Modified Strain-Based Geometrically Nonlinear Beam Formulation for Modeling Slender Wings with Deformable Cross-Sections

A strain-based geometrically-nonlinear beam formulation has previously been developed and applied in analyzing slender wings of very flexible aircraft. This formulation features strains and curvatures of the beam reference line as the independent variables in the solution. In this study, the deformation of beam cross-sections (warping) is allowed in the modeling process. The warping field of the beam is represented by the Ritz approximation functions at each cross-section, as well as their spatial variations along the beam span. This treatment enhances the one-dimensional beam formulation associated with large-scale beam bending/twist curvatures, with the additional elastic degrees of freedom that consider smallscale local deformations of the cross-sections. It has the potential to provide an efficient solution base for preliminary design and time-domain analysis of flexible aircraft with compliant airfoils, as well as the shape and load control of very flexible aircraft with active actuations.