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Inertia Matrix Math Model

Brandon White 2/14/2008 Structures Group Contact Inertia Matrix Math Model Tank Buckling Math Model. Inertia Matrix Math Model. O. PROP. Calculates I xx , I yy , I zz at the Center of Mass for the different time steps requested by the D&C group.

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Inertia Matrix Math Model

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  1. Brandon White2/14/2008Structures Group ContactInertia Matrix Math ModelTank Buckling Math Model AAE 450 Spring 2008

  2. Inertia Matrix Math Model O PROP • 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) F O PROP F O PROP F AAE 450 Spring 2008 “Structures, it’s a good thing.” – Martha Stewart

  3. 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. • Additional Credit: Steven Izzo Support Rings Tank Structure 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

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

  5. 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. Critical Buckling Stress AAE 450 Spring 2008 “Without ME, your life would just be AWESO.” – Brandon White

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

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