1. AAE 450 Spring 2008 Steven Izzo 2/7/2008 Structures Buckling Analysis Function for Stages with help from Brandon White

2. AAE 450 Spring 2008 Inputs –Masses Nose Cone, Avionics, Payload, Fuel, Oxidizer, Tanks, Engine –Dimensions Length, Diameter, Thickness –Material Same values used in tank code by Steven Hiu Function Features –Euler Buckling Load –Applied Load2G’s –Add up masses Outputs –Required number of support rings –Total mass for next stage/skirt Structures

3. AAE 450 Spring 2008 Results  Ran for several cases based on model analysis code  Little to no extra support needed for buckling. Structures Future Work  Incorporate with other structures codes. –Mass, Sizing, Load/Stress, Cost

4. AAE 450 Spring 2008 Structures %Buckling Analysis Function for Stages %Created by Steve Izzo with help from Brandon White %Inputs: % mat- material for each stage tank section % d- diameter % t- thickness % L- length % m_ox- mass of oxidizer % m_fuel- mas of fuel % m_tank_ox- oxidizer tank mass % m_tank_fuel- fuel tank mass % m_engine- engine mass % m_above- total mass of above tank section %Outputs: % num_rings- number of required support rings required for structure % m_total- total mass of structure to be inputted for lower skirts and stages Code pg.1

5. AAE 450 Spring 2008 function [num_rings,m_total] = stress1(mat,d,t,L,m_ox,m_fuel,m_tank_ox,m_tank_fuel,m_engine,m_above) %get material data %same data used as tank function by Steven Hiu if mat== 'S' %Steel 17-4PH E= 196.5E9; %Young's Modulus, Pa elseif mat== 'A' %Aluminum 7075 E= 67.9E9; elseif mat== 'T' %Titanium Ti-5Al-2.55Sn E= 109E9; elseif mat== 'C' %Carbon Fiber Composite E= 150E9; end %calculate critical buckling load I=.25*pi*(d*.5)^4-.25*pi*(d*.5-t)^4; num_rings=1; load_cr= pi^2*E*I/((L/num_rings)^2); Code pg.2

6. AAE 450 Spring 2008 Code pg.3 %calculate applied load gload= 2*9.80665; %assume acceleration is 2g's load_ap=gload*m_above; %compare stresses, add appropriate number of rings while load_ap> load_cr; num_rings= num_rings+1; load_cr= pi^2*E*I/((L/num_rings)^2); end num_rings= num_rings-1; %total up masses for next skirt/stage m_total= m_above+m_ox+m_fuel+m_tank_ox+m_tank_fuel+m_engine; return

7. AAE 450 Spring 2008 Sources  Bedford, A, Fowler, W, Liechti, K. Statics and Mechanics of Materials, Prentice Hall, Englewood Cliffs, NJ, 2002.  Function “Tanks.m” by Steven Hiu