Plates - Basic assumptions and principles

Search site :

A plate

1. order linear thin plate theory is developed under the following assumptions:

  • The plate thickness, t, is much smaller than the plates dimensions in the x-y-plane.
  • Small deformations (less than 0.3 times the thickness).
  • The plates material is linear elastic, homgeneous, and isotropic.

A plate introduced to external load will have a deformation out of its own plane. The linear thin plate theory's aim is to establish equations to describe this deformation. To do this, we use three conditions, which are the same as for shell theory:

  • Equilibrium
    By looking at a small element of the plate, dxdy, we demand that stresses keep the plate element in equilibrium. The plate can now be comprised of a set of infinite small plate elements, who all satisfy this equilibrium.
  • Kinematic compatibility
    When the plate is deformed, the material still has to be continous. This condition implies that openings or overlap between the plate elements are not allowed.
  • Linear elastic material
    For a linear elestic material we have to have a linear relationship between stress and strain. This means that equilibrium and compatibility can be expressed unambiguously by either stress or strain.