Nonlinear Membrane Inverse Finite Element Model for Pliant Wings

Thin structural components, characteristic of a broad class of Micro-Aerial Vehicles (MAV), are analyzed using a direct solution approach in co-simulation with fluid-dynamics solvers. The procedure is integrated within a general-purpose multibody system dynamics formulation. A variational formulation is developed for the inverse problem of the reconstruction of full-field structural displacement of membrane wings subjected to static and unsteady loads, utilizing surface strain measurements estimated from Digital Image Correlation (DIC). Moving Least Squares are used to smooth and remap measurements as needed by the inverse solution meshing, and to map the structural and fluid interface kinematics and loads during the fluid-structure co-simulation. The inverse analysis is verified by reconstructing the deformed solution obtained with the analogous direct formulation applied on a different mesh and subsequently re-sampled. Both the direct and the inverse analyses are validated by comparing the direct predictions and the reconstructed deformations with experimental data for prestressed rectangular membranes subjected to static and unsteady loads.