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Elasticity: Elastic Deformation of a Thin Plate

In: An Introduction to Scientific Computing

Author

Listed:
  • 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)

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.

Suggested Citation

  • Ionut Danaila & Pascal Joly & Sidi Mahmoud Kaber & Marie Postel, 2023. "Elasticity: Elastic Deformation of a Thin Plate," Springer Books, in: An Introduction to Scientific Computing, edition 2, chapter 0, pages 205-219, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-35032-0_9
    DOI: 10.1007/978-3-031-35032-0_9
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