Size -dependent behaviour of functionally graded sandwich microbeams based on the modified strain gradient theory

This paper studies the bending, buckling and free vibration analyses of functionally graded (FG) sandwich microbeams using the third-order beam theory. The modified strain gradient theory (MSGT) with three material length scale parameters (MLSPs) is used to capture the size effect. The Mori-Tanaka homogenization scheme is employed to model the material distributions through the thickness. Finite element model is formulated to solve the problems. Verification studies for epoxy and FG microbeams are carried out to validate of the present model. Comparisons of the results of three different models such as MSGT, the modified couple stress theory (MCST) and classical continuum theory (CCT) are presented. Effects of small size, gradient index, shear deformation and boundary conditions on the structural behaviours of microbeams are investigated. Some new results of FG sandwich microbeams for both models (MCST and MSGT) are presented for the first time and can be used as benchmark in future studies. © 2020 Elsevier Ltd