* the thickness of the plate does not change during a deformation.

Displacement field

The Kirchhoff hypothesis implies that the displacement field has the formwhere and are the Cartesian coordinates on the mid-surface of the undeformed plate, is the coordinate for the thickness direction, are the in-plane displacements of the mid-surface, and is the displacement of the mid-surface in the direction.

If are the angles of rotation of the normal

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