Brandon White 2142008 Structures Group Contact Inertia Matrix

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

Inertia Matrix Math Model § 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_v 3. m (ref. Doyle, Schoenbauer) – CM_stg. m (ref. Childers) P R O P O F O PROP F AAE 450 Spring 2008 “Structures, it’s a good thing. ” – Martha 2

Tank Buckling Math Model § § 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. Support Tank Rings Structure Additional Credit: Steven Izzo D Future Work L § Incorporate further complexities into Inertia calculations. – Engines, Nozzles, Payload, Avionics, Support Structure § Support Ring Design § Integrate both models into MAT analysis main code. AAE 450 Spring 2008 “He that falls in love with himself will have no rivals. ” – Ben Franklin 3

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 AAE 450 Spring 2008 “You can’t spell love without LO. ” –Peter Griffin 4

Backup Slides – Method 3 versus Euler Method 3 Euler Curvature Parameter Buckling Coefficient § 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. AAE 450 Spring 2008 “Without ME, your life would just be AWESO. ” – Critical Buckling Stress 5

§ 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 M<= 3050 kg 0 Rings 3050 kg<M<4300 kg 5300 kg<M<6100 kg 6950 kg<M<7475 kg 1 Ring 3 Rings 5 Rings AAE 450 Spring 2008 “There is no remedy for love except to love more. ” –Henry 9700 kg <= M <10 Rings 6