Differences analysis between beam and shell theory in preliminary aircraft design

Kurzfassung

Before the detailed design of a new aircraft can be initiated, basic design parameters have to be defined and evaluated in the preliminary aircraft design. For this task fast and accurate methods are required to achieve results in an adequate computing time. This study analyzes the differences in using finite shell elements instead of beam elements for preliminary wing design. Therefore a wide range of conceivable wing geometries, including the A320 and A330 wings, as well as different load cases are computed with both theories and afterwards evaluated and compared. As results can be condensed that for wings, having geometry parameters comparable with current aircraft, the difference between the two computation theories concerning tip displacement, spanwise bending angle as well as torsion due to torsion moments is mostly smaller than ±5% for all load cases. But torsion due to the skew clamping at the root of swept wings is not covered by the beam theory. Therefore deltas in the angle of attack computation up to round +80% for 40° swept wings appear. The values of the computation of the integral von Mises stresses are between +1% and +9% higher in the beam computation than in the finite element shell computation for realistic wings. These deltas are mainly caused by differences in the shear stress computation at tapered wings and by the complex normal stress distribution at the root, which cannot be computed by the beam theory. Summarizing all results of this study, it can be said that the beam theory is a fast method for preliminary wing sizing that often leads to results within the demanded accuracy. Using the shell theory, nameable improvements relating to the torsion computation and some parts of the stress computation could get achieved.