Rotating a 6x6 matrix
Rotating a 6x6 matrix
(OP)
Hello,
I have a matrix called compliance matrix (6x6) in 3d-stress space.
It looks like:
x y z 0 0 0
x1 y1 z1 0 0 0
x2 y2 z2 0 0 0
0 0 0 a 0 0
0 0 0 0 b 0
0 0 0 0 0 c
I want to make a rotation. I should turn X axis 45° towards y-axis.
My question is, how can I form my 6x6 rotation matrix? Is there an already implemented code in excel?
I really appreciate your help.
I have a matrix called compliance matrix (6x6) in 3d-stress space.
It looks like:
x y z 0 0 0
x1 y1 z1 0 0 0
x2 y2 z2 0 0 0
0 0 0 a 0 0
0 0 0 0 b 0
0 0 0 0 0 c
I want to make a rotation. I should turn X axis 45° towards y-axis.
My question is, how can I form my 6x6 rotation matrix? Is there an already implemented code in excel?
I really appreciate your help.
Best Regards,
Sartor





RE: Rotating a 6x6 matrix
TTFN
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RE: Rotating a 6x6 matrix
When I change the element axis, compliance matrix is changing.
I think it is rotation.
but unfortunately I am not sure.
can it be also composition of linear transformation?
Best Regards,
Sartor
RE: Rotating a 6x6 matrix
RE: Rotating a 6x6 matrix
http
You'll have to modify it for 3 dimensions
TTFN
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RE: Rotating a 6x6 matrix
X2 = 0.707X+0.707Y
Y2 = -0.707X+0.707Y
RE: Rotating a 6x6 matrix
could you show me a way how I can modify it?
I found a table from a book (please see the attached file), however, I can not form myself a Matrix which will rotate my 6x6 compliance matrix.
rb1957:
yes, it is just the axis rotation.
unfortunately i still could not manage it for 6x6 matrix.
Best Regards,
Sartor
RE: Rotating a 6x6 matrix
h
in this address, there is half of what I want.
However,
S'13, S'14 and some of the other 6X6 matrix elements are missing.
How can I write that missing parts in terms of the old values (like given in the formulas)?
Best Regards,
Sartor
RE: Rotating a 6x6 matrix
http://
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Rotating a 6x6 matrix
Because my 6x6 matrix is called compliance matrix in ansys.
However, it is not directly related to stiffness of the material.
But at the end of the day,
I have a 6x6 matrix, and I think I need to build a rotation matrix (6X6, composed of sin and cos values)to rotate that 6x6 compliance matrix. In the attachment, there are some already done ones(like for plane stress condition or reduced compliance) but that will not work for my case.
my matrix has values on 4x4, 5x5, 6x6. I have to rotate them also I think. I am quite confused at the moment.
Do you have any ideas how to solve this problem, i would really appreciate any road maps.
Best Regards,
Sartor
RE: Rotating a 6x6 matrix
TTFN
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RE: Rotating a 6x6 matrix
But I have to write a report and tell them it is not working due to matrix rotation. But i just dont want to write them that but also show them.
Best Regards,
Sartor
RE: Rotating a 6x6 matrix
i'm not too sure about columns/rows 4,5,6 ... this is bending stiffness (i think), i suspect it's the same (rotate rows/columns 4,5) ...
GL !
RE: Rotating a 6x6 matrix
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RE: Rotating a 6x6 matrix
http://www.ohiocae.com/piezo-paper.htm
You could perhaps use it as a check on your math when you are done though.
I was reading this wiki article (http://gpwiki.org/index.php/3D:Matrix_Math) and there is a link at the bottom that may provide more answers, but I can't say for sure because I can't access that page at work:
http://www.makegames.com/3drotation/
I feel that you may be able to do the rotations by using the matrices at the bottom of the wiki article by extending the matrix to a 6x6 by adding addition rows/columns of 0's with 1's on the diagonal. But, that idea needs to be backed up by someone else who remembers more than I do.
Further more, when I was doing a lot of work with some very large matrices I can tell you that excel should be able to handle basic matrix operations (multiplication etc.) for matrices upto 25x25.
One last thing to keep in mind. You can't just apply rotations at random, the order in which you apply the rotations is important, see the article below for a good (if not simplistic) explanation.
(under subheading "Successive Rotations")
http://www
I don't know if this has been any help. But good luck!
K
RE: Rotating a 6x6 matrix
http:/
Particularly, look at Section 3.2.11 Basis change formulas for anisotropic elastic constants.
RE: Rotating a 6x6 matrix
I've put a spreadsheet together with the information, as I understand it, from the link by TERIO, but I don't quite grasp the math behind this stuff yet. If you put in a rotation angle of zero the equation doesn't seem to return the original compliance matrix.
Can anyone explain what I'm missing?
Thank you,
K
RE: Rotating a 6x6 matrix
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RE: Rotating a 6x6 matrix
Thank you!
I've updated the spreadsheet for anyone interested. I would appreciate it if someone would check the math behind the result matrix to be sure I multiplied the matrices correctly.
K
RE: Rotating a 6x6 matrix
In the original spreadsheet the sin(radians) cells were reading the cos cell, not the radians cell. When you deleted the rows containing the conversion to radians you corrected the sin rows to read from the cells labelled as degrees, but the angle should be entered in radians.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Rotating a 6x6 matrix
RE: Rotating a 6x6 matrix
In short, I will check your second file to give a feedback with more details.
Best Regards,
Sartor
RE: Rotating a 6x6 matrix
RE: Rotating a 6x6 matrix
Sorry for the late reply. I did not have time to go over your document. However, I found something which I believe, would be helpful for you as well.
9. Solutions for anisotropic materials
http://www
I hope it helps you to see if your excel files are working or not (at least in terms of formulation)
Best Regards,
Sartor