A formulation for sensitivity analysis of fully coupled time-dependent aeroelastic problems for multipoint design optimization is given in this paper. Both forward sensitivity and adjoint sensitivity formulations are derived that correspond to analogues of the non-linear aeroelastic analysis problem. Both sensitivity analysis formulations make use of the same iterative disciplinary solution techniques used for analysis, and make use of an analogous coupling strategy. The fully coupled aeroelastic analysis formulation is first verified to effectively perform performance predictions of a four bladed HART2 rotor in forward flight started impulsively from rest. Upon successful verification of the fully coupled adjoint formulation, it is used to perform trim and aerodynamic shape design optimization for helicopter rotors in forward flight conditions. The formulation is further extended to perform multi-point blade shape optimization in two simultaneous design points, namely, hover and a forward flight condition.
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