Membrane Shape and Transverse Load Reconstruction Using Inverse FEM

Thin structural components characterize a broad class of Micro-Aerial Vehicles (MAV). This work presents an original approach for the determination of transverse load distribution based on distributed strain measurements. 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. Surface strain measurements are 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 an analogous direct formulation, based on nonlinear membrane structural analysis implemented in a general-purpose multibody solver and tightly coupled in co-simulation with a CFD solver. The direct analysis is performed 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. The reconstructed load distributions are compared with the corresponding ones obtained using the direct analysis.