Augmented Lévy–Michell equations for flexural plates

A new sixth order, isotropic elastic and flexural plate theory is presented based on the fourth order equations of Lévy (1877) and Michell (1900). The lack of surface loading in these Lévy–Michell equations is overcome by including the dominant flexural component of Dougall’s (1904) solution for a point load on the surface of a three dimensional isotropic, elastic layer. The augmented plate equations are arranged to fit the form of a consistent sixth order system of isotropic plate equations which include the well known work of Reissner and static equations of Mindlin. Numerical applications to two three dimensional problems with analytical solutions show good comparative results.