Large Deformation Shape Sensing Using a Nonlinear Strain to Displacement Method

A three-dimensional strain to displacement method based on a nonlinear modal formulation is proposed. Strain and deformation modes are used for the mapping procedure with the recently developed Modal Rotation Method (MRM) for the nonlinear three-dimensional geometry reconstruction. The method is demonstrated numerically on a test case of a complex beam-like structure. A sensitivity study is then presented for the effects of different solution parameters, such as the number of modes and sensors, and the measurement noise. The method is then applied on an experimental test case of the Pazy wing that was designed to undergo extremely large deformations (over 50% span). The wing is equipped with fiber optic strain sensors (FOS) and motion-tracking cameras. The study incorporates an experimental displacement-strain modal analysis to obtain the modal data directly from the instrumented wing. Results from a structural test are then used to validate the scheme. Wing deformation measured using cameras is correlated with deformation obtained by applying the proposed nonlinear strain-based method, a linear strain-based method, and the direct integration of strain. The new method is applied with modal parameters obtained from a finite element analysis and from vibration tests. Finally, the deformation of a highly flexible wing measured in a wind tunnel test is correlated with the proposed nonlinear strain-based method.