A Quasi 3D Modified Strain Gradient Formulation for Static Bending of Functionally Graded Micro beams Resting on Winkler-Pasternak Elastic Foundation

Abstract

This paper presents the bending analysis of simply supported functionally graded (FG) size dependent beams based on modified strain gradient theory. The shear and normal deformations are considered in displacement field 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. Effects of Winkler-Pasternak elastic foundation parameters are studied for different side to thickness ratios. Effects of different aspect ratios, elastic foundation parameters, power law gradient indexes and different loading conditions are investigated. The efficiency and accuracy of present model is demonstrated by comparing to the existing results in especial cases.