Inverse problem of elastica in the design of flexible-walled wind tunnel

This paper presents a method of segmented linearization to solve the inverse problem of elastica in the design of flexible-walled wind tunnels. The flexible wall whose configuration is controlled by some actuating cylinders is subjected to air pressure, gravity and several forces, and simplified to be a beam which is fixed at one end and can slide freely over a hinge at the other end. The configurations of the flexible wall under certain Mach numbers, the air pressure and gravity, as well as the position of the controlled points are given, while the values of the forces are determined. By the amendment of simple beam theory, the segmented linearization method is suggested. A group of equations about deformation are established, and the approximate results are obtained. Furthermore, several deformation curves are obtained by an accurate nonlinear method, and compared with the design curves.