Etabs Numerical Problems Encountered During Equation Solution

[Frederic Laureano]

GenerallyAbaqus issues such warnings when the system matrix is not positive definite. Mathematically, the appearance of a Abaqus negative eigenvalue indicates the lack of positive definiteness in the system matrix.

Structural instability: Negative eigenvalues can also indicate structural instability or buckling. Buckling occurs when a structure becomes unstable under compressive loads, causing it to suddenly deform or collapse. In such cases, negative eigenvalues can be an indication that the structure is in an unstable state.

The use of anisotropic elasticity with shear moduli that are unrealistically very much lower than the direct moduli. In this case, ill-conditioning may occur, triggering negative eigenvalues during shearing deformation.

The use of a pretension node that is not controlled by using the *BOUNDARY option and lack of kinematic constraint of the components of the structure. In this case, the structure could fall apart due to the presence of rigid body modes. The warning messages that result may include one related to negative eigenvalues.

8. Inadequate boundary conditions: Incomplete or incorrect constraint definitions can cause negative eigenvalues. Ensure that you appropriately constrain the degrees of freedom that should be fixed, while leaving the necessary degrees of freedom free to deform.

9. Mesh quality issues: Poor mesh quality, such as distorted elements, element aspect ratio problems, or inadequate element density, can lead to inaccurate results and negative eigenvalues. Ensure that your mesh is well-designed and captures the structural behavior effectively.

10. Modeling geometric nonlinearity as linear: If your structure exhibits significant geometric nonlinearity (large deformations or rotations), modeling it as linear can lead to unrealistic results, including negative eigenvalues. In such cases, consider using a nonlinear analysis approach to accurately capture the behavior of the structure.

11. Neglecting contact or interface behavior: If your structure involves contact or interface interactions, neglecting or improperly modeling these behaviors can lead to negative eigenvalues. Ensure that you appropriately define and model contact conditions between different parts or surfaces.

Developing a consistent practice of reviewing the message file for negative eigenvalues holds significant importance. In cases where negative eigenvalue warnings surface during converged iterations, it becomes crucial to scrutinize the solution thoroughly to ensure its accuracy.

To rectify negative eigenvalues, it is advisable to reassess the material models employed and verify the realism of the boundary conditions and loading conditions. When analyzing the outcomes of a model exhibiting negative eigenvalues, it is essential to focus on identifying regions that might be susceptible to buckling or excessive strain. Additionally, reevaluating the interplay between the loading and boundary conditions in those specific areas is recommended.

If the negative eigenvalue issue persists after trying these solutions, it may be helpful to consult Abaqus documentation, seek assistance from experienced users, or contact Dassault Systmes SIMULIA support for further guidance.

Although this article will help you to start your Abaqus project, FEM simulation is a little complicated, and based on our feedback from hundreds of students and researchers during the last three years, the Abaqus course has saved a lot of time when simulating in Abaqus, and prepared codes in this package without any bugs or errors can speed up your simulation.

During the solution process, Abaqus checks to ensure the system is in equilibrium and stable. The basic reason for this warning message is stability. Mathematically, the appearance of a negative eigenvalue means that the system matrix is not positive definite. Therefore, if Abaqus gives this warning, it means the stiffness matrix has become unstable.

In practice, the messages can be issued for a variety of reasons, some associated with the physics of the model and others associated with numerical issues. Physically, negative eigenvalue messages are often associated with a loss of stiffness or solution uniqueness in the form of either material instability or the application of loading beyond a bifurcation point (possibly caused by a modeling error).

For analyses that do converge, if the warnings appear in converged iterations, however, the solution must be checked to make sure it is physically realistic and acceptable. It may be the case that a solution satisfying the tolerance for convergence has been found for the model while it is in a non-equilibrium state.

There are some recommendations to remove the instability warning. The user should re-evaluate material models. Then, re-check to ensure realistic all boundary conditions and loading conditions. After that, find the areas that might be buckling or overly strained.

Citations:

[1] -eigenvalues-messages/

[2] -to-solve-negative-eigenvalue-in-Abaqus-CAE

[3] -abaqus-standard-negative-eigenvalue-messages/

[4] -eigenvalue-is-negative-in-abaqus

[5] -element-modeling-aa/negative-eigenvalues-problem-in-abaqus/

Negative eigenvalue! what a irritating error. Users may encounter this one more than once. So, they ask questions about it. We answered a few of them and based on the question we recommended the best services we have. You can see some of them below.

I am doing a strain-controlled low cycle fatigue simulation on Abaqus, where displacement is applied as the load with triangular waveform amplitude, and in return, the strain should be controlled throughout the simulation.

For our shell, I have performed some analysis for different element sizes. On the drawing above you can see the outcome for few selected meshes. Please notice, that for the biggest elements actual eigenvalue shape is different than in the case of models with more refined mesh.

Note that the obtained curve is almost linear which is usually the case in most models. From the equation provided by Excel, it is easy to derive the correct answer when x = 0. At this stage, since we know the correct answer, we can calculate how big errors were made in the estimation of results for each finite element size. Below is a chart showing dependence between error and computing time, and between error and finite element size:

I have over 10 years of practical FEA experience (I'm running my own Engineering Consultancy), and I've been an academic teacher for a decade. Here, I gladly share my engineering knowledge through courses, and on the blog!

I've never tested TRI elements in slabs - just run a check between TRI and QUAD for the mesh size and dimensions you usually do, and check for yourself. I don't have a ready answer here (I almost never use TRI as a rule...), but I would guess that it's either the same or TRI is too stiff... still hard to say by how much - just test it yourself :)

Hi, I hope you are doing well. Is there a way by which we can see the maximum mesh size we can create? Usually, mesh fails and I have to minimize the mesh size in multiple attempts to check what is the maximum I can do.

Yea... I'm afraid that this is how you "normally do it". You do the MESH, and then smaller mesh, and even smaller mesh and check for convergence. I don't know any better rules than those that work universally.

Of course, after some time you get a "feeling" of what a good mesh looks like, and then you do mesh convergence less often, but this takes experience of course, you gain with doing mesh convergence in the first place!

I have been working on femoral bone designing and dynamic loading. I'm stuck in the meshing part because of the structured meshing requirement. Can You please assist me with the structured meshing on a kind of basketball shape object? most importantly, inner strutured mesh?

Hi Lukasz, I have an issue regarding mesh in ansys here. Basically I have a plate with a notch in the middle (surely the highest stress area). I have around 8 subareas. When I do mapped meshing of all subareas, the mesh size that give the highest value is 3.5mm. ( I have 3000 elements as my maximum limits). So based on your article, you said that i should refine the maximum stress area to get better result right? if so then how should i define the mesh sizes of the other area? is it as big as possible? thank you

Well having a 3000 element limit definitely limits (!) what you can do in mesh convergence. Normally I would just increase the number of elements in the area of interest (i.e. where the highest stresses are, or when I want to know the answer). But with your limitation, reducing the number of elements on the "other regions" of your model (to allow more elements in the area of interest while steel meeting the 3000 element limit) may be necessary.

Just be careful, since the "switch" from super coarse to super fine mesh in itself is an issue, and if you produce elements with low quality this may "shift artificially" the place where the maximal stresses are (i.e. instead of near the notch, you will get a stupid high-stress ins an element on the transition area from coarse mesh to the small one, because that element quality is super low).

1. I will assume here, that by "can't get the mesh to converge" you mean that you did several analyses with various meshes and the answer does not converge (i.e. stress is getting higher and higher without any signs of "slowing down". If that is the case - just to be sure, make a model with much smaller mesh and run it overnight (unless you are already at the 4-5h of computing level). Sometimes things get a bit more to converge, and initially, it seems as if it will never stop, but it eventually does! This is a good example, wherein the first few tries answer didn't even look as if it will converge: -convergence/

2. If you do the above and it still doesn't work (or maybe even before you do it) check if this is not a stress/boundary singularity. In such cases it will never converge, as the problem is with the model, not the mesh: -singularity-an-honest-discussion/

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