Kirchhoff–Love plate theory

Summary

Kirchhoff–Love plate theory is the classical plate theory for thin plates. It assumes that straight lines normal to the mid-plane stay straight, stay normal to the deformed mid-plane and keep their length. Then the whole deformation is determined by the in-plane displacements and the deflection $w$ of the mid-plane. For a linear isotropic plate the deflection solves the biharmonic plate equation $D \Delta^2 w = q$. It is the two-dimensional analogue of the Euler–Bernoulli beam equation.