Membrane Shape and Load Reconstruction from Measurements Using Inverse Finite Element Analysis

An original variational formulation is developed for the inverse problem of reconstructing full-field structural displacement and pressure distribution of membrane wings subjected to steady loads from membrane strain distribution. A direct solution approach in cosimulation with fluid-dynamics solvers is also presented. Moving least squares are used to smooth and remap surface strain measurements, estimated from digital image correlation, as needed by the inverse solution meshing. The same approach is used to map the structural and fluid interface kinematics and loads during the fluid-structure cosimulation. 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 subjectedtostatic and unsteady loads. The load distributions reconstructed using the inverse analysis are compared with the corresponding loads obtained using the direct analysis. The inverse analysis runs on standard off-the-shelf PCs and can be implemented in real time, providing load-distribution estimates at a rate in the order of tens of data sets per second