Designing helical surfaces related to coordinate curvature lines - Пилипака, Тарас Сергійович; Пилипака, Олександр Андрійович (Technology audit and production reserves, 2014)
A method of designing surfaces based on a directional helix line is considered in the paper. The surface is formed by means of a moving trihedral, shifting along the directional line with a uniform curvilinear generatrix, located in its normal plane. The main objective of the research lies in developing an analytical description of the surface in the way that its coordinate lines coincide with curvature lines. As on the surface, which is not related to the curvature lines, the search of the latter is resolved itself to setting up differential equations, which generally cannot be solved, the method of designing the surface, a priori related to the network of coordinate curvature lines, is proposed in the paper. The given method allows obtaining parametric equations of a surface with a specified property. For this purpose, the algorithm retains a special turn of a generatrix curve in a normal plane of a moving trihedral shifting along a directional helix line. The obtained results can be used in calculating the strength of shells, as they are simplified significantly in such surface representation. With the generatrix curve of an optional form the obtained surface will be quasi-helical and in the case, when the generatrix is a circle with the center at the top of the moving trihedral, helical, i.e. a tubular surface.