In the past decade, MDO researchers have developed capabilities to simultaneously optimise the shape and internal structure of aircraft based on coupled high fidelity Computational Fluid Dynamics and Finite Element Analysis. However, to date the finite element methods used for the structural analysis are typically linear and are known to be inaccurate for structures experiencing large deformations, as modern high aspect ratio wings do. To address this challenge, robust and efficient solution strategies for nonlinear structural analysis and coupled aerostructural analysis have been developed for the high-fidelity MACH MDO framework. Structural and aerostructural analyses and optimisations are then performed to investigate the effect of geometrically nonlinear structural phenomena on the results of high-fidelity aerostructural analyses and, consequently, how these changes effect the optimal design of aircraft wings.