Tip deflecton of antilevered beam made of materail with different stiffness (EI)

Tip deflecton of antilevered beam made of materail with different stiffness (EI)
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Posted by: aa2105 ^®

03/30/2009, 02:57:07

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Hi
For an initial approximate, I am modelling an aicraft wing as a cantilevered beam. I want to model the beam to incorporate the different materials used; a composite plate is sandwiched between a foam material and therefore the stiffnesses are different. How can I take this into account or figure out the overall stiffness and hence calculate the tip deflection? I plan to eithe model and lift distribution as triangular or elliptical with the peak load at the root.

For simplicity, the cross section is rectangular.

Also, as the foam is wider than the composite plate and so the moment of inertia, I, is different. How do I model this? Here is a sketch (left hand side is clamped, and RHS is free):

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Foam, thickness 10mm
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Composite, thickness 3mm
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Foam, thickness 10mm
==============================

The cross-section looks like:

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Foam, width 160mm
-------------
Composite, width 95mm
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Foam, width 160mm
=====================

Thank you in advance.

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: Tip deflecton of antilevered beam made of materail with different stiffness (EI)

: Tip deflecton of antilevered beam made of materail with different stiffness (EI) -- aa2105 Post Reply Top of thread Engineering Forum

Posted by: zekeman ^®

03/31/2009, 18:06:41

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You "load" the beam with M/EI and set it equal to the second derivative of y with respect to x.For any loading you can get M and E is a function primarily of x and the compositr material.
The free end is where x=L and the fixed end is x=0 and where fortuitously the slope or 1st derivative dy/dx=0 and where y=0
To solve it, you integate this numerically from 0 to L.
Now you have dy/dx or the slope as a function of x, You integrate this function once more from 0 to L to get y, the deflection at the free end being y(L).
If you understand this we can next discuss the development of M/EI function.

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: Tip deflecton of antilevered beam made of materail with different stiffness (EI)
: Tip deflecton of antilevered beam made of materail with different stiffness (EI) -- aa2105	Post Reply	Top of thread	Engineering Forum