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This calculation was performed using Ansys. Bending of plates, or plate bending, refers to the deflection of a plate perpendicular to the plane of the plate under the action of external forces and moments. The amount of deflection can be determined by solving the differential equations of an appropriate plate theory.
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.
The aim of plate theory is to calculate the deformation and stresses in a plate subjected to loads. Of the numerous plate theories that have been developed since the late 19th century, two are widely accepted and used in engineering. These are the Kirchhoff–Love theory of plates (classical plate theory)
Deformation of a plate highlighting the displacement, the mid-surface (red) and the normal to the mid-surface (blue) The Reissner–Mindlin theory of plates is an extension of Kirchhoff–Love plate theory that takes into account shear deformations through-the-thickness of a plate.
A structure is called a plate when it is flat and one of its dimensions is much smaller than the other two. There are several theories that attempt to describe the deformation and stress in a plate under applied loads two of which have been used widely. These are the Kirchhoff–Love theory of plates (also called classical plate theory)
where E is the Young's modulus of the plate material (assumed homogeneous and isotropic), υ is the Poisson's ratio, h is the thickness of the plate, w is the out–of–plane deflection of the plate, P is the external normal force per unit area of the plate, σ αβ is the Cauchy stress tensor, and α, β are indices that take values of 1 and ...
Deflection (f) in engineering. In structural engineering, deflection is the degree to which a part of a long structural element (such as beam) is deformed laterally (in the direction transverse to its longitudinal axis) under a load. It may be quantified in terms of an angle (angular displacement) or a distance (linear displacement).
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).