Asymptotic homogenization for modeling of wingbox structures

The asymptotic homogenization technique has been used to analyze a wing box structure consisting of trapezoidally arranged reinforcements encased within thin rectangular plates. Ignoring stress concentration effects at the region of the overlap between the various components, the wingbox structure can be analyzed by handling each constituent independently from each other. To this end, a simpler structure was first considered which was made up of a base plate and a single stiffener web; the results were then extrapolated to those of the wingbox structure via superposition by adding in the contributions of each constituent of the overall unit cell. The work culminated in closed-form expressions for the effective in-plane elastic coefficients of the wingbox. This result demonstrates the attractiveness of the methodology in that it can be used in engineering analysis and design to customize the architecture of a thin-walled reinforced composite by changing some material or geometrical parameters of interest. Such parameters could be the material of the base plate, the spatial arrangement of the reinforcements, the relative sizes of the different constituents.