The bending-gradient theory for laminates and in-plane periodic plates

In a recent work, a new plate theory for thick plates was suggested where the static unknowns are those of the Kirchhoff-Love theory, to which six components are added representing the gradient of the bending moment (Lebée and Sab, Int J Solids Struct, 48(20):2878-2888, 2011a). This theory, called the Bending-Gradient theory, is the extension to multilayered plates and to in-plane periodic plates of the Reissner-Mindlin theory which appears as a special case when the plate is homogeneous. The Bending-Gradient theory was derived following the ideas from Reissner, J Appl Mech, 12(2):69-77, (1945). However, it is also possible to derive it through asymptotic expansions. In this lecture, the latter are applied one order higher than the leading order to a laminated plate following monoclinic symmetry. Using variational arguments, it is possible to derive the Bending-Gradient theory. Then, some applications are presented and the theory is finally extended to in-plane periodic plates.