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.

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