A quasi-3D modi ed strain gradient formulation for static bending of functionally graded micro beams resting on Winkler-Pasternak elastic foundation

This paper presents the bending analysis of simply supported Functionally Graded (FG) size-dependent beams based on modi ed strain gradient theory. Shear and normal deformations are considered in displacement eld according to hyperbolic shear deformation theory. Governing equations and corresponding boundary conditions for FG micro beam are derived utilizing principle of minimum total potential energy. Mori- Tanaka homogenization scheme and the classical rule of mixture are used for prediction of material properties through the thickness. E ects of Winkler-Pasternak elastic foundation parameters are studied at di erent side-to-thickness ratios. E ects of di erent aspect ratios, elastic foundation parameters, power law gradient indexes, and di erent loading conditions are investigated. The eciency and accuracy of the presented model is demonstrated against the existing results in particular cases.