几何非线性机翼本征梁元素模型的高效化改进

 采用Hodges等提出的时间-空间离散化的几何精确非线性本征梁通用模型处理柔性机翼结构动力学问题时,当离散化的节点数增大时,该方法的未知数数量成倍地增长,而且方程组是严重病态的,因此数值模拟计算的速度非常缓慢。针对机翼中最常见的悬臂梁结构,根据空间离散化的边界条件,提出了空间缩聚法把空间离散差分方程缩聚为常系数矩阵格式,得到了只与时间相关的微分方程组,进一步推导得到了该方程组的雅可比矩阵,因而大大减少了方程组的数量以及求解过程的循环和迭代步数。采用Gear方法分别求解了原始的本征梁元素模型和本文提出的缩聚模型,结果表明空间缩聚模型在相同条件下可提高运算速度约5.1倍,而且对不同类型的外载荷都具有较好的通用性、稳定性和高效性。

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.