This thesis proposes a framework for the design optimization of geometric nonlinearities developed by active elements embedded in truss-like aerospace structures for the purpose of attenuating their dynamic aeroelastic response under turbulent aerodynamic gust conditions. Dynamic aeroelastic responses are analyzed considering random Power Spectral Density (PSD) and Tuned Discrete Gust (TDG) excitation profiles. MSC NASTRAN is employed for the development of the dynamic aeroelastic models where the random PSD gust with a continuous Davenport spectrum (DS) and the TDG with a One-minus cosine (OMC) wind excitation profiles are developed. A multi-objective genetic optimization algorithm (MOGA) is utilized to determine optimal prestress values through active element actuations for the purpose of tuning the geometric stiffness and therefore modal response of the structure when exposed to gust excitations. Two case studies are presented to minimize the pointing error of both a simplified and high-fidelity Earth-based very-long baseline interferometry antenna structure.