Bending, vibration, buckling analysis of bi-directional FG porous microbeams with a variable material length scale parameter

Finite elemen model for the structural behaviours of bi-directional (2D) FG porous microbeams based on a quasi-3D theory and modified strain gradient (MSGT) is presented. As main novelty this study, in order to capture accurately size effects, MSGT employed with three material length scale parameters (MLSPs) rather than modifed couple stress (MCST) only one MLSP. The properties including MLSPs are varied both axial thickness directions as well porosity. By using theory, which inludes normal shear deformations, governing equations static, vibration buckling analysis derived solved by Hermite-cubic beam element various boundary conditions. Through numerical examples, effects variable MLSP porosity index two deflections, natural frequencies loads 2D examined.