Construction of Developable Surfaces with Two Director Curves

An analysis of a number of published materials regarding four types of developable surfaces with two director (supporting) algebraic curves of the second order lying in parallel or in intersecting planes has been conducted. Three types of developable surfaces are shortly described with references to sources, and visualizations of each type of developable surface are presented. For the developable surfaces with two supporting curves with intersecting axes in intersecting planes, the construction technique and the method of obtaining parametric equations are given. This method is illustrated with three examples. It is established that to date, there are no studies on the strength of thin shells in the form of the presented developable surfaces defined in curvilinear conjugate non-orthogonal coordinates that coincide with the external contour of the shells. It is shown that there are suggestions of application of the studied surfaces in architecture, shipbuilding, and agricultural machine engineering.