A new trigonometric beam model for buckling of strain gradient microbeams

In this paper, a new microstructure-dependent sinusoidal beam model for buckling of microbeams is presented using modified strain gradient theory. This microbeam model can take into consideration microstructural and shear deformation effects. The equilibrium equations and corresponding boundary conditions in buckling are derived with the minimum total potential energy principle. Buckling problem of a simply supported microbeam subjected to an axial compressive force is analytically solved by Navier solution procedure. Influences of thickness-to-length scale parameter and slenderness ratios on buckling behavior are discussed in detail. It is observed that the size dependency becomes more important when the thickness of the microbeam is closer to material length scale parameter. Also, it can be said that the effects of shear deformation are more considerable for short and thick beams with lower slenderness ratios.