R3DC Report 2-08

Endplate Deflection

Point Load Deflection

A simple calculation based on the definition of Young's modulus can yield an order of magnitude level estimate for the deflection of an endplate made from Aluminum. According to the definition of Young's modulus

[math]Y \equiv \frac{F}{4wy} \left( \frac{l}{t}\right )^3[/math]

where

[math]Y = 7 \times 10^{10}N/m^2 \equiv[/math] Young's Modulus for Aluminum

[math]F = 1027 N \equiv[/math]point force/load

[math]w =0.526 m \equiv[/math] width of the endplate

[math]y \equiv[/math] deflection of endplate due to point force

[math]l =4.83 m \equiv[/math] length of the endplate

[math]t = 0.05 m \equiv[/math] thickness of the endplate

A deflection of 6 mm is expected for a 5 cm thick Aluminum endplate, after solving the above equation for [math]y[/math] and inserting the given values. If a 5 cm thick stainless steel [math](Y=2 \times 10^{11} N/m^2 )[/math] endplate were used, the deflection would drop a factor of 3 from 6 mm to 2 mm due to the linear dependence of the deflection on Young's Modulus. The cubic dependence of the deflection on the thickness [math](t)[/math] of the endplate, however, can be used to reach the minimum endplate deflection criteria of 50 [math]\mu m[/math] instead of using stiffer material. Composite materials were considered in order to increase the thickness of the material without substantially increasing the weight of the endplate.

Material	Youngs Modulus	Density
	MPa	[math]\frac{kg}{m^3}[/math]
Polyeurethane Foam FR-3700	140	240
Hexacell with holes
Carbon Fiber Rods	210	580

Carbon Rod Buckling

Buckling FEA

=3-D Analysis

Summary

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