Elasticity: Elastic Deformation of a Thin Plate

Ionut Danaila (), Pascal Joly, Sidi Mahmoud Kaber and Marie Postel
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Ionut Danaila: Université de Rouen Normandie, CNRS, Laboratoire de mathématiques Raphaël Salem
Pascal Joly: Laboratoire Jacques-Louis Lions
Sidi Mahmoud Kaber: Sorbonne Université, CNRS, Université Paris Cité, Laboratoire Jacques-Louis Lions
Marie Postel: Sorbonne Université, CNRS, Université Paris Cité, Laboratoire Jacques-Louis Lions

Chapter Chapter 9 in An Introduction to Scientific Computing, 2023, pp 205-219 from Springer

Abstract: Abstract We study in this chapter the deformation of a thin plate. In our example, the plate is part of a condenser microphone, such as one may find inside a telephone (or a cellular phone). When the user speaks, the plate moves in response to changes in the acoustic pressure induced by sound waves. The deformation is modeled by a scalar nonlinear PDE (involving the Laplacian and the bilaplacian operators) on a 2D bounded domain. The presented numerical method is based on second-order finite differences for the space discretization and a fixed point algorithm to handle the nonlinearity.

Date: 2023
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DOI: 10.1007/978-3-031-35032-0_9

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