Estimation of plate parameters from vertical displacement data using a family of plate models

Date

2023-02-17

Authors

White, Luther W.
Malysheva, Tetyana
Karlstrom, Leif

Journal Title

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Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

We develop a method for estimation of parameters of an elastic plate resting on a Winkler-type elastic foundation solely from data on the vertical displacements of the plate. The method allows one to estimate components of the external body force density field, plate thickness, elastic foundation stiffness parameters, horizontal displacements of the plate, and stresses. The key idea of the method is that multiple plate models are used simultaneously, namely the proposed reduced three-dimensional (R3D) plate model, the Mindlin plate model, and the thin plate model. The three plate models form a hierarchy of elastic plate models based on assumptions imposed on stresses, with the R3D plate model being the most generalized model and the thin plate model being the most constrained one. The hierarchical relationship among the plate models allows one to incorporate prior information into the estimation technique. The applicability of the proposed estimation method is illustrated by a numerical example.

Description

Keywords

Elastic plate model, Linear elasticity, Parameter estimation, Force estimation, Laccolith

Citation

White, L., Malysheva, T., & Karlstrom, L. (2023). Estimation of plate parameters from vertical displacement data using a family of plate models. <i>Electronic Journal of Differential Equations, 2023</i>(15), pp. 1-24.

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Attribution 4.0 International

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