Improving the geometrically nonlinear intrinsic beam element model of wing for high efficiency

The geometrically exact, nonlinear intrinsic beam element model proposed by Hodges, et al. is known as its space-time conservation law. Its shortcoming is that, in dealing with the structural dynamics of a flexible wing, the number of independent variables increase exponentially while the discrete nodes increase; furthermore, the set of equations become stiff and lead to low efficiency in numerical calculation. In order to improve the structural dynamics model of a common cantilever wing, this paper derives a spatial condensation method according to the boundary conditions of a spatial discrete model to convert the spatial discrete equations to ordinary matrix equations, and then the original equations become ordinary differential equations related to time domain only. Thus, the number of equations and the looping steps in their solution can be decreased greatly, and the Jacobian matrix can also be derived easily from the improved equations. The Gear method is employed to solve the original intrinsic beam element model and the condensation model proposed in this paper respectively. The results show that the proposed spatial condensation model can improve the operating rate by about 5.1 times as compared with the original model under the same conditions, and it exhibits high universality, stability and efficiency for different force models.