Aeroelastic Reduced Order Model for composite material wings


– Antonio Gil Megías
– Luis Miguel García-Cuevas González
– Pedro Manuel Quintero Igeño
– Andrés Cremades Botella


Aeroelastic calculations have been crucial in the design and optimization of structural components of UAVs. Traditionally, aeroelastic phenomena have been predicted using simplified theories as an equivalent section, due to the high computational cost associated with the solution of the coupled continuity equations for the solid and the fluid. In addition, the aerodynamic loads are usually simplified with potential and linear theories. The previous simplifications lead to a lack of accuracy when dealing with nonlinear aerodynamics: near stall, vortex shedding, bluff bodies… Moreover, the traditional section does not consider bending-twist coupling, as may appear in orthotropic materials. The present work tries to overcome the described limitations while maintaining a low computational cost. A Reduced Order Model (ROM) is developed. The solid physics are simulated by an orthotropic thin wall cross-section 1D beam. Relative to the aerodynamics, a hybrid method is used. This method combines the quasi-steady polar of the 2D section, the tip vortex effects of Prandtl Lifting Line Theory and a neural network to include the unsteady effects.


The aeroelastic ROM can be divided in three main blocks: initialization, load estimation and coupled solver.

The initialization block contains the information relative to the initial and boundary conditions, as the initial position, velocity and acceleration of the beam, its kinematic restrictions and the free stream definition. Moreover, this block reduces the cross-section of the beam into a stiffness, a mass and a damping matrices following Librescu’s theory.

Aerodynamic loads are calculated as the quasi-steady forces corrected with the dynamic effects. The quasi-steady forces are interpolated from the 2D problem and corrected with the three dimensional effects applying LLT. The dynamic effects are calculated from a Feed-Forward Neural Network.

The coupled solver calculates the displacement, velocity and acceleration of the beam nodes by a modal transformation and truncation of the degrees of freedom. Then the nodal coordinates are recalculated and the time step is advanced.


For a certain aerodynamic surface and using the aerodynamic data calculated though CFD simulations and a neural network to include the dynamic aerodynamic effects, fiber directions are evaluated to optimize its dynamic behavior. The results of a laminated flat plate beam of two plies (carbon fiber and Styrofoam) show that a good selection of the fiber orientation can improve flutter velocity by a 12%.  The code is also applied to a wing section allowing and restricting warping. The results evidence the influence of the fiber direction in the aeroelastic response.


Due the high stiffness to weight ratio of composite materials, their use in modern aircraft structures has been increased. A correct orientation of the fiber may take benefit from the bending-coupling effects of the section, increasing its dynamic limitations without weight penalty. This work provides a fast calculation tool to consider previous effects. In addition, the present work allows the user to also include nonlinear aerodynamics. Thus, structural behavior near stall conditions can be evaluated with a relative low computational cost.

Palabras clave

Aerodynamics Aeroelasticity Computational Fluid Dynamics Neural Networks Reduced Order Model

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Pedro Manuel Quintero Igeño

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