Numerical Methods For The Nonlinear Aeroelastic Problems With Large Amplitude Geometric Deformations

The flexible large-amplitude deformation of highly flexible air vehicles will cause complicated nonlinear aeroelastic problems.Large-amplitude deformation,on the one hand,will change the aerodynamic characteristics of the vehicle dramatically.On the other hand,it will likely cause the structure to run beyond the strength limit of materials.Actually,the last few decades have already witnessed the flight collapse accidents caused by the nonlinear aeroelastic problems of flexible structures that happened in real engineering problems.Therefore,the nonlinear aeroelastic effect must be considered during the design stage of flexible air vehicles.Currently,the nonlinear aeroelastic problems of three-dimensional flexible structures with large-amplitude deformations have not been studied systematically.The research is of great significance for the study of the aerodynamic load,structural response and the stability of flight dynamics of flexible aircraft near flutter boundaries.The difficulty of aeroelastic modeling with large amplitude geometric deformations mainly lies in three aspects: 1)geometric nonlinearity caused by flexible deformations;2)unsteady aerodynamic problems caused by large-amplitude structural deformations;3)the coupling between these two aspects.The study in this paper is mainly dealt with the above three problems.The aim of this paper is to establish time-domain nonlinear aeroelastic models and to study the nonlinear aeroelastic behaviors of flexible air vehicles based on three dimensional plate structures.The research contents,the main conclusions and the innovations of this paper are listed as follows:1.The abilities in modeling large amplitude aeorelastic responses of different finite elements are studied.Based on a standard cropped delta wing model,the difference between a mulit-variable solid shell element and von Karmann nonlinear plate element,corotational shell element and high order solid element in ANSYS software is studied.The comparison of computed results with experimental results indicates that the solid shell element used in the current study has the best performance in eliminating shear locking problems caused by large amplitude structural deformations.2.The modeling of the unsteady aerodynamics caused by large amplitude structural deformations is also studied.The difference between a potential flow theory and a computational fluid dynamics method in the nonlinear aeroelastic simulations is studied.Numerical results show that,although the aeroelastic responses with the two methods are similar in trend with each other,the simulation with a CFD method is more coincident with experimental results than that with a potential flow theory.Besides,in the aeroelastic simulations with large amplitude structural deformations of a cantilever plate model,the transient structural response with the unsteady vortex lattice method lasts longer than that with the computational fluid method.The traditionally believed advantage of computational efficiency for an unsteady vortex lattice method over the computational fluid dynamics method is not apparent anymore.The reason may likely lies in the fact that the aerodynamic damping of an unsteady vortex lattice method is weaker than that of a computational fluid dynamics method.3.The problem of coupling strategy in the nonlinear aeroelastic modeling is studied.A traditional loose coupling strategy,an improved loosely coupled strategy and a strong coupling strategy are adopted to combine the computational structural dynamics solver and the computational fluid dynamics solver in the nonlinear aeroelastic modeling.The numerical simulation for a flexible cantilever plate illustrates that,in small-amplitude limit cycle oscillations,the results of the improved loose coupling strategy are close to that of the strong coupling strategy.While the difference between the traditional loose coupling strategy and the strong coupling strategy becomes larger and larger with time evolves due to time staggering problems.In large-amplitude limit cycle oscillations,both the traditional and the improved loose coupling strategies cause big differences in structural responses compared with the strong coupling strategy.Moreover,numerical results illustrate that,in the nonlinear aeroelastic simulations of low-aspect-ratio structures,when only geometric nonlinearity dominates structural responses,the difference between different coupling strategies is not very significant.When both geometric and aerodynamic nonlinearities dominate the response,the traditional and the improved loose coupling strategies will cause remarkable errors compared with the strong coupling strategy.4.The post flutter characteristics of a three dimensional cantilever plate are studied.Numerical simulations illustrate that after the inflow velocity goes beyond the flutter boundary of the plate,the structure will first undergoes period-1 limit cycle oscillation.With the increase of inflow velocity,high-frequency components in the structural responses become strong.The limit cycle oscillation transits from period-1 to period-3 motions.The structural response shows chaotic movements under high inflow velocities.The effects of different nonlinearities are also studied.In large-amplitude limit cycle oscillations,geometric nonlinearity changes the stiffness of the structure,which constrains the structural response to a limited amplitude.The aerodynamic nonlinearity caused by wing tip vortices will also cause significant influence on the structural response.Besides,the impact of wing tip vortices is much stronger than that caused by wake vortices.5.The aeroelastic characteristics of the cantilever plate under large angles of attack are investigated.Numerical simulations illustrate that,under a relatively large initial angles of attack,quasi-periodic or chaotic movements may exist in structural responses.The effects of geometric and aerodynamic nonlinearities are remarkable in the transient structural responses.The leading edge vortices on the structure will be influenced by the wing tip vortices.Consequently,the leading edge vortices will move toward the symmetric plane of the structure during the process of shedding toward the trailing edge.The vortices will finally form a vortex ring above the leeward side of the structure,which are an important source of aerodynamic nonlinearity.