JAX-based aeroelastic simulation engine for differentiable aircraft dynamics

A novel methodology is presented in this paper for the structural and aeroelastic analysis of large flexible systems with slender, streamlined components, such as aircraft or wind turbines. Leveraging on the numerical library JAX, a nonlinear formulation based on velocities and strains enables a highly vectorised codebase that is especially suitable for the integration of aerodynamic loads which naturally appear as follower forces. In addition to that, JAX automatic differentiation capabilities are used to obtain gradients that allow the solver to be embedded into broader multidisciplinary optimization frameworks. The general solution starts from a linear Finite-Element (FE) model of arbitrary complexity, on which a structural model order reduction is performed. A nonlinear description of the reduced model follows, with the corresponding reconstruction of the full 3D dynamics. It is shown to be highly accurate and efficient on representative aircraft models are shown. An extensive verification has been carried out by comparison with MSC Nastran full-FE linear and nonlinear solutions. Furthermore the nonlinear gust response of a full aircraft configuration with over half a million degrees-of-freedom is computed, and it is faster than its frequency-based, linear equivalent as implemented by a commercial package. Therefore this could be harnessed by aircraft loads engineers to add geometrically nonlinear effects to their existing workflows at no extra computational effort. Finally, automatic differentiation on both static and dynamic problems is validated against finite-differences, which combined with a near real-time performance of the solvers opens new possibilities for aeroelastic studies and design optimization.

本文提出一种面向带有细长流线型部件（如飞行器或风力涡轮机）的大型柔性系统的结构与气动弹性分析的新型方法。借助数值库JAX，基于速度与应变构建的非线性公式可实现高度向量化的代码库，尤其适配天然以随动载荷形式出现的气动载荷集成。此外，利用JAX的自动微分功能可获取梯度，使得求解器能够嵌入更广泛的多学科优化框架中。该通用求解流程始于任意复杂度的线性有限元（Finite-Element, FE）模型，随后对其执行结构模型降阶。随后对降阶模型进行非线性描述，并完整重构全三维动力学特性。该方法在典型飞行器模型上展现出极高的精度与效率。研究通过与MSC Nastran全有限元线性及非线性求解结果进行对比，完成了全面的验证工作。此外，研究针对拥有超50万自由度的完整飞行器构型的非线性阵风响应进行了计算，其计算速度快于商业软件基于频率的线性等效求解方案。因此，飞行器载荷工程师可利用该方法在现有工作流程中加入几何非线性效应，且无需额外的计算开销。最后，针对静力学与动力学问题的自动微分通过有限差分法进行了验证，结合求解器近乎实时的性能表现，为气动弹性研究与设计优化开辟了全新的可能性。