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 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.

Creative Commons License

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.

Publication Date

2015

Comments

Originally published in "Mathematical Problems in Engineering" 2015,

http://dx.doi.org/10.1155/2015/290301

Document Type

Article

Department, Program, or Center

School of Mathematical Sciences (COS)

Campus

RIT – Main Campus

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