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The principal advances in the design and construction, as well as the static, vibrational, and buckling analysis of thin-walled structures and buildings in the shape of general and axisymmetric ellipsoidal shells are summarized in this review. These shells are particularly useful as internally pressurized vessels or as heads and bottoms of cylindrical tanks and vessels. Reinforced concrete and structural steel domes of buildings, air-supported rubber-fabric shells, and underwater pressure vessels are also made in the form of ellipsoidal, shells. Knowing the geometry of ellipsoids, one can solve various problems in physics, optics, and so on. Basic results of theoretical and experimental investigations of the stress-strain state, buckling, and natural and forced vibrations contained in 209 references are presented in the review. The influence of temperature on the stress-strain state of the shells in question is also discussed. Some parts of the review are also devoted to an analysis of the literature on the stress-strain state of ellipsoidal and torispherical heads of pressure vessels with openings.

Commercial production of synthetic resin has begun at the beginning of the XX century. In 1950s in the USA, small-span dome roofs, scanner assemblies and spherical hangars for radars made of plastic began to appear. Later, invention of reinforced plastics gave a possibility to use them in thin-walled shells for civil and industrial buildings. The subject of the paper associates with today’s renewed interest in thin shells. The modern theoretical base of strength analyses of composite structures give a possibility to design different structures and buildings. The possibility of the application of composites as the basic elements of thin-walled shell structures of industrial and civil purpose are illustrated by the concrete examples. The paper presents information on the well-known composite shells of positive Gaussian curvature in the form of spherical and umbrella domes or with more complex middle surfaces and presents materials that are absent in other publications. The paper contains 9 figures and 15 references.

The geometry of helical surfaces has been well studied. Several available methods of strength analysis of helicoidal shells give one a choice in solving one-dimensional or two-dimensional problems. The basic problems considered in this review article, which contains 181 references, include geometrical research, approximation and bending of helical surfaces, static analysis of helicoidal shells by analytic and numerical methods, the vibrations of pre-twisted cantilevered plates, helical tubular shells, the generation of helical surfaces by mated surface of revolution, and the application of the helicoidal constructions.