Size dependent large displacements of microbeams and microframes

Abstract

The size dependent large displacement behavior of planar microbeams and microframes is studied in this paper using a corotational beam element. To account for the size effect, the modified couple stress theory (MCST) is employed in conjunction with Euler-Bernoulli beam theory in deriving the internal force vector and the tangent stiffness matrix of the beam element. The Newton-Raphson based iterative procedure is used in combination with the arc-length method to solve the nonlinear equilibrium equation and to trace the equilibrium paths. Various microbeams and microframes are analyzed to show the influence of the size effect on the large deflection behavior of the microstructure. The obtained result reveals that the size effect plays an important role on the large deflection response, and the displacements of the structure are over estimated by ignoring the size effect. A parametric study is carried out to highlight the influence of the material length scale parameter on the large displacement behavior of the microbeams and microframes.