A composite structure is manufactured by joining a first material, preferably made of a magnetically permeable material and having a first joining surface in which a recess having an overhang surface is formed, to a second material preferably made of an electrically conductive material and having a second joining surface to be joined to the first joining surface of the first material. On the second joining surface is integrally formed a protrusion having an outer configuration substantially corresponding to the inner shape of the recess. The first and second materials are firmly mechanically joined to each other by, for example, a casting method, a rolling method, a pressing method, or a method utilizing plastic flow of the second material.