A Meshfree Proportional Topology Optimization of Bi-Directional Functionally Graded Plates Based on Third-Order Shear Deformation Theory

Abstract

This work develops a meshfree topology optimization formulation for plates composed of bidirectional functionally graded materials (2D-FGM). The plate response is described using the third-order shear deformation theory, allowing transverse shear effects to be incorporated without shear correction factors. The radial point interpolation method (RPIM) is adopted to construct the approximation field, thereby reducing the reliance on conventional mesh-based discretization. The spatial variation of material properties in the two in-plane directions is defined through a power-law model. For topology optimization, a proportional topology optimization (PTO) strategy is employed to iteratively redistribute material according to the structural response without requiring sensitivity gradients. Several numerical studies are carried out to assess the performance of the proposed approach. The results indicate that the present formulation can produce stiff and smooth material layouts for 2D-FGM plates. The proposed RPIM-PTO framework therefore provides an effective computational tool for the lightweight design of advanced graded plate structures.