Effect of plate length on modulus with shear-extension coupling.

[RPstress]

I have a note I made some time ago which says that for a plate with significant shear-extension coupling (A13<>0), the modulus will vary with the length-to-width ratio. I even have an equation for it. If Ex is the theoretical classical plate modulus (i.e., for an infinite plate) then the modulus Ex' of a finite strip would be:

Ex' = Ex * [ 1 - 3*A13^2/(3*A11*A33 + 2*A11^2*L/W) ]

However, like a fool I didn't note the reference when I made the note, and I can't find it mentioned anywhere in my current refs. Does anybody know if there's any truth in this statement and equation??

-R.

 

[YoungTurk]

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.

 

[RPstress]

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.

 

[edrush]

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.

 

[edrush]

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.