This work provides a detailed theoretical and numerical study of the inverse problem of identifying flexural rigidity in Kirchhoff plate models. From a mathematical standpoint, this inverse problem requires estimating a variable coefficient in a fourth-order boundary value problem.This inverse problem and related estimation problems associated with general plates and shellmodels have been investigated by numerous researchers through an optimization framework using the output least-squares (OLSs) formulation. OLS yields a nonconvex framework and hence it is suitable for investigating only the local behavior of the solution. In this work, we propose a new convex framework for the inverse problem of identifying a variable parameter in a fourth-order inverse problem. Existence results, optimality conditions, and discretization issues are discussed in detail. The discrete inverse problem is solved by using a continuous Newton method. Numerical results show the feasibility of the proposed framework.
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Jadamba, Baasansuren; Khan, Akhtar A.; Kahler, Raphael; Raciti, F.; and Winkler, B., "Identification of Flexural Rigidity in a Kirchhoff Plates Model Using a Convex Objective and Continuous Newton Method" (2015). Mathematical Problems in Engineering, 1-11. Accessed from
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