The inverse Finite Element Method (iFEM) is applied to reconstruct the displacement field of a shell structure which undergoes large deformations using discreet strain measurements as the prescribed data. The iFEM computations are carried out using an incremental procedure where at each load step, the incremental strains are used to evaluate the incremental displacements which in turn update the geometry of the deformed structure. The efficacy of the proposed approach to predict large displacements is examined using two case studies involving a cantilevered wing-shaped plate and a clamped plate. The incremental iFEM procedure is demonstrated to be sufficiently accurate in terms of reproducing the correct nonlinear character of the load-displacement curve even when a reduced number of strain sensors is used. Therefore, this approach may have important implications for real-time monitoring of aerospace structures that undergo large displacements.
Methods for real-time reconstruction of structural displacements using measured strain data is an area of active research due to its potential application for Structural Health Monitoring (SHM) and morphing structure control. The inverse Finite Element Method (iFEM) has been shown to be well suited for the full-field reconstruction of displacements, strains, and stresses of structures instrumented with discrete or continuous strain sensors. In practical applications, where the available number of sensors may be limited, the number and sensor positions constitute the key parameters. Understanding changes in the reconstruction quality with respect to sensor position is generally difficult and is the aim of the present work. This paper attempts to supplement the current iFEM modeling knowledge through a rigorous evaluation of several strain–sensor patterns for shape sensing of a rectangular plate. Line plots along various sections of the plate are used to assess the reconstruction quality near and far away from strain sensors, and the nodal displacements are studied as the sensor density increases. The numerical results clearly demonstrate the effectiveness of the strain sensors distributed along the plate boundary for reconstructing relatively simple displacement patterns, and highlight the potential of cross-diagonal strain–sensor patterns to improve the displacement reconstruction of more complex deformation patterns.
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