On extended models of plates based on linear strain gradient elasticity

Here we discuss the possible ways of derivation of two-dimensional (2D) plate equations starting from the three-dimensional (3D) linear strain-gradient elasticity. Among various approaches we consider the direct approach, the through-the-thickness integration procedure and variational approaches based on minimization of total energy functional and other variational principles. We show that the non-classic boundary conditions of the 3D strain gradient elasticity and the reduction method may generally lead to different plate model, in general. As a result, the mechanics of plates based on strain gradient elasticity is broader than the classic theory.