Verification of Mass Matrix

[bariserkus]

We have been encountering an issue with the mass and probably with the mass matrix.

We have considered a simple weightless linear cantilever column, where a lumped mass is attached at the top, as a MWE.

We hand-calculate the period of the example and show that it is same as the period obtained from a SAP2000 analysis. However, OpenSees give a different value:
Hand Calculated: 0.46171793 sec
SAP2000: 0.461718 sec
OpenSees: 0.51982 sec

The OpenSees and SAP files are located at https://1drv.ms/f/s!Aqx30_D8oGfG5GJJerOAn4-i8TXi (hope the system allows access)

We are guessing that the stiffness matrix is estimated correctly, but the mass (or the mass matrix) is multiplied with a factor of approximately 1.13 in OpenSees.

We have not checked the stiffness for the cantilever example, but we have checked the stiffness matrix of a single bay/single story frame example in OpenSees and found that the stiffness matrix is identical to that of obtained from SAP2000. Again, for the frame example, we can only get the same periods if the mass values are scaled down with the factor of approximately 1.13. We can post the frame example as well if needed.

So, did anybody verified the mass matrix in OpenSees, at least for a linear problem?

[bariserkus]

We have identified the error and verified it with the frame example (thanks to Ufuk Yazgan). The error was the assignment of translational mass value to the rotational degree of freedom by mistake. If the model is a 2D model where 3 DOFs are defined a given point, then the a lumped mass should include two translational mass and one rotational mass.

We have posted the frame example to the same link: https://1drv.ms/f/s!Aqx30_D8oGfG5GJJerOAn4-i8TXi
Interested readers may have a look the files. We were able to get almost same results with SAP and OpenSees for a zero-damping time-history analysis. We have verified the stiffness matrices as well.

It is unfortunate that we cannot extract the mass matrix easily, while stiffness matrix can be extracted using PrintA command.

[selimgunay]

You can obtain the mass matrix with PrintA command if you use a central difference integrator and zero damping.