A shape memory alloy (SMA) actuated aerostructure operable to dynamically change shape according to flight conditions is disclosed. Deformable structures are actuated by SMA actuators that are coupled to face sheets of the deformable structures. Actuating the SMA actuators produces complex shape changes of the deformable structures by activating shape changes of the SMA actuators. The SMA actuators are actuated via an active or passive temperature change based on operating conditions. The SMA actuated aerostructure can be used for morphable nozzles such as a variable area fan nozzle and/or a variable geometry chevron of a jet engine to reduce engine noise during takeoff without degrading fuel burn during cruise.