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Aeroelastic Effect Considering Structural Geometrical Nonlinearity
Guowei Yang, Guannan Zheng, Xueyuan Nie

Last modified: 2018-06-25


High-altitude, long-endurance aircrafts are being considered for long-term surveillance, environmental sensing and communication relay. Due to the requirements of high performance and light weight, these aircraft are usually designed with high-aspect-ratio wings, which will have large structural deformation in flight. Linear structural theory fails to accurately analyze their aeroelastic characteristics. The aeroelastic analyzing method with the consideration of structural geometrical nonlinearity needs to be developed.

In the paper, firstly, Simo’s geometrically exact rod model was introduced. Since the rotation field of the rod is represented by a curve in the special orthogonal group, the configuration becomes a nonlinear differentiable manifold. The governing equation of rod motion and the weak forms of balance question can be described. Then the numerical analysis method was developed. Finally, some example cases were used to validate the developed method.

Then the Steklov-Poincare nonlinear operators are introduced for the solution of the fluid-structure interaction problem(FSI). One of the advantages of the method is that the FSI problem is reduced to an equation only involving the interface variables and can be solved by the fixed-point algorithm with dynamic Aitken relaxation. By the coupling iteration between fluid and structural equations, the kinematic and dynamic conditions at the fluid-structure interface can be accurately satisfied.

Two solvers are developed for the FSI problems which the geometrically exact rod model is used for the structural simulation. The only difference is the solution of fluid equation. One is to use Theodorsen’s theory to calculate aerodynamic loads and PK method to solve the flutter equation in frequency domain. Another is to use the computational fluid dynamics (CFD) for the solution of the fluid equation in time domain.

Flow induced oscillation problem, namely an elastic beam is attached to a rigid square, is simulated with the developed CFD/CSD coupling method. The vortices in the wake of the rigid square interact with the beam and excite large amplitude oscillations. The vertical beam tip displacement is displayed versus time and its oscillating frequency and the amplitude are compared with other reference’s results calculated.

For a high-aspect-ratio wing with the thrust and the mass of engine simplified as the lateral follower force and the centered mass, and with the developed frequency domain method, the parametric influences on aeroelastic characteristics are analyzed by the changes of the vertical bending-torsional rigid ratio, centered mass, lateral follower force and the location of centered mass. The CFD/CSD coupling method is also used for the solutions of some typical cases and their result differences of the two methods are compared with each other.


Aeroelastic Effect;Structural Geometrical Nonlinearity;Steklov-Poincare nonlinear operators

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