Plate Element

A plate can be considered as a 2D extension of a beam.

Basic assumptions

1. Thickness \(t \ll\) in-plane dimensions \(b, c\), generally \(t < \frac{1}{10} \min(b, c)\)
2. Transverse deflection \(w \ll t\)
   • otherwise, “von Kármán plate”

Kirchhoff assumptions

1. Normals remain normal
   • \(\gamma_{yz} = \gamma_{xz} = 0, \, \gamma_{xy} \neq 0\).
   • Shear in plane
2. Normal stress is negligible: \(\sigma_z = 0\), and also neglecting thickness change \(\varepsilon_z = 0\).
3. In-plane forces neglected: deflection \(w \ll t, \, u(x, y, 0) = v(x, y, 0) = 0\).