Torsional stiffness of rectangular plate

[cpinz]

Hi all,
a response to the following general problem would be appreciated very much.

I have a rectangular plate made of n plies , its section is rectangular . Long edges aligned with x axis, short ones with y axis
It is constrained (built in) at its left edge, free on other edges; pure torque is applied on right short edge and acting around x axis .

My question: if torsional stiffness around x axis must be maximized, is it worth to maximize the membranal shear modulus only, or also the bending shear modulus should be investigated ?

 

[ESPcomposites]

The torsional stiffness, GJ, of a rectangular section is directly defined as 4b/d66, where d66 is determined via lamination theory.

Provided the laminate is symmetric, the stacking sequence will not affect the in-plane shear stiffness. However, the d66 term can vary significantly with various layups, and hence so would the torsional stiffness.

Pushing the higher in-plane shear stiffness layers towards the outside will increase the torsional stiffness. I also verified this eLaminate.

Brian

http://www.espcomposites.com

 

[cpinz]

Hi Brian,

thank you for your quick reply.

I did the same, and I reached the same conclusion ( laminate is symmetric and balanced). After some hand calculation and some runs on ABD matrix, I run a simple case on fem; cross-checking all procedures I saw that, effectively, d66 terms influence G modulus but also a66 term does it.
Nevertheless I wondered if it was correct to discard a66 term and consider d66 terms only; this doubt came from ther fact that , imaging the plate under pure torsion, "I saw" only membranal loads acting, while it was more difficult to understand how bending shear applied.

About your last sentence: as expected I reached the max. torsional stiffness placing outside the higher in-plane shear stiffness layers.

Cpinz

 

[ESPcomposites]

The only term that ultimately matters is d66. But of course d66 is a function of a66, they are not decoupled. Have a look at the formula for [D] and you will see that A66 and the stacking sequence, in combination, yield D66 (and in turn d66).

Clearly, the max torsional stiffness occurs by having the highest A66 layers located towards the outermost surface.

Brian

http://www.espcomposites.com

 

[SWComposites]

"run a simple case on fem; cross-checking all procedures I saw that, effectively, d66 terms influence G modulus but also a66 term does it"
> draw a FBD; you do not have a case of pure torsion, therefore the entire ABD matrix will effect the displacement. How did you determine "G modulus" from the FEM?

SW

 

[cpinz]

SW,

- I didn't use the fem to determine G modulus;I used it only to check the angle of torsion; I compared this value with that obtained from two hand calculation where I used the G moduli obtained from a66 (G_membranal)first and b66 (G_bending) then.

-"you do not have a case of pure torsion, therefore the entire ABD matrix will effect the displacement"
Could you explain that further please ?