We present a three-dimensional (3D) partitioned aeroelastic formulation for a flexible multibody system interacting with incompressible turbulent fluid flow. While the incompressible Navier–Stokes system is discretized using a stabilized Petrov–Galerkin procedure, the multibody structural system consists of a generic interaction of multiple components such as rigid body, beams and flexible thin shells along with various types of joints and connections among them. A co-rotational framework is utilized for the category of small strain problems where the displacement of the body is decomposed into a rigid body rotation and a small strain component. This assumption simplifies the structural equations and allows for the incorporation of multiple bodies (rigid as well as flexible) in the system. The displacement and rotation constraints at the joints are imposed by a Lagrange multiplier method. The equilibrium conditions at the fluid–structure interface are satisfied by the transfer of tractions and structural displacements via the radial basis function approach, a scattered data interpolation technique, which is globally conservative. For the coupled stability in low structure-to-fluid mass ratio regimes, a nonlinear iterative force correction scheme is employed in the partitioned staggered predictor–corrector scheme. The convergence and generality of the radial basis function mapping are analyzed by carrying out systematic error analysis of the transfer of fluid traction across the non-matching fluid–structure interface where a third-order of convergence is observed. The proposed aeroelastic framework is then validated by considering a flow across a flexible pitching plate configuration with serration at the trailing edge. Finally, we demonstrate the flow across a flexible flapping wing of a bat modeling the bone fingers as beams and the flexible membrane as thin shells in the multibody system along with the joints.

我们提出了一个三维（3D）分区的气动弹性配方，用于与不可压缩的湍流相互作用的柔性多体系统。虽然不可压缩的Navier–Stokes系统使用稳定的Petrov–Galerkin程序离散化，但多体结构系统由多个组件（如刚体，横梁和柔性薄壳）以及各种类型的接头和连接之间的类属相互作用组成。同向旋转框架用于小应变问题的类别，其中，身体的位移分解为刚体旋转和小应变分量。该假设简化了结构方程，并允许在系统中合并多个刚体（刚体和柔体）。接头处的位移和旋转约束是通过拉格朗日乘数法施加的。通过径向基函数方法（一种分散的数据插值技术）进行牵引力和结构位移的传递，可以满足流固界面的平衡条件，该方法是全局保守的。为了在低结构与流体质量比状态下实现耦合稳定性，在分段的交错预测器-校正器方案中采用了非线性迭代力校正方案。径向基函数映射的收敛性和一般性通过对跨非匹配流体结构界面的流体牵引传递进行系统误差分析来进行分析，其中观察到三阶收敛。然后，通过考虑在后缘具有锯齿的柔性俯仰板结构上的流动来验证所提出的气动弹性框架。最后，我们演示了在蝙蝠的柔性拍打翼上的流动，以及在关节上将骨头手指建模为梁，将柔性膜建模为薄壳。