Download - Inertia Matrix Math Model
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AAE 450 Spring 2008 1<#>
Brandon White2/14/2008
Structures Group Contact
Inertia Matrix Math ModelTank Buckling Math Model
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AAE 450 Spring 2008 2<#>
Inertia Matrix Math Model
“Structures, it’s a good thing.” – Martha Stewart
Calculates Ixx, Iyy, Izz at the Center of Mass for the different time steps requested by the D&C group.
Includes calculations for an oxidizer and fuel tank in each stage, as well as skirts between stages.
Only utilizes inputs from codes that are already in place:– Tanks.m (ref. Hiu)– Skirt_v3.m (ref. Doyle,
Schoenbauer)– CM_stg.m (ref. Childers)
O
O
O
F
F
F
PROP
PROP
PROP
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AAE 450 Spring 2008 3<#>
Tank Buckling Math Model
“He that falls in love with himself will have no rivals.” – Ben Franklin
Future Work
No longer utilizing Euler buckling loading. Instead, using Method 3 from Baker, Kovalevsky, and Rish (ref.
Kane) Calculations at a maximum G-loading of 30 g’s. Additional Credit: Steven Izzo
Incorporate further complexities into Inertia calculations.– Engines, Nozzles, Payload, Avionics, Support Structure
Support Ring Design Integrate both models into MAT analysis main code.
D
L
Tank Structure
Support Rings
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AAE 450 Spring 2008 4<#>
Backup Slides – References Baker, E.H., Kovalevsky, L., Rish, F.L., Structural Analysis of Shells, Robert E. Krieger
Publishing Company, Huntington, NY, 1981, pgs. 229-240.
Bedford, A., Fowler, W., and Liechti, K.M., Statics and Mechanics of Materials, Prentice Hall, Upper Saddle River, NJ. 2003
“You can’t spell love without LO.” –Peter Griffin
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AAE 450 Spring 2008 5<#>
Backup Slides – Method 3 versus Euler
2
2
L
EIP
Euler Method 3
2
21L
ZRt
Curvature Parameter
0.750.85( )sk Z Buckling Coefficient
22
212(1 )s
cr
k E tP
L
Critical Buckling
Stress
Euler buckling is a very good method when L/D ~ 100, Method 3 satisfies any L/D calculation.
Euler provides a max Force that can be placed on a cross section, while Method 3 provides a max Stress value.
“Without ME, your life would just be AWESO.” – Brandon White
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AAE 450 Spring 2008 6<#>
Backup Slides – Example of Method 3 Consider an Aluminum tank is supporting various masses above it.
– Length: 6 meters– Diameter: 1 meter– Thickness: 0.002 meters
0 Rings 1 Ring 3 Rings 5 Rings <10 Rings
M<= 3050kg 3050kg<M<4300kg 6950kg<M<7475kg5300kg<M<6100kg 9700kg <= M
“There is no remedy for love except to love more.” –Henry David Thoreau