We consider the aeroelastic simulation of flexible mechanical structures submerged in subsonic fluid flows at low Mach numbers. The nonlinear kinematics of flexible bodies are described in the total Lagrangian formulation and discretized by finite elements. The aerodynamic loads are computed using the unsteady vortex-lattice method wherein a free wake is tracked over time. Each implicit time step in the dynamic simulation then requires solving a nonlinear equation system in the structural variables with additional aerodynamic load terms. Our focus here is on the efficient numerical solution of this system by accelerating the Newton algorithm. The particular structure of the aeroelastic nonlinear system suggests the structural derivative as an approximation to the full derivative in the linear Newton system. We investigate and compare two promising algorithms based in this approximation, a quasi-Newton type algorithm and a novel inexact Newton algorithm. Numerical experiments are performed on a flexible plate and on a wind turbine. Our computational results show that the approximation can indeed accelerate the Newton algorithm substantially. Surprisingly, the theoretically preferable inexact Newton algorithm is much slower than the quasi-Newton algorithm, which motivates further research to speed up derivative evaluations.

翻译：本文研究低马赫数亚音速流场中柔性机械结构的气动弹性模拟问题。采用全拉格朗日格式描述柔性体的非线性运动学特性，并通过有限元方法进行离散化。气动载荷通过非定常涡格法计算，其中自由尾涡随时间追踪。动态模拟中每个隐式时间步需要求解包含附加气动载荷项的结构变量非线性方程组。本文重点研究通过加速牛顿算法实现该方程组的高效数值求解。气动弹性非线性系统的特殊结构表明，可采用结构导数近似线性牛顿系统中的全导数。基于该近似，我们研究并比较了两种有前景的算法：拟牛顿型算法和新型不精确牛顿算法。数值实验在柔性板与风力涡轮机上进行。计算结果表明，该近似方法确实能显著加速牛顿算法。令人意外的是，理论上更优的不精确牛顿算法比拟牛顿算法慢得多，这促使我们进一步研究加速导数评估的方法。