MECHANICAL BEHAVIOR ANALYSIS OF MICRO-SCALED FUNCTIONALLY GRADED TIMOSHENKO BEAMS BY THE STRAIN GRADIENT THEORY

摘要

In this paper, a size-dependent formulation is developed for Timoshenko beams made of functionally graded materials (FGM). The developed formulation is based on the strain gradient theory; a non-classical continuum theory able to capture the size-effect in micro-scaled structures. Considering the material length scale parameters of the FG beams vary through the thickness, the new equivalent length scale parameters are proposed as functions of the constituents' length scale parameters to describe the size-dependent static and dynamic behavior of FG microbeams. The governing differential equations of equilibrium and both classical and non-classical sets of boundary conditions are derived for the proposed strain gradient FG Timoshenko beam using variational approach. As case studies, the static bending deformation of the new model is investigated for an FG simply supported beam made of tungsten/copper (W/Cu) in which properties are varying through the thickness according to a power law. The results of the new model are compared to those of the modified couple stress and the classical theories where the two latter theories are special cases of the strain gradient theory.