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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. This theory is an extension of Euler-Bernoulli beam theory and was developed in 1888 by Love [ 1 ] using assumptions proposed by Kirchhoff .
The Kirchhoff–Love theory is an extension of Euler–Bernoulli beam theory to thin plates. The theory was developed in 1888 by Love [2] using assumptions proposed by Kirchhoff. It is assumed that a mid-surface plane can be used to represent the three-dimensional plate in two-dimensional form.
This permits a two-dimensional plate theory to give an excellent approximation to the actual three-dimensional motion of a plate-like object. [1] There are several theories that have been developed to describe the motion of plates. The most commonly used are the Kirchhoff-Love theory [2] and the Uflyand-Mindlin.
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. The theory was proposed in 1951 by Raymond Mindlin. [1] A similar, but not identical, theory in static setting, had been proposed earlier by Eric Reissner in 1945. [2]
In the Kirchhoff–Love plate theory for plates the governing equations are [1], = and , = In expanded form, + = ; + = and + + = where () is an applied transverse load per unit area, the thickness of the plate is =, the stresses are , and
In the derivation of the Föppl–von Kármán equations the main kinematic assumption (also known as the Kirchhoff hypothesis) is that surface normals to the plane of the plate remain perpendicular to the plate after deformation. It is also assumed that the in-plane (membrane) displacements are small and the change in thickness of the plate is ...
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)
Kirchhoff (crater) Kirchhoff equations; Kirchhoff integral theorem; Kirchhoff–Love plate theory; Kirchhoff's circuit laws; Kirchhoff's law of thermal radiation; Kirchhoff's theorem; Kirchhoff's diffraction formula