“…There is p lenty of research on the small-scale effect, but these studies simultaneously introduce many controversies [ 4 , 9 , 12 , 13 , 14 ]. In most existing research, the classical beam model is modified through non-local theories to consider the small-scale effect [ 4 , 14 , 15 ]. These theories mainly include the stress gradient theory, , and the strain gradient theory, .…”