An asymptotic analysis of anisotropic heterogeneous plates with consideration of end effects

A finite element-based asymptotic analysis tool is developed for general anisotropic plates. The formu-lation 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 func-tion 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 orthog-onality 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. 1.