Bending analysis of FG microbeams resting on Winkler elastic foundation via strain gradient elasticity

Abstract

In this study, bending response of non-homogenous microbeams embedded in an elastic medium is investigated based on modified strain gradient elasticity theory in conjunctions with various beam theories. The governing differential equations and related boundary conditions are derived with the aid of minimum total potential energy principle. Elastic medium is modeled by Winkler foundation model. Bending problem of simply supported microbeams made of functionally graded materials is solved by Navier’s solution procedure. A detailed parametric study is performed to investigate the effects of the material length scale parameters-to-thickness ratio l/h, material property gradient index k, slenderness ratio L/h, Winkler modulus kw and shear correction factor on the bending behavior of embedded functionally graded microbeams.