A method for the attachment of a hollow element to a component (130) consisting of a composite material being one of a plastic part having a fiber reinforcement in a plastic matrix material or a plastic part having a fabric reinforcement in a plastic matrix material, with the hollow element having a flange part (102) and a shaft part (104) or a rivet section (106) extending away from the flange part (102), wherein the rivet section (106) can also be formed at a free end of a shaft part (104), wherein the hollow element has a central passage (108), passing an auxiliary convergent tip (126) from either a flange side of the element (100) remote from the shaft part (104) through the passage (108), or introducing the auxiliary convergent tip from a side of the free end of the shaft part into the passage (108), such that a converging region (128) of the auxiliary tip (126) projects from the free end of the shaft part or of the rivet section (106);
- pressing the hollow element (100) with the tip (126) to a fore against the component (130) and piercing the component forming a pierced hole and pressing the convergent tip through the component thereby dilating the pierced hole in the component (130) and displacing the fibers or fabric of the plastic material and engaging a plastic matrix material with a side (114) of the flange part adjacent to it, the tip (126) thus pierces a hole (132) in the component and the material which is displaced by means of the tip builds up at at least one of an underside and an upper side of the component 130 in a form of thickened portions 134 and 136 respectively, removing the auxiliary convergent tip and forming the rivet section into a rivet bead trapping the component between the flange part and the rivet bead.