Closing device comprising a frame and a structure which consists of a series of sections articulated in pairs, which can be deployed between the two parallel planes of the frame, and can be folded in the manner of a concertina in a storage zone, and is associated with drive means that are capable of driving it in translation in the direction of folding and/or deployment, each of the sections being associated with two indexing means (12; 120, 121; 50), which are slidingly engaged with a guide path, which branches off into two secondary branches (21, 22) at the storage zone, in a configuration which allows, when moving in the direction of said storage zone, in association with auxiliary switching means, one of said indexing means to take a secondary branch (21, 22) which is different from that taken by the indexing means which follows or precedes it, wherein the secondary branches (21, 22) and the storage zone are arranged vertically with respect to the guide path such that the mass of the stacked sections ensures that the stacked sections are held one on top of the other; and wherein the switching means consist of a distribution cam which is pivotally movable about a horizontal axis (XX') parallel to the plane of the structure, which cam is designed to assume, according to its pivoting movement, positions which alternately switch the indexing means towards one or other of the two secondary branches (20, 21), and in such a way that the pivoting movement, in order to assume a position which switches an indexing means towards a secondary branch (20, 21), is generated by the movement in the other secondary branch (20, 21) of the indexing means which precedes it in said guide path; and wherein every second section, starting with the section closest to the storage zone, comprises, partly or entirely on the longitudinal edge thereof arranged on the side of the storage zone when said section is inserted in the guide path, an extension which projects beyond the pin of the indexing means of the section close to said edge, while the frame comprises a support element which is arranged at the edge of the secondary branch that is intended to be taken by the indexing means, and outside of said branch the support element, as well as the extensions, are shaped, arranged and sized such that, when the section tilts to assume its storage position, the extension thereof moves beyond the support element in order to bear upon it. and wherein the switching means consist of a distribution cam which is pivotally movable about a horizontal axis (XX') parallel to the plane of the structure, which cam is designed to assume, according to its pivoting movement, positions which alternately switch the indexing means towards one or other of the two secondary branches (20, 21), and in such a way that the pivoting movement, in order to assume a position which switches an indexing means towards a secondary branch (20, 21), is generated by the movement in the other secondary branch (20, 21) of the indexing means which precedes it in said guide path; and wherein every second section, starting with the section closest to the storage zone, comprises, partly or entirely on the longitudinal edge thereof arranged on the side of the storage zone when said section is inserted in the guide path, an extension which projects beyond the pin of the indexing means of the section close to said edge, while the frame comprises a support element which is arranged at the edge of the secondary branch that is intended to be taken by the indexing means, and outside of said branch the support element, as well as the extensions, are shaped, arranged and sized such that, when the section tilts to assume its storage position, the extension thereof moves beyond the support element in order to bear upon it.