Multi-gradation coupling effects in FGM plates

New coupling effects are revealed and described in plates with multi-gradation of material coefficients. Three variants of plate bending theory (such as the Kirchhoff-Love theory, the 1st and 3rd order shear deformation plate theory) are considered within unified formulation. It is known that transversal gradation of Young's modulus gives rise to coupling between the bending and in-plane deformation modes in plates under transversal loading. In this paper it is shown that combination of transversal gradation of Young's modulus with in-plane gradation of Young's modulus and/or variation of plate thickness leads to deflections of such plates subject to in-plane loading. The governing equations and boundary conditions for static problems are derived in the unified formulation using the variational principle. For numerical simulations of multi-gradation coupling effects, it is developed the strong formulation with using the meshless approximation of field variables by the Moving Least Square (MLS) approximation. Several numerical examples are presented for illustration of the multi-gradation coupling effects in bending of elastic FGM (Functionally Graded Material) plates. The role of the boundary conditions as well as the thickness and shear deformations is studied via numerical simulations and comparisons of the plate responses obtained in three plate bending theories.