A powerful numerical approach for the axisymmetric bending response of shear deformable two-directional functionally graded (2D-FG) plates with variable thickness

Abstract

In the present article, a powerful numerical approach is applied to the axisymmetric bending of 2 D-FG circular and annular plates with variable thickness. The mechanical properties of the materials of the plate are assumed to vary continuously both in the radial and thickness directions. The principle of minimum total potential energy is used to obtain the governing equations. Shear deformation is considered based on the first-order shear deformation theory (FSDT). These ODEs are solved via the Complementary Functions Method (CFM) for the first time. The novelty of this paper is the infusion of the CFM to the axisymmetric bending of a wide range of annular or circular plates, with variable thickness, radially FG (RFG), FG in thickness direction, or 2D-FG. In addition to adopting this effective numerical approach to the present class of problems, various parametric studies are presented to show the influence of material variation parameters and geometric constants on the axisymmetric bending response of the considered structures. Results of the proposed approach are validated with those carried out by FEM and those of the available published literature. An excellent agreement is observed.