A moving Kriging meshfree approach for free vibration and buckling analyses of porous metal foam plates

In this paper, the free vibration and mechanical buckling analyses of the metal foam plates with porosities via a moving Kriging meshfree method based on the higher-order shear deformation theory are studied. The displacement fields are approximated by the moving Kriging shape functions, which satisfy Kronecker’s delta property. Thanks to that property, the essential boundary conditions can be directly imposed the same with finite element method. In this study, the porosities are distributed by uniform, symmetric, and asymmetric distributions along the thickness direction. The natural frequency and critical buckling load of the metal foam plate are determined by solving the explicit governing equations, which are derived through the variational formulation. The influence of the porosity distribution, porous coefficient, width-to-thickness ratio and boundary condition on the natural frequency and critical buckling load of the porous metal foam plate is investigated and discussed in detail. Numerical examples indicate that the present approach is stable and well accurate predictions for investigating vibration and buckling behaviors of the porous metal foam plate. Moreover, an increase of the porous coefficient makes a decline of the natural frequencies and critical buckling loads of the plate.