A finite element-based asymptotic analysis tool is developed for general
anisotropic plates. The formulation begins with three-dimensional equilibrium
equations in which the thickness coordinate is scaled by the characteristic
length of the plate. This allows us to split the equations into two parts,
such as the one-dimensional microscopic equations and the two-dimensional
macroscopic equations, via the virtual work concept. The one-dimensional
microscopic analysis yields the through-the-thickness warping function at each
level, which does not require two-dimensional macroscopic analysis. The
two-dimensional macroscopic equations provide the governing equations of the plate
at each level in a recursive form. These can be solved in an orderly manner, in
which proper macroscopic boundary conditions should be incorporated. The
displacement prescribed boundary condition is obtained by introducing the
orthogonality condition of asymptotic displacements to the plate fundamental
solutions. In this way, the end effects of the plate are kinematically corrected
without applying the sophisticated decay analysis method. The developed
asymptotic analysis method is applied to semiinfinite plates with simply
supported and clamped-free boundary conditions. The results obtained are
compared to those of three-dimensional FEM, three-dimensional elasticity, and
Reissner–Mindlin plate theory. The usefulness of the present method is also
discussed.
