ON ASYMPTOTIC EXPANSIONS FOR THE 6TH-ORDER LINEAR-THEORY PROBLEM OF TRANSVERSE BENDING OF ORTHOTROPIC ELASTIC PLATES

We extend earlier considerations of the sixth-order linear theory problem of shear deformable orthotropic plates by a systematic analysis of the boundary layer problem along straight edges parallel to the directions of elastic symmetry of the plate. We extend the concept of 'soft' support as a condition for the smooth transition from sixth-order theory to fourth-order theory in the limit of vanishing plate thickness to a concept of 'almost soft' support. Additionally, we obtain a generalized version of an earlier result concerning a system of boundary conditions for the differential equations of the classical fourth-order theory which is such that this fourth-order theory accounts for transverse shear deformation effects of the first order.