发表机构
School of Aeronautic Science and Engineering, Beihang University（北京航空航天大学航空科学与工程学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对变形柔性多体飞行器，提出基于几何精确梁的组合气动弹性算子框架，通过相对对数和附着映射统一结构应变与气动几何，验证显示三次修正降低位移误差。
AI 中文摘要
变形柔性多体飞行器要求结构应变、气动几何、表面速度和广义载荷在接头和柔性部件改变构型时保持兼容。本文围绕每个升力面与几何精确梁之间的假定材料连接，发展了一种组合公式。将部件根部姿态与截面场分离表明，部件的体应变和弹性势能取决于其自身的弹性坐标，而上游运动进入动能项和外载荷拉回。在单元层面，精确的相对对数$d$提供应变和势能，而参考锚定的截面坐标$\sigma$提供变形后的截面几何。有限阶展开精确保留有限参考几何，仅截断端点扰动。随后，附着映射从共同的截面运动学生成表面点、切线、法线、速度和力雅可比。欧拉-庞加莱梁平衡、运动表面势流关系、图余切组装以及相关的半离散功率恒等式在共同的扭转-扳手约定下表述。区分配置点、压力、等效载荷和结构驻点以揭示其近似误差。验证给出了度-$N_d$相对对数展开的预期$N_d+1$收敛阶。在几何非线性悬臂梁比较中，三次静态流形修正将四个已完成载荷工况的平均全记录位移误差从$0.479$降低到$0.255$。这些结果提供了结构和界面层面的证据，而非对完整飞行器气动弹性预测的验证。
英文摘要
Morphing flexible multibody aircraft require structural strain, aerodynamic geometry, surface velocity, and generalized loading to remain compatible as joints and flexible components change configuration. A compositional formulation is developed around an assumed material attachment between each lifting surface and a geometrically exact beam. Separating the component root pose from the section field shows that the body strain and elastic potential of a component depend on its own elastic coordinates, while upstream motion enters kinetic terms and external-load pullbacks. At element level, an exact relative logarithm $d$ supplies strain and potential energy, whereas a reference-anchored section coordinate $σ$ supplies deformed section geometry. Finite-order expansions retain the finite reference geometry exactly and truncate only endpoint perturbations. The attachment map then generates surface points, tangents, normals, velocities, and force Jacobians from common section kinematics. Euler--Poincare beam balance, moving-surface potential-flow relations, graph cotangent assembly, and the associated semidiscrete power identity are stated in a common twist--wrench convention. Collocation, pressure, equivalent-load, and structural-station sites are distinguished to expose their approximation errors. Verification gives the expected $N_d+1$ convergence order for degree-$N_d$ relative-log expansions. In a geometrically nonlinear cantilever comparison, a cubic static-manifold correction reduces mean full-record displacement error from $0.479$ to $0.255$ over four completed load cases. These results provide structural and interface-level evidence rather than validation of a complete aircraft aeroelastic prediction.
Comments30 pages, 2 figures, 2 tables
