Transonic aeroelasticity solutions using finite elements in an arbitrary Lagrangian-Eulerian formulation

In this dissertation, a finite element technique for the solution of transonic aeroelasticity problems is presented and demonstrated using several two-dimensional configurations. The flow field behavior is represented by the unsteady Euler equations, written in an arbitrary Lagrangian-Eulerian form, while the structural motion is described using Lagrange's equations. Both the fluid and structural equations are discretized in the spatial domain using finite element methods. The solution technique uses a novel approach in which the fluid equations are solved simultaneously with the structural equations using the same Runge-Kutta time marching scheme for both.; Transonic solutions are presented for prescribed oscillatory motion of an isolated airfoil in both pitch and plunge degrees of freedom. Airfoil surface pressures computed using this technique show good agreement with published analytical results and test data. Flutter solutions are also presented for the airfoil and are compared to the results of other analytical techniques. Supercritical as well as subcritical bifurcation to a stable limit cycle was observed in the solutions. Under certain conditions the limit cycle oscillations were observed to modulate between two different amplitudes.; A detailed panel flutter study is also presented for the Mach number range from 0.8 to 2.5. The two-dimensional panel used in the study is represented by nonlinear finite elements that account for in-plane stretching induced by transverse deflections. The existence of traveling wave motion with shocks moving across the panel surface is shown. When the dynamic pressure was raised above the stability limit, divergence was observed at Mach numbers below unity, flutter and divergence were observed at Mach one, and only flutter was found in supersonic flows. Flutter was also found in very thin panels at high transonic Mach numbers. Near Mach one, flutter consists of traveling wave motion with shocks on the surface of the panel. In the Mach number range from about 1.3 to 1.5, the higher modes of the panel respond, resulting in high stresses. The aeroelastic response of these modes is shown to be effectively eliminated by the addition of damping.