A computer-implemented method for the additive manufacturing of a structure from an alloy with shape memory properties, comprising the following steps: obtaining (10) a set of geometric parameters characteristic of the structure to be manufactured; defining (20) sections (S) to generate a surface to which sinusoidal fibers (F) will be adapted based on said parameters; determining (30) the amplitude of each fiber (F) at each point of the corresponding region based on the intersections with other fibers (E) and the required distance at each point; defining (40) at least one sinusoidal fiber (E) that topologically fits each generated surface, thus generating (70) the volumetric structure to be manufactured; and additively manufacturing (80) each of the fibers to obtain the structure. (Machine-translation by Google Translate, not legally binding)