A connection device for fluid transmission piping of an aircraft or spacecraft, the connection device being suitable for connecting two tubes to one another, the connection device comprising an injection-molded tip that has at least one bent or curved zone and that is made from a composite material comprising a thermoplastic matrix reinforced by a reinforcing system comprising carbon fibers, the injection-molded tip having a median longitudinal mold parting plane, wherein said carbon fibers extend in an axial direction of the molded tip along the injection-molded tip, said injection-molded tip incorporating mechanical and vibrational stiffening means that are molded with the injection molded tip and with said composite material to be integral with the injection-molded tip and extend in said at least one bent or curved zone and/or in the immediate vicinity of that zone, said mechanical and vibrational stiffening means extending in said median longitudinal mold parting plane or symmetrically relative to that median longitudinal mold parting plane and comprising said carbon fibers.