LAUSR

This paper proposes a spherical–deviatoric splitting of the strain gradient tensor to reinterpret the meanings of strain gradient components. The strain gradient theory of Zhou et al. is re-expressed in a more direct form, and, in parallel, the corresponding reduced theories are also obtained as comparisons. The effect of each strain gradient component is investigated by an application on static and dynamic analyses of an FGM micro-beam. To facilitate the modeling, the governing equation, initial condition and boundary conditions are derived by using Hamilton’s principle. The present model can reduce to the corresponding models based on the reduced strain gradient theories. The static bending and free vibration problems of a cantilever beam are solved. Numerical results reveal that the present model can predict a smaller deflection and a larger natural frequency compared with the reduced models, and the differences of results predicted by these different models are decreasing or even diminishing with the increase in beam thickness. The present theory predicts a stronger size effect since the contributions from all strain gradient components are considered. In addition, as far as the beam problems, the contributions from the symmetric part of strain gradient are ignorable compared with the contributions from the antisymmetric part of the strain gradient.