Nonlinear bending and post-buckling of extensible microscale beams based on modified couple stress theory

Abstract

This study proposes a computationally efficient approach to nonlinear bending and thermal post-buckling problems in Euler–Bernoulli microbeams based on modified couple stress theory under geometrically accurate relationships. The governing equations, which consider the size effect and the axis extensibility, are formulated via the equilibrium of an infinitesimal element. The proposed model, which encompasses the size-independent and Von Kármán nonlinear theory, is solved using the shooting technique after transformation into a two-point boundary value problem. The proposed method was validated based on comparisons with several case studies using existing simulations. The influences of the length scale parameter and the Poisson ratio on the bending and thermal post-buckling behaviors of microbeams are discussed in detail. The numerical results show that the intrinsic size dependency of the material and the Poisson ratio make the microbeam behave in a relatively stiff manner, thereby leading to smaller deformations and greater increases in the buckling temperature.