Numerically Generated Tangent Sti↵ness Matrices for Geometrically Non-Linear Structures Sonia Lebofsky A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Aeronautics and Astronautics University of Washington 2013 Reading Committee: Eli Livne, Chair Keith Holsapple Program Authorized to O↵er Degree: Aeronautics & Astronautics