Luther White, Tetyana Malysheva, Leif Karlstrom
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.
Submitted February 28, 2022. Published February 17, 2023.
Math Subject Classifications: 35Q74, 74B05, 74K20, 35Q86, 86-10.
Key Words: Elastic plate model; linear elasticity; parameter estimation;
force estimation; laccolith.
DOI: https://doi.org/10.58997/ejde.2023.15
Show me the PDF file (1457 KB), TEX file for this article.
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Luther W. White Oregon Applied Mathematics Institute 2130 Ridgeway Dr., Eugene, OR 97401, USA email: oregami.lwhite@gmail.com |
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Tetyana Malysheva Department of Mathematics & Statistics Resch School of Engineering University of Wisconsin-Green Bay 2420 Nicolet Drive, Green Bay, WI 54311, USA email: malyshet@uwgb.edu |
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Leif Karlstrom Department of Earth Sciences 1272 University of Oregon Eugene, OR 97403, USA email: leif@uoregon.edu |
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