ*test(0.5*(uZ^2+vZ^2+wZ^2)))

Solid 2D:

-(solid2.SX*test(0.5*(uX^2+vX^2))+2*solid2.SXY*test(0.5*(uX*uY+vX*vY))+solid2.SY*test(0.5*(uY^2+vY^2)))*solid.d

Henrik

]]>Thanks for a detailed explanation and some nice tricks, the one with combined static and buckling loads is of high interest, I had though of something like that but hadn’t dare try it to now, but I’ll check it next time I need a buckling analysis, as for me it applies to most of my buckling cases. (PS what about typing out in text the corrected formula for 3D, as we cannot “Cut&Paste from the bitmap image

I always complete my buckling modal analysis by non-linear analysis, even if these can take a few hours (or days) when the solver starts to loop around. In fact, often the true non-linear geometry part is only a small fraction of my model volume, (but often half the mesh number) so it could be nice to be able to split the task to lower the non-linear DOFs. Any suggestions how to reduce the model complexity.

Rigid domains is one way, but with complex geometries it still uses many mesh DOFs

What I notice is that if one only rely on single beam buckling analysis, and try to apply that to complex “compliant (flexing) structures”, one fails, as many of the buckling modes are suppressed by the full 3D geometry layout, and in some loaded cases one can get the 3rd or 5th mode only that accepts to buckle, hence a safety factor 2-4 times higher than thought. As well as cases where the catastrophic buckling (when the supporting force tends to zero after the buckling knee) might transform to a constant force solution, which is often sufficient for a structure to survive.

But I can only stress, the importance of testing, as FEM is just a model of reality and models are to be admired, not really to trust, alone …

Sincerely

Ivar