Velaroidal Shells and Shells of the Velaroidal Type

Abstract

A group of velaroidal surfaces and surfaces of the velaroidal type belong to the class of "Translation Surfaces". In contrast to the direct translation surfaces, velaroidal surfaces are formed by curves of variable curvature so that the formed surface rests on straight lines of a flat rectangular contour. Only about a dozen velaroidal surfaces have been described and studied in the scientific and technical literature. Velaroidal surfaces are also formed by curves of variable curvature but supported by a flat oval or circular contour. A super ellipse can be taken as a flat contour. The contour may consist of fragments of two identical curves located symmetrically about the axis of symmetry. In Russia velaroidal surfaces are studied so far only in the Peoples' Friendship University of Russia (RUDN University), Moscow. They are popular with both research geometrists and students - architects and builders, who believe that these shapes can be used within parametric, nonlinear, evolutionary and generative architecture. The article provides information with reference to the extensive used bibliographic material on the geometry of known velaroidal surfaces and surfaces of the velaroidal type. Information on the construction and visualization of new velaroidal surfaces with an oval flat contour as a super ellipse, as well as with a frame and a guide super ellipse. The data on determination of the stress-strain state of thin shells with median surfaces in the form of the surfaces under consideration is given. The fields of practical application of velaroidal shells and velaroidal shells are indicated. As shown in the sources used, geometers and calculation engineers have solved almost all the issues related to the design of these shells. Architects use velaroidal shells rarely, mostly to cover industrial buildings. Enclosures of velaroidal type have been used only in draft designs and in diplom works of architecture students.