Richardson extrapolation and strain energy based partition of unity method for analysis of composite FG plates.

This work focuses on numerical analysis of static bending and free vibration of Functionally Graded plates (FGP) using Reissner–Mindlin theory with interior holes employing an effective Richardson extrapolation-based reduced integration (REQ) approach and strain energy. The partition of unity method is used to articulate stabilizing function locally, which possesses the local stabilizing ability to avoid zero-energy or hourglass effects, for each sub-quadrilateral or sub-cells (SCs) in the REQ scheme. The current technique computes element stiffness matrices and mass matrices for the bending and shear energies of the FGPs at the location (0,0) in the standard mapped (ξ , η) plane using reduced integration. It identifies the required local stability and refinement for field variable function from sub-cells to parent quadrilaterals, enhances the computational accuracy at a low cost, possesses a better convergence rate, and avoids shear-locking phenomenon in the analysis. Numerous benchmark numerical examples are considered for static bending and free vibration analysis with different types of boundary conditions with cutouts. The calculated final normalized central deflection and frequency values are compared with reference data available in literature, which confirms the accuracy, rate of convergence, shear-locking issues and computational performance of the developed REQ method. Investigations are conducted on FGPs with internal holes using various material gradient indices, boundary conditions, and geometric aspect ratios. • Richardson extrapolation based integration scheme simplifies the computation process using reduced integration scheme. • The computational time is significantly reduced as compared to the conventional quadrature. • Quite efficient method for analyzing with plate elements without much burden on number of integration points in the element. [ABSTRACT FROM AUTHOR]