In my example I have a composite tube with material fibers oriented 30º (orthotropic material). I have obtained cross sectional properties of this model and I have repeated the exercise but changing the material definition. Instead of defining the material by means of E1, E2, E3 ... and fiber angle of 30º, I have introduced the equivalent material properties of the material oriented 30º: E1', E2',E3'... and a 0º fiber angle. The results of both test should be equal but it is not the case. I have big differences in EA, EI1, EI2...
This is because that after the transformation, if you still define the material as orthotropic using nine constants, you lose some properties in the generalized Hooke's law. If you want to use the equivalent material properties, then you need to treat the material as general anisotropic and provide all 21 constants in VABS. In this way, you can find that the cross-sectional stiffness is the same as the original one.
You can calculate the 6x6 elastic constants matrix in the material frame using the 9 engineering moduli. Then transform it to the global frame according to the rotating angle theta. This is what you need in the VABS input file. You can also compute the compliances matrix, and get engineering moduli in the global frame from there. This is what you originally used. I have attached a pdf explaining the theory and a spreadsheet for doing the transformation.
The simple E*A does not work for your problem. Strictly speaking, it only works for isotropic homogeneous beams. The reason is that for your case, the extension is coupled with other deformation modes.
---- Emailed forum response from wenbinyu@purdue.edu
Maria Resano @ on — Edited @ on
In my example I have a composite tube with material fibers oriented 30º (orthotropic material). I have obtained cross sectional properties of this model and I have repeated the exercise but changing the material definition. Instead of defining the material by means of E1, E2, E3 ... and fiber angle of 30º, I have introduced the equivalent material properties of the material oriented 30º: E1', E2',E3'... and a 0º fiber angle. The results of both test should be equal but it is not the case. I have big differences in EA, EI1, EI2...
I have attached both cases files.
Thank you in advanced.
María
VABS-test.zip
242 KBClick to download
Su Tian @ on
Hi Maria,
This is because that after the transformation, if you still define the material as orthotropic using nine constants, you lose some properties in the generalized Hooke's law. If you want to use the equivalent material properties, then you need to treat the material as general anisotropic and provide all 21 constants in VABS. In this way, you can find that the cross-sectional stiffness is the same as the original one.
I have attached the correct VABS input file.
cylinder30degD-vabs.dat
520 KBClick to download
Maria Resano @ on
Thank you Su. I want to ask you how did you calculate the 21 constants because I do not obtain same values as you.
Su Tian @ on
Hi Maria,
You can calculate the 6x6 elastic constants matrix in the material frame using the 9 engineering moduli. Then transform it to the global frame according to the rotating angle theta. This is what you need in the VABS input file. You can also compute the compliances matrix, and get engineering moduli in the global frame from there. This is what you originally used. I have attached a pdf explaining the theory and a spreadsheet for doing the transformation.
transformation.zip
707 KBClick to download
Maria Resano @ on
Hello Su,
thank you very much for your help.
Maria Resano @ on
Hello,
now that I have changed the material input from orthotropic to anisotropic, I have detected some program bug.
When I run preVabs in order to generate vabs file, The *.dat file created has the material input lines missing.
I have attached the aforementioned files.
Thank you
example.zip
123 KBClick to download
Maria Resano @ on
Hello,
I have obtained the section properties of the example above and I have repeated analytically the axial stiffness and I have found differences.
what they owe?
I have attached the analytical calculus.
Wenbin Yu @ on — Edited @ on