Molly Kane January 31, 2008 Structures Group Fuselage Buckling Analysis AAE 450 Spring 2008

Matlab Code Assumptions: perfect cylindrical shell, constant radius, uniaxial stress, unpressurized, radius is taken to be from the center of cylinder to half-way through the thickness Dimensions taken from Tsohas’ rocket: L = 8.44 m R = 0.457 m Inputs: Material specifications (Young’s Modulus, Poisson’s Ratio, density) Length, radius, thickness Outputs: Critical pressure, amount of material, (eventually pricing) AAE 450 Spring 2008 Structures Group

Future Work Add material selections, add effects of internal supports, account for changing radius with stages, welding AAE 450 Spring 2008 Structures Group

Backup Slides Method 1 from Wang, Wang, Reddy Ncr = 1 (Et2/R) √(3(1-ν2)) Method 2 from Brush, Almroth Pea = [(πa/L)2 + n2]2 *(n/a)2 + (πa/L)4 . Eh n2 12(1-v2) (n2[(πa/L)2 + n2]2) Where n is an integer representing the number of half – waves present in along the structure Method 3 from Baker, Kovalevsky, Rish Pcr = Kc π2E (t/L)2 Kc = 4√(3) γZ Z = L2 √(1-v2) 12(1-v2) π2 Rt Where γ is representative of the R/t ratio. AAE 450 Spring 2008 Structures Group

References Baker, E.H., Kovalevsky, L., Rish, F.L., Structural Analysis of Shells, Robert E. Krieger Publishing Company, Huntington, NY, 1981, pgs. 229-240. Brush, D.O., Almroth, B.O., Buckling of Bars, Plates, and Shells, McGraw Hill, 1975, pgs. 161-165. Grandt, A.F., AAE352 Class Notes, Spring 2007, Purdue University Jastrzebski, Zbigniew D., The Nature and Properties of Engineering Materials, 2nd edition, SI Version, John Wiley & Sons, Inc. Wang, C.Y., Wang, C.M., Reddy, J.N., Exact Solutions for Buckling of Structural Members, CRC Press, Boca Raton, FL, 2005. AAE 450 Spring 2008