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

Electronic Journal of Differential Equations

article

Luther W. White¹  Tetyana Malysheva²  Leif Karlstrom³ 

[1] Oregon Applied Mathematics Institute 2130 Ridgeway Dr.;Department of Mathematics & Statistics Resch School of Engineering University of Wisconsin-Green Bay 2420 Nicolet Drive;Department of Earth Sciences 1272 University of Oregon Eugene

关键词: Elastic plate model;    linear elasticity;    parameter estimation;    force estimation;    laccolith;   

DOI  :  10.58997/ejde.2023.15

学科分类：数学（综合）

来源: Texas State University

【 摘 要 】

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.

【 授权许可】

CC BY