A quasi-3D theory for functionally graded porous microbeams based on the modified strain gradient theory

In this paper, the size-dependent responses of functionally graded (FG) porous microbeams using a quasi-3D theory and the modified strain gradient theory are investigated. Three different porosity distribution models of the FG porous microbeams are considered. By using the rule of mixture, all material properties including the material length scale parameters (MLSPs) are functions of the thickness, porosity coefficient and gradient index. The size-dependent governing equations are derived, and beam element is used to solve the problems. The verification of the proposed model is carried out and the effects of variable MLSP, porosity coefficient, gradient index and boundary conditions on the structural responses of FG porous microbeams are investigated. It can be observed that the effect of variable MLSP is significant and should be included for an accuracy analysis of the FG porous microbeams.