A dynamic asymptotic model of linear elastic orthotropic plates: first and second-order terms

By using the asymptotic method combined with variational approach a new dynamic model of elastic orthotropic plates is derived. This model accounts for rotational inertia and takes into account second order terms U 2 and σ 2 in the asymptotic expansions of displacements and stresses. To avoid the boundary layer analysis, the boundary conditions for U 2 are satisfied in a suitable averaged sense. Convergence theorem is formulated. Influence of the second-order terms on plate response in the static case is investigated.