Buckling of micropolar beams by an improved first order deformation theory

In this paper, we present a variational formulation to study the buckling behavior of micropolar beams by using an improved 3D deformation theory. A micropolar continuum applied to beams has been developed using its natural Lagrangian kinematic relations. The Rodriguez rotation measure was used to describe the rotational degrees of freedom. Additionally, a Taylor expansion was performed to linearize the kinematic relations. For the buckling analysis, the Trefftz criterion procedure was applied. A finite element model was derived for the solution of the variational problem using spectral interpolation functions for a higher convergence rate and for avoiding shear locking problems. The results describe the influence of the micropolar parameters and size-dependent behavior. Finally, the model was used to evaluate the buckling loads of simply-supported functionally graded beams considering experimental material parameters.