Low-fidelity isogeometric aeroelastic analysis has not received much attention since the introduction of the isogeometric analysis (IGA) concept, while the combination of IGA and the boundary element method in the form of the potential flow theory shows great potential. This paper presents a two-dimensional low-fidelity aeroelastic optimization framework consisting of a loosely coupled isogeometric potential flow model and isogeometric curved Timoshenko beam model. Application of the framework to the optimization of the landing performance for an active morphing airfoil shows its potential, although the absence of viscosity in the aerodynamic model has a detrimental effect.