3D Beam transformation matrix?
3D Beam transformation matrix?
(OP)
Anyone have an online resource for programming the transformation matrix for a 3D beam (or better yet, frame) element? I can only find one which omits the rotation of the axis along the beam to describe how the major and minor axes are defined.





RE: 3D Beam transformation matrix?
3D Beam
Has open source VBA code.
Look at the rigid_jointed function for code to set up a full 3D stiffness matrix.
The code is based on Fortran code in Programming the Finite Element Method by Smith and Griffiths, which is worth getting if you want to program this yourself.
There are also some on-line resources, but I'll need to look them up.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: 3D Beam transformation matrix?
Matrix Structural Analysis
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: 3D Beam transformation matrix?
RE: 3D Beam transformation matrix?
another day in paradise, or is paradise one day closer ?
RE: 3D Beam transformation matrix?
RE: 3D Beam transformation matrix?
Both links work for me, but I have attached the pdf file from the second link.
The first link is to my blog. Please let me know if that is the one that didn't work.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: 3D Beam transformation matrix?
RE: 3D Beam transformation matrix?
i.e. If I have beam I want to input and I know the orientation of the section in space, then how do I come up with alpha? I can see it has something to do with the angle between some intermediate coordinate system and the principle axes.
RE: 3D Beam transformation matrix?
See:
Defining beam orientation in 3D
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: 3D Beam transformation matrix?
They should have all this information from a section analysis tool in the procedure where this simple 3D frame FEA computation will come into play.
RE: 3D Beam transformation matrix?
That's the easiest way in a structural engineering context, where the rotation is usually zero. In other contexts it may be easier to define one of the planes of the local member axes with a third node, and calculate the rotation from that.
Or have a database of standard shapes with the required properties that users can select from.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: 3D Beam transformation matrix?
I've looked through your source code of 3DFrame and it seems like to me there's a discrepancy in the second and third row of the rotation matrix between that code (R0 array) and Saoma's notes (eq. 4.39) which you linked to. It repeatedly uses something proportional to (x2-x1)^2+(z2-z1)^2 and yours is proportional to (x2-x1)^2+(y2-y1)^2. What is the reason for the difference?
RE: 3D Beam transformation matrix?
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/