A Variational Principle for Reconstruction of Elastic Deformations in Shear Deformable Plates and Shells

ABSTRACT A variational principle is formulated for the inverse problem of full-field reconstruction of three-dimensional plate/shell deformations from experimentally measured surface strains. Theformulation is based upon the minimization of a least squares functional that uses the completeset of strain measures consistent with linear, first-order shear-deformation theory. Theformulation, which accommodates for transverse shear deformation, is applicable for the analysisof thin and moderately thick plate and shell structures. The main benefit of the variationalprinciple is that it is well suited for C 0 -continuous displacement finite element discretizations,thus enabling the development of robust algorithms for application to complex civil andaeronautical structures. The methodology is especially aimed at the next generation of aerospacevehicles for use in real-time structural health monitoring systems. 1. INTRODUCTION Structural health monitoring is recognized as a key technology that is needed for thedevelopment of the next generation of aerospace vehicles. The principal purpose is real-timemonitoring of the aerospace vehicle structural integrity using a network of in-flight sensors thatmeasure quantities such as temperature and strain. Using such measurements, general structuraldeformations need to be identified, together with the material or structural failure modes. A greatdeal of recent work on structural health monitoring can be found in [1, 2].Real-time OreconstructionO of full-field structural displacements is also essential technologyfor providing feedback to the actuation and control systems for the morphed wings of the nextgeneration aircraft. It is envisioned that load-carrying structural components will be instrumentedwith a network of sensors measuring surface strains (e.g., fiber optic sensors with Bragggratings). The reconstruction of the displacement vector at every material point of the structure(i.e., full-field reconstruction) from a set of strain measurements represents an inverse problem.Knowing a detailed state of structural deformations also implies that other essential responsequantities such as stress and failure criteria can be assessed.

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