Plate
A plate is flat body whose thickness is very small compared to other dimensions. Due to this reason 2D finite elements are sufficient for analysis of plates. Plate carries a lateral load by bending. Plates develop bending moments in two directions and and a twisting moment in one direction.
Depending on whether transverse shear deformation is considered or neglected, two plate theories are available. In Kirchhoff theory or thin plate theory the transverse shear deformation is not considered i.e a normal to the undeformed midsurface remains normal to the deformed midsurface. In Mindlin theory or Mindlin-Reissner theory transverse shear deformation is accounted and normal to the midsurface donot remain normal to the deformed midsurface.
The forces or loads acting on plates can be in plane (plane stress) or/and out of plane (bending). For the in plane loads the state of strain is uniquely described by two displacement u and v. For the out of plane loads the state of strain is uniquely described by the displacement in the normal direction to the plate i. e w and two rotations. The displacements prescribed for 'in plane' forces do not affect the bending deformations ans vice versa. The rotation around the normal to the plate does not enter as a parameter into definition of deformations in either of the modes.
Finite Element Analysis of Plates:
Check the following pages for finite element analysis of plates.
2. Plane Stress
5. Natural Frequencies of Plate