A modified strain gradient meshfree approach for functionally graded microplates

We propose a size-dependent moving Kriging meshfree approach for bending, free vibration and buckling analyses of functionally graded (FG) microplates using the refined plate theory (RPT) and modified strain gradient theory (MSGT). The RPT retains only four variables and reduces one variable when comparing to the original higher order shear deformation theory. For microstructures, three length-scale parameters (LSPs) related to size effects are enhanced in the classical RPT. Material properties of FG microplates are calculated by a rule of mixture. The virtual work principle is used to form the weak forms, and the displacements, natural frequencies and buckling loads of FG microplates are then determined using moving Kriging meshfree method. Numerical validations are shown to evaluate effects of geometrical parameters, boundary conditions, volume fraction and LSPs on displacements, natural frequencies and buckling loads of FG microplates. As observed results, an increase and decrease of natural frequencies, buckling loads and displacements of FG microplates are respectively confirmed. In addition, the modified couple stress model or classical RPT model is recovered when a few LSPs are negligible.

Automated summary

A size-dependent moving Kriging meshfree approach is proposed for analyzing bending, free vibration, and buckling of functionally graded microplates. The study uses virtual work principle, mixed rule for material properties, and refined plate theory to determine displacement, natural frequencies, and buckling loads of FG microplates. Results demonstrate that natural frequencies, buckling loads, and displacements of FG microplates are influenced by geometrical parameters, boundary conditions, and length-scale parameters.