AAE 450 Spring 2008 1<#>

Brandon White2/14/2008

Structures Group Contact

Inertia Matrix Math ModelTank Buckling Math Model

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

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

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

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

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