Reverse Classical Laminate Theory

General Composites Discussions Engineering Talk
#1

Hi, has anyone tried performing classical laminate theory in reverse, i.e. getting lamina stiffness and strength values from experimental laminate data? I have been attempting to do so but I can’t seem to get my formulation to work correctly. I’m 99% sure it is correct because I can go from Q Matrix [FONT=Wingdings]—>[/FONT] A Matrix, but not the reverse calculation.

Surprisingly there doesn’t appear to be any commercial software that calculates this, and I have only found two academic papers which mention the reverse process. I’ve attached a PDF showing my workings as that will be a lot clearer than writing it out here.

#2

I can’t say that I have tried to calculate the lamina properties from laminate properties but mathematically if it works in 1 direction it should work in the other direction.

The notation I am familiar with is slightly different than yours so it is a little difficult to follow what you are saying. If you work out your example problem working it forward from lamina properties to laminate properties and then try to work from laminate properties to lamina properties I am more than willing to take a look at it.

#3

I have managed to get my program to work but I had to make some tweaks to it. I was writing out a complete answer for you (i.e. from lamina to laminate to lamina again) when I worked out what the problem is. Basically for a balanced laminate the A11 and A22 equations are the same, e.g. for a 0/90/90/0 laminate:

A11 = [2Q11 + 2Q22] * t
A22 = [2Q11 + 2Q22] * t

(Note that Q11 and Q22 are of course reversed for 0 and 90 plies but as they are the same value the summation is still the same result)

This means that it is impossible to find a unique solution of Q11 and Q22. The only way you can do this is if you eliminate one of the unknowns and choose a value for it – so I got rid of the Q22 equation as I can calculate E2 from micromechanics. It’s quite annoying and feels wrong to have to use a theoretical calculation to derive experimental results. I am not a mathematician so I can’t explain why these equations won’t reverse to a unique solution