Hi folks,
I’m a mechanical engineer starting to learn about composites. I have been attending a course on classical laminate theory but the level of math (especially matrix calculations) was a bit over my head which caused me to loose track. I am now trying to understand things by reading the text again. I eventually want to do my calculations by computer (ABD matrix or laminator program) but I want to know what’s happening inside the code. I know the way to go for analyzing a laminate is as follows:
- compose base layers
- create compliance matrix
- rotate the system
- stack the layers
- calculate the laminate strain
- rotate the system back to fiber orientation
- calculate stresses in principal directions
- unleash a criterium (Tsai Hill or Tsai Wu) to check for failure
- calculate progressive failure of ply’s
However I am not completely clear on how to implement this. I am now guessing this is what happens: create compliance matrix and calculate strains as if stressing in the fiber direction, then rotate the strains by multiplying them with the N matrix which will make them larger (?), then calculate new ‘apparent laminate stiffness properties’ by using the imposed stresses and new strains, do this for every layer, weigh all the new stiffness properties of the layers according to the thickness of the layer and calculate stiffness properties of the laminate. With the imposed stresses it will now be possible to calculate the strains for the entire laminate. Looking at a single laminate now multiply this strain by the inverse of the N matrix (?) to know strains in the fiber direction which gives me stresses in the fiber direction from the stiffness matrix which can be used as input for Tsai-Wu?
Wow, did that just come out of my keyboard?
My lack of mathematical talent makes it really hard to follow any text on CLT. It’s not my desire to make the calculations myself, I would just like to know what’s happening.
Can anyone point me in the right direction?
Thanks!