Approximation theory of three-dimensional elastic plates and its boundary conditions without using Kirchhoff-Love assumptions (Q1891992)

A plate theory is derived for a linear-elastic isotropic layer without using Kirchhoff-Love assumptions. The theory is based on the principle of stationary potential energy for a three-dimensional body, with relaxed geometric boundary conditions. By means of special trial functions and integration with respect to the thickness direction, the problem is reduced to a two-dimensional one, whose first order approximation is worked out particularly. This reduced problem is characterized by six unknown functions to be determined. The discussion of the boundary conditions is not satisfactory, and no reference is made to related papers in the literature.