Post-buckling analysis of microscale non-prismatic beams subjected to bilateral walls

Microdevices, consisting of axially loaded elements at the microscale, are typically designed as bilaterally constrained microbeams with non-prismatic shape configurations. The literature has been mainly focused on uniform microbeams. Here we report a novel class of non-prismatic, microscale beams confined by bilateral walls. A size-dependent theoretical model is developed to investigate the post-buckling response of the microbeams using the modified couple stress theory and Euler-Bernoulli beam theory. The size effect is considered by the material length scale factor l, the shape asymmetry is taken into account using the non-prismatic bending stiffness Bmx, and the bilateral constraints are solved using an energy method that minimizes the total energy of the deflected microbeams. Experiments and numerical simulations are carried out to validate the theoretical model at the macro- and microscale, respectively. Parametric studies are conducted to investigate the effects of the material factor l and shape configuration on the post-buckling behavior of the non-uniform microbeams. The highest achievable buckling mode is examined with respect to the ratios of beam length-to-constraints gap η=Lh and thickness-to-material length factor γ=tl. The model presented in this study can be used to tune the post-buckling response of the bilaterally constrained microbeams with non-prismatic shape configurations.