Dynamic Shape Reconstruction of Three-Dimensional Frame Structures Using the Inverse Finite Element Method

Abstract eng:
A robust and efficient computational method for reconstructing the threedimensional displacement field of truss, beam, and frame structures, using measured surfacestrain data, is presented. Known as “shape sensing”, this inverse problem has important implications for real-time actuation and control of smart structures, and for monitoring of structural integrity. The present formulation, based on the inverse Finite Element Method (iFEM), uses a least-squares variational principle involving strain measures of Timoshenko theory for stretching, torsion, bending, and transverse shear. Two inverse-frame finite elements are derived using the interdependent interpolations whose interior degrees-of-freedom are condensed out exactly at the element level. In addition, relationships between the order of kinematic-element interpolations and the number of required strain gauges are established. As an example problem, a thin-walled, circular cross-section cantilevered beam subjected to harmonic excitations in the presence of structural damping is modeled using iFEM; where, to simulate strain-gauge values and to provide reference displacements, a high-fidelity MSC/NASTRAN shell finite element model is used. Examples of low and high-frequency dynamic motion are analyzed and the solution accuracy examined with respect to the increased fidelity of the iFEM’s discretization and the number of strain gauges.

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