Kirchhoff–Love plate theory

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 using assumptions proposed by Kirchhoff. The theory assumes that a mid-surface plane can be used to represent a three-dimensional plate in two-dimensional form.

The following kinematic assumptions that are made in this theory:

Let the position vector of a point in the undeformed plate be ${\displaystyle \mathbf {x} }$. Then

The vectors ${\displaystyle {\boldsymbol {e}}_{i}}$ form a Cartesian basis with origin on the mid-surface of the plate, ${\displaystyle x_{1}}$ and ${\displaystyle x_{2}}$ are the Cartesian coordinates on the mid-surface of the undeformed plate, and ${\displaystyle x_{3}}$ is the coordinate for the thickness direction.

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