# Inertia Relief and Buckling SOL105 in Nastran

Has anyone ever tried running buckling simulations in Nastran where inertia relief is invoked? I am just using a simple plate and I am getting "funny" modes (unrealistically low eigenvalues which correspond to in-plane deformations - no buckling). I went through the documents and they do not seem to suggest that it should be avoided or anything of the sort. In fact the following is stated under PARAM,INREL,-2 that "This method leads to indeterminate matrices which are not supported by buckling. If attempted the solution will fail."

But i am using PARAM,INREL,-1 and the model runs through. The *.f06 files looks ok too (OLOAD, epsilon, strain energy and so on..)

Can anybody shed any light or suggestions on how to proceed with this?

Thanks!

PS:

I have a plate modeled with CQUAD4s referencing a PCOMP and i am trying to find its eigenvalues. The loads on the plate are a combination of all in plane loads (Nx, Ny, Nxy). Due to the existance of in-plane shear, the setting up of the boundary conditions is not a trivial task and that is the reason inertia relief was considered. Also, with inertia relief in the model and along with the "funny" modes, i also get realistic ones, the eigenvalues of which match those i get with ESAComp and ESDU 81047. So to summarise:

• If i could get the eigenvalues ESAComp and ESDU 81047 gives without inertia relief i would gladly do it
• The fact that the first realistic eigenvalue i get with inertia relief in the model matches those from above suggests (imo) that it is somehow doable.
• This is an old post I wanted to ask how the analysis concluded. I'm running an bucking analysis with inertia relief but facing some problems with support in PARAM,INREL,-1. May 20 '19 at 8:06

Here is what inertia relief does: Let's say that we have a flexible free body (e.g. satellite in space). We apply some forces to it. The forces are going to do two things. First, they are going to cause a rigid body acceleration according to F=ma. i.e. the center of mass of the object is going to accelerate based on the sum of the forces. But, because we have a flexible body, these forces are also going to cause local deformations and stresses. We don't care about the rigid body acceleration of the center of mass. We only care about the local stress.

Now, we could solve a transient dynamic solution (i.e. sol 109 in NASTRAN), to get both the rigid body acceleration and the local deformation, and then afterward subtract off the rigid body acceleration to get just the local deformation that we care about. The problem is that would be computationally expensive. We are spending a lot of CPU resources to compute something that we are just going to through away anyway.

So what we want to do is to solve just a static solution (i.e. sol 101 in NASTRAN). But there is a problem. Because the structure is unconstrained (free), the stiffness matrix is singular. We cannot invert it.

We could add a fake support to the structure somewhere, just for the sake of constraining it to get an invertible stiffness matrix. But the reaction forces at this constraint will cause local deformations and stresses that are not real and will mess up the answer.

So we have a problem, we don't want to solve a transient dynamic problem because it would take too long, but a static solution doesn't work.

So here is what inertia relief does. First, we add a constraint. i.e. we make the structure fixed at the boundary instead of free. Then, we add a distributed body force to the entire structure that exactly balances out the rigid body acceleration. That means that the reaction force at our new dummy constraint is zero. So, the system is now constrained, so the stiffness matrix is non-singular, so now we can invert it. But, the reaction force at the dummy support is zero, so it doesn't have any effect on the local deformations and stresses.

This might help to illustrate: https://www.simutechgroup.com/tips-and-tricks/fea-articles/251-fea-tips-tricks-ansys-static-analysis-inertia-relief

So, having said all that, can you use inertia relief for buckling? If you are trying to model buckling of a free body that is accelerating, then I don't see why not. For example, if you have a satellite in space, and this satellite has some flexible structure with thruster attached to it, and you want to know what thrust it will take to buckle your structure, then inertia relief makes sense. The added fake constraints are only going to constrain out rigid body motion which should not affect the buckling results.

But if you have a constrained structure that is not accelerating, then I don't see how it makes sense. I guess what you are doing is deleting the boundary conditions entirely (because they are hard to model), so fictitiously unconstraining the model, and then using inertia relief to put them back in... Inertia relief is going to try to generate a body force over your entire structure in order to enforce a zero reaction at the fictitiously created constraints. But your structure really does have real constraints, and so there should be a non-zero reaction at the real constraints. So the applied body force will be wrong.

Not quite sure how NASTRAN handles that body force. If it uses it with all of the other loads in generating the differential stiffness matrix, then you definitely get the wrong answer. But if it ignores it when generating the differential stiffness matrix, then you might get the right answer, if the supports that got added back in were equivalent to the ones that got deleted.

So that was a really long winded answer... bottom line, although it might work, unless there is something special about how NASTRAN does this that I'm not aware of, I would not recommend it. Spend some extra time to get the boundaries modeled correctly.

We apply a few forces for it. The forces are likely to do two different things. To begin with, they will create a rigid body acceleration in accordance with F=ma. I.e. the middle of mass of this item will accelerate dependent on the amount of their forces. However, since we've got a flexible figure, these forces will also be likely to trigger localized deformations and stresses. We do not care about the stiff body acceleration of the middle of mass. We just care about the neighborhood strain.

We can address a transient energetic solution (i.e. sol 109 at NASTRAN), for both the stiff body acceleration as well as also the local deformation, then afterward subtract the stiff body acceleration to receive only the neighborhood deformation we care for. We're spending lots of CPU resources to calculate something which we're simply going to through out anyhow.

So what we would like to do would be to resolve only a static answer (i.e. sol 101 at NASTRAN). However, there's an issue. We can't invert it.

We can add a bogus support to the construction someplace, just for the interest of constraining it to find an invertible stiffness matrix. However, the reaction forces in this restriction will lead to localized deformations and stresses which aren't real and will wreck the response.

So we've got a issue, we do not wish to address a transient dynamic difficulty since it might take a long time, but a static remedy does not work.

So this is what inertia relief will. We add a restriction. I.e. we create the construction fixed at the border rather than free. Then we put in a distributed body force to the whole arrangement that just balances out the stiff body acceleration. That usually means that the response force at our brand new dummy restriction is zero. However, the response force in the service is zero, therefore it will not have some influence on the regional deformations and stresses.

If you're attempting to model buckling of a free figure that's quickening, then I do not understand why not. The additional fake constraints are just likely to constrain out rigid body movement that should not impact the buckling results.

But in case you've got a constrained structure that's not accelerating, then I really don't see how it is logical. I guess what you're doing is deleting the border conditions entirely (since they're tough to model), therefore fictitiously unconstraining the model, then utilizing inertia relief to place them back into... Inertia relief will attempt and create a body force on your complete structure so as to apply a zero response in the fictitiously generated limitations. However, your arrangement does have actual limitations, so there should be a non-zero response in the actual constraints. So the body force will probably be incorrect.

Not quite certain how NASTRAN manages that body pressure. If it uses it together with all the additional loads in creating the differential stiffness matrix, and then you get the incorrect answer.

So that has been a very long winded answer... bottom line, though it may work, unless there's something particular about how NASTRAN does so I am unaware of, I wouldn't suggest it. Spend a little excess time to acquire the bounds modeled properly.

From the theory, I can't see how trying to use inertia relief makes any sense at all, except for (linear) stress analysis of a free body which is accelerating.

Since you haven't given any information about what you are actually trying to model, it's hard to give any advice on "how to proceed!"

• Thanks for the reply! All typical inertia relief examples involve accelerations, that is true, but i do not see why it could not be "extended" for use elsewhere. I edited the question. I hope it is more clear now.
– Ma0
Nov 24 '16 at 9:32
• @alephzero, why can only linear stress analysis be done using the inertia relief method? I mean if the body is flexible and a force is applied on it, The body would accelerate but it could also turn (meaning that the stiffness along the principal co-ordinates has to change in the stiffness matrix) and also it could elongate (meaning that the stiffness of the elements itself is changing hence the stiffness matrix has to change). These two features mean that the geometric non-linearity should be considered in the analysis. Moreover, there might also exist contact non-linearity. Sep 1 at 17:01