Described is a method of manufacture of 3D objects from composite materials. The method includes the use of an extrusion nozzle configured to extrude the composite material, including a multistrand filament with a thixotropic acrylic matrix material surrounding the multistrand filament. Extruding a 3D object surface segment spanning in the air over at least a segment of a discontinuous work surface and operating concurrently a source of curing energy to pin and enhance the strength of a 3D object surface segment spanning in air. The 3D object extruded surface segment spanning in the air is sufficiently rigid and maintains its shape without the use of a mandrel.