Aeroelastic wing response analysis using finite elements in a large deformation direct Eulerian-Lagrangian formulation

In this dissertation, a finite element wing structural model with nonlinear large deformation capabilities is developed for the three-dimensional transonic flutter problem and aeroelastic calculations are presented for a series of flexible wings. The flow field is represented by the unsteady Euler equations, written in the Direct Eulerian-Lagrangian approach based on the Galerkin finite element method that employs a tetrahedral unstructured mesh. The nonlinear structural model is also based on the Galerkin finite element method, which employs the in-plane and out-of-plane degrees-of-freedom, stiffener elements and element attached Lagrangian coordinate systems in conjunction with a fixed Eulerian coordinate system to apply the shear deformable von Karman plate theory in the element level.; As a part of the Direct Eulerian-Lagrangian approach, the aerodynamic and structural models are integrated simultaneously using a four-stage explicit Runge-Kutta scheme. This insures the governing conservation laws are implemented correctly and prevents any spurious energy generation at the wing boundary. This approach, combined with a dynamically deforming mesh ensures that these models are coupled properly to each via boundary conditions at the fluid-structure interface and aerodynamic loads acting on the structure are determined correctly. The aerodynamic mesh moves with the wing surface during the aeroelastic response, and is deformed smoothly away from the wing using a spring analogy.; Several static and dynamic aeroelastic calculations are presented for the selected wing models and comparisons are done for different angles of attack, initial conditions and structural configurations. Compared to the old aeroelastic code, it is observed that the new in-plane and out-of-plane coupling effects and the element level calculations and kinematics used in the consistent aerodynamic load calculations and the dynamic mesh motion have significant importance in improving the accuracy of the new aeroelastic code. For example, the new aeroelastic code predicts that the ONERA M6 wing with thickness ratio h/croot = 0.0255 is on the stability boundary, as opposed to the old version, which sets this boundary at the ratio h/croot = 0.025.