Mixed Torsion Theory of Narrow Tapered Thin Plates

The problem of mixed torsion of tapered thin-walled member has long been one of the theory issues with a lot of controversy. Theoretically, a tapered, open thin-walled member can be taken as the combination of tapered flat plates. Therefore, the problem of mixed torsion of the tapered flat plates is the fundamental problem for the theoretical investigation on tapered thin-walled members. As a result, here on the basis of Kirchhoff’s thin plate theory and Vlasov’s rigid section assumption, the energy variational model and differential equation model for the problem of mixed torsion of narrow tapered thin-plates are established, respectively. Furthermore, by making use of the energy variational model and differential equation model, respectively, the approximate and exact analytical solutions of twist angle for the cantilever case of a narrow tapered thin-plate under toque applied at the free end is derived and presented. Its correctness of the new mixed torsion theory for the narrow tapered thin-plate is verified by the numerical example problems.