1. AAE 450 Spring 20081 Brandon White 2/14/2008 Structures Group Contact Inertia Matrix Math Model Tank Buckling Math Model

2. AAE 450 Spring 20082 Inertia Matrix Math Model “Structures, it’s a good thing.” – Martha Stewart  Calculates I xx, I yy, I zz 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 PROPPROP PROPPROP

3. AAE 450 Spring 20083 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

4. AAE 450 Spring 20084 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

5. AAE 450 Spring 20085 Backup Slides – Method 3 versus Euler Euler Method 3 Curvature Parameter Buckling Coefficient 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

6. AAE 450 Spring 20086 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<7475kg 5300kg<M<6100kg 9700kg <= M “There is no remedy for love except to love more.” –Henry David Thoreau