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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 290301, 11 pages
http://dx.doi.org/10.1155/2015/290301
Research Article

Identification of Flexural Rigidity in a Kirchhoff Plates Model Using a Convex Objective and Continuous Newton Method

1Center for Applied and Computational Mathematics, School of Mathematical Sciences, Rochester Institute of Technology, 85 Lomb Memorial Drive, Rochester, NY 14623, USA
2Department of Mathematics and Computer Science, University of Catania, 95125 Catania, Italy
3Institute of Mathematics, Martin Luther University of Halle-Wittenberg, 06120 Halle (Saale), Germany

Received 29 March 2015; Revised 17 August 2015; Accepted 20 August 2015

Academic Editor: Evangelos J. Sapountzakis

Copyright © 2015 B. Jadamba et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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 shell models 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.