NUMERICAL SIMULATION OF DYNAMIC LARGE DISPLACEMENTS OF HALE AIRCRAFT WINGS

Resumo

We revisit a classical structural engineering problem, fist solved by Euler and Bernoulli, that
of large transversal displacements of cantilever beams. Their pioneering work, in the 16th century,
stablished that curvature is proportional to the applied bending moment. In this context, many posterior
authors simplified the resulting differential equation by assuming that, for small displacements, this
curvature could be taken as the second partial derivative of the beam’s axis transversal displacement
with respect to the its longitudinal coordinate. This assumption may be adequate for Civil, Naval and
Mechanical Engineering usual purposes, as in these fields of application such displacements are usually
small. In recent aerospace applications this assumption is no long acceptable. HALE (High-Altitude
Long-Endurance) aircraft wings are known to undergo large flexural displacements, due to their
relatively small stiffness. Further, they are usually built of new high technology flexible materials. Thus,
it is a design necessity to evaluate its deformed shape along time as it interferes with aeroelastic and
aerodynamic concerns. In this paper, we present a simple, low cost, numerical solutions of the exact
Euler-Bernoulli differential equation of the “elastica”, to be compared to contemporaneous nonlinear
large-scale Finite Element models via available either academic or commercial codes. The proposed
algorithms basically numerically integrates the exact Euler-Bernolli differential equation using the
MATLAB ode 45 code. The goal is always simulation of the dynamic behavior of such aircraft wings
under turbulent aerodynamic excitation.