I am running some simulations in Abaqus to extract the stiffness matrix of a FE model with geometric nonlinearity.
I want to provide to Abaqus a set of nodal displacements (all the dofs in the model), and read out the tangent stiffness matrix.
To impose the displacements and request the stiffness matrix I add this part in the input file:
"
*Step, name=staticAnalysis1, nlgeom=YES
*Static
1., 1., 1e-05, 1.
**
*Boundary,
Assembly.Part-1-1.129, 4, 4, 1.123750e-12
Assembly.Part-1-1.130, 4, 4, 2.193221e-12
Assembly.Part-1-1.131, 4, 4, 3.323135e-12
Assembly.Part-1-1.132, 4, 4, 4.416019e-12 ....
*End Step
** SECOND STEP TO REQUEST TANGENT STIFFNESS
*Step, name = "matrix generate1"
*Matrix generate, stiffness
*Matrix output, stiffness, format=coordinate
*End Step
"
The analysis runs perfectly returning with the tangent stiffness matrix in a .mtx file.
However, while the off diagonal terms seems to be correct, the terms on the diagonal of are all 1E36.
e.g. K(i,i) = 1E36
Does somebody know how to solve this issue?
Thanks in advance,
Alexander
ABAQUS and many other finite element software impose essential boundary conditions (Dirichlet type) via the penalty method. In computational terms, this method basically adds a high stiffness value to the diagonal terms of the stiffness matrix associated with the degrees of freedom that you want to impose as a kinematic constraint. If you try to impose displacements on all the degrees of freedom in your model, Abaqus will automatically place very high stiffness values on all the diagonal terms of your stiffness matrix.
I temporarily fixed the problem by including an additional fictitious 'dynamic' step of time span dt = 1e-6s between the static step and the matrix generate step.
In more details:
1) I first constrain all the displacements of all the nodes in the model to a given displacement field in the static analysis step with keyword *BOUNDARY,
2) I introduce a fictitious dynamic analysis step, in which I remove all the constraints except for the BCs of the original model. I integrate for 1e-6. Obviously the structure won't move in such a short time.
3) I then eventually write the step 'Matrix generate' to retrieve the Tangent stiffness matrix.
This methods seems to properly work for S4R and S3R shell elements. However, it lacks of efficiency and most of time in this process is lost however in the dynamic step (from the list of the computation file in the msg file).
I would like to find a better way. Does somebody has suggestions in this regards?
NOTE: Abaqus issues a warning when I impose finite rotations to the model (constraining all the nodes and dofs). I remind you that I am using shell elements.
The warning is : 'finite rotation boundary condition specified in multistep three-dimensional analysis. type=velocity should be used '.
I am trying to figure out the meaning of it. Does somebody know?
Could it be related to the singularity of the diagonal elements of the tangent stiffness matrix?
Thanks again.
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