Pylypaka T. The natural equations of curves in problems of bending of a sheet material

Dissertation is devoted research and transformation of the curves set by the natural equations, and their use in some engineering problems, in particular, in problems of bending of a sheet material. Leading bending of metal sheet at the fictitious form from such calculation that after a spring back the detail has gained the real form is in-process observed. Other cases - absolutely elastic bending of a strip and bending of an elastic material which does not oppose to bending. At these problems the length of a line on a surface at its bending does not vary, but the form most the curve varies. Such modification is caused by transformation of the natural equation of a curve, which nature in each case the. In particular, at leading bending of a sheet material it is shown, that at a line strain on surfaces it is necessary to decompose its curvature to geodesic and normal components and to increase a normal component as the geodesic component does not vary at surface bending.