Biharmonic plate equation

Summary

The biharmonic plate equation $D \Delta^2 w = q$ gives the deflection $w$ of a thin elastic plate under a transverse load $q$. It is the main equation of linear Kirchhoff–Love plate theory, with bending stiffness $D = Eh^3/(12(1 - \nu^2))$. It is a fourth-order elliptic equation built from the biharmonic operator, and a clamped or simply supported edge supplies two boundary conditions. It is the two-dimensional analogue of the Euler–Bernoulli beam equation $EI w'''' = q$.