Geometrical modeling of a composite folded membrane by a developable membrane with parabolic guidelines of any order

The geometric modeling of a folded composite membrane using method of approximation of a folded composite membrane by a developable surface with parabolic guidelines of any order is an aim of this work. This approach is carried out on a one-way expandable composite membrane with thermosetting polyester matrix reinforced by fiberglass. The geometric model is done in two steps: first one replaces the membrane of reference by a system of developable membranes from which then plane quadrilaterals arranged in a well-defined manner are constructed. This need the establishment of mono parametric equation of the family of the plans and the equation of the cuspidal edge of the developable surface basing on which it is carried out the development of algorithms for the construction of the folded composite membrane and that of the developed of the twisted membrane.