A refined isogeometric plate analysis of porous metal foam microplates using modified strain gradient theory

In this paper, we study the free vibration and buckling analyses of the porous metal foam microplates based on the isogeometric approach. Three types of porosity distribution along the plate thickness including uniform, symmetric and asymmetric are used to describe the material properties of the microplate. The modified strain gradient theory (MSGT) with three length scale parameters is incorporated into the refined higher-order shear deformation plate theory (RPT) to investigate small-scale effect on free vibration and buckling behaviors of the plate at micro level. The RPT has only four unknown variables to save computational costs. The explicit governing equations of the microplates are derived by using Hamilton's principle and then solved by isogeometric analysis (IGA), which is suitable for a numerical implementation of the size-dependent model within required third-order derivatives in the weak form. The influences of length scale parameters, porosity distributions, porous coefficient and geometric parameters on the natural frequencies and critical buckling loads of the microplates are discussed. Small scale effects and porous coefficient lead to an increase and a decrease in the stiffness of the microplate, respectively.