Identification of Flexural Rigidity in a Kirchhoff Plates Model Using a Convex Objective and Continuous Newton Method. (8th September 2015)

• Record Type: Journal Article
• Authors: Jadamba, B.; Kahler, R.; Khan, A. A.; Raciti, F.; Winkler, B.
• Other Names: Sapountzakis Evangelos J. Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2015(2015)
• Publication Date: 2015-09-08
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2015/290301
• Languages: English
• ISSNs: 1024-123X

Abstract

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.