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Bending of a rectangular plate under the action of a distributed force per unit area. For rectangular plates, Navier in 1820 introduced a simple method for finding the displacement and stress when a plate is simply supported.
For an isotropic, homogeneous plate under pure bending the governing equation is ... The boundary conditions along the edges of a rectangular plate are
Deformation of a thin plate highlighting the displacement, the mid-surface (red) and the normal to the mid-surface (blue) The Kirchhoff–Love theory of plates is a two-dimensional mathematical model that is used to determine the stresses and deformations in thin plates subjected to forces and moments.
Vibration mode of a clamped square plate. The vibration of plates is a special case of the more general problem of mechanical vibrations.The equations governing the motion of plates are simpler than those for general three-dimensional objects because one of the dimensions of a plate is much smaller than the other two.
The plate elastic thickness (usually referred to as effective elastic thickness of the lithosphere). The elastic properties of the plate; The applied load or force; As flexural rigidity of the plate is determined by the Young's modulus, Poisson's ratio and cube of the plate's elastic thickness, it is a governing factor in both (1) and (2).
In the absence of a qualifier, the term bending is ambiguous because bending can occur locally in all objects. Therefore, to make the usage of the term more precise, engineers refer to a specific object such as; the bending of rods , [ 2 ] the bending of beams , [ 1 ] the bending of plates , [ 3 ] the bending of shells [ 2 ] and so on.
The Mindlin hypothesis implies that the displacements in the plate have the form = (,) ; =, = (,)where and are the Cartesian coordinates on the mid-surface of the undeformed plate and is the coordinate for the thickness direction, , =, are the in-plane displacements of the mid-surface, is the displacement of the mid-surface in the direction, and designate the angles which the normal to the mid ...
Normally, = / for a rectangular section. is a distributed load (force per length). is the displacement of the mid-surface in the -direction. is the angle of rotation of the normal to the mid-surface of the beam.
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