Off the top of my head, I'd say that's one confusing equation you posted.  Being trained in mechanics, I'm not sure at all what your A coefficients refer to.  In addition, by strict definition the modulus is a material property and not a property of the plate.  Therefor, the modulus will not depend on the geometry, ever.

On the other hand, I try to be practical once in awhile.  Perhaps someone did a transformation based upon the STRESS differences between the infinite and finite plate and ended up with an effective modulus.  I think most engineers would agree that the proper analysis would look at an effective stiffness rather than an effective modulus, because stiffness is indeed a property of the plate.

The 'A's are coefficients from the laminate's A-matrix. A13 is the one which gives coupling between extension and shear
(analagous to poisson's ratio coupling between X- and Y-stretching, which is covered by A12).

Say you regard the true Ex for the material to be for an infinite plate. What the formula says is that in a tensile test, measuring stress and extensional strain will give a different stress/strain ratio (i.e., modulus) for plates with different L/W ratios.

You will need to send money before I consider hurting my brain thinking about this stuff.

No luck with standard texts?  Jones?  Halpin?

I can't remember that particular coefficient, but it makes sense that if restrain the width-wise contraction you will increase the apparent longitudinal modulus.  So yes, I believe it.

I probably misinterpreted what you are looking for.  After a little more thought I looked in a text book and after 5 minutes I put it away and wished you good luck.  Sorry, it's been to long since I was into the math.  You got what you paid for.