Linear and nonlinear analyses of micro and nano structures based on higher-order elasticity theories

In this study, bending and buckling analyses of micro and nano beams have been investigated by modified couple stress theory and modified strain gradient elasticity theory. Bernoulli-Euler and Timoshenko beam models are used. Results are obtained for various loading at simply and cantilever boundary conditions. The effect of additional material length scale parameters in equations is observed. When the results of both bending and buckling analyses are investigated, it is determined that the values which are obtained by Modified Strain Gradient Elasticity Theory are very different than the values of classical theory. Furthermore, the values based on Modified Couple Stress Theory are comparatively closer to the values of classical theory than Modified Strain Gradient Theory.