Nomenclature and definition of the elastic axis

[LeonardoAVONI]

Dear all,

I hope this message finds you well.

I'm working on exporting SHARPy data from the SuperFLEXOP aircraft case (link to case) for use in ASWING (another flight mechanics oftware), and I’ve run into a few questions regarding the frame of reference for the stiffness_db and mass_db matrices in SHARPy.

I'm currently wrapping up work using the original SHARPy data for the SuperFLEXOP aircraft (https://github.com/ImperialCollegeLondon/sharpy_cases/tree/main/MultibodyFLEXOP), and I had a few questions regarding the frame of reference used for the stiffness_db and mass_db matrices in SHARPy. The stiffness_db matrix (at the wing root node) is shown below

From my reading of the documentation (https://ic-sharpy.readthedocs.io/en/main/content/casefiles.html#fem-file), it appears that both matrices are defined with respect to the elastic axis — that is, the spanwise axis shown in elastic_axis.png, along which the nodes and frame B are located. This axis seems to be specified by the coordinates[:, :] array (please, correct me if I am wrong)

However, I’m having some doubts I’d like to clarify:

Doubts concerning the elastic axis definition in SHARPy

If stiffness_db is indeed defined about the elastic axis, why are the submatrices stiffness_db[:3, 3:] and stiffness_db[3:, :3] non-zero? (orange submatrices)
These entries suggest a coupling between forces and rotations, which, theoretically, shouldn’t occur when forces are applied directly on the elastic axis — they should cause only bending, not rotation. This makes me wonder: is the "elastic axis" shown in elastic_axis.png (and used for the definition of stiffness_db and mass_db) truly the elastic axis, or is it simply a reference axis?

For the mass_db matrix, I understand that non-zero values in mass_db[:3, 3:] and mass_db[3:, :3] are acceptable, since the mass centroid may not lie exactly on the elastic axis.

Doubts concerning the SuperFLEXOP specifically:

Based on the setup script, the elastic axis is positioned at 0.57c from the leading edge at the wing root. This positioning is obtained from the source .csv data, that specifies an offset of -0.14c, to which an offset of +0.71c is applied. I wonder why this offset has a 0.71c value, and/or if this value has something to do with the real elastic axis

Additional doubts

Is there information available about the center of mass? SHARPy seems to apply the mass matrix at the axis shown in elastic_axis.png, but I may be misunderstanding this.

Also, concerning the elastic_axis variable in the case.aero.h5 file. Am I correct in understanding that this variable defines the chordwise position (as a percentage from the leading edge) of the elastic axis shown in elastic_axis.png? I’ve tried modifying this value, and it seems the "elastic axis" remains fixed while the wing shifts forward or aft. This seems to suggest that the elastic axis is actually defined by the coordinates[:, :] array — is that the correct interpretation?

Conclusion

I am sorry for this long message, I hope it does not take away too much of your time.

[ben-l-p]

Hi Leonardo,

The coordinates array defines the points which describe the beam, and the aerodynamic paneling is created relative to this beam. I would expect that for this model that the nodes do not perfectly coincide with the elastic axis, and so the cross coupling terms are added to correct for this. Unfortunately I did not make the original model for this aircraft, however I would assume your conjecture on the choice of elastic axis position to be correct.

The centre of mass for the full aircraft would need to be computed separately if you require it, as I don't believe it is explicitly stored anywhere during the solution process, with the mass matrix in frame A used for solution. I have not come across a SHARPy utility to obtain the centre of mass from this, but there may be one.

In the aero case file, the elastic axis position denotes where the aero panels should be placed relative to the beam (hence its inclusion as an aerodynamic parameter). This is the convenient definition here as SHARPy creates the beam first, and then maps the aerodynamic grid to it.

Hope this helps,
Ben

[LeonardoAVONI]

Hi Ben,

Thank you for the quick reply! Yes, this clarifies the issue, thanks a lot!

Gratefully,

Leo

[LeonardoAVONI]

Hello again,

I’ve been able to make some good progress on the study and wanted to share a quick update.

I’m continuing to work on the SuperFLEXOP case study originally developed by Stefanie Düssler, as described in the following papers:

• LQG-based Gust Load Alleviation Systems for Very Flexible Aircraft (2024)
• Modelling for Design and Performance Evaluation of Gust Load Alleviation Systems for Flexible Aircraft (2023)

Now that I’ve successfully replicated the geometry in ASWING, I was wondering whether any control-related data — such as the ABCD matrices used for the LQR/LQG controllers — might be available for this case. I wasn’t able to locate them in the sharpy_cases repository, but I do noticed the description of the Q and R matrices on the original papers.

Any guidance or pointers would be greatly appreciated!

With thanks,
Leo

[ben-l-p]

Hi Leo,

Very happy to hear about good progress :) I had a small dig on Github, and unfortunately I was not able to come across any of the data from this project as I don't believe it was published.

Sorry I can't be of more help!

[LeonardoAVONI]

Hi Ben,

Thank you for your help, understandable; will do with what I have. Thanks again for your quick reply and have a nice weekend =)

Leo