On the Buckling of a Two-Dimensional Micropolar Strip

Abstract

This study examines the buckling of a single strip of material, modeled as a two-dimensional (2D) micropolar solid. The effects of material microstructure are incorporated by modeling the material using micropolar theory. By setting the micropolar constants to zero, the equations of classical elasticity are obtained and these results are compared to the buckling analysis performed by previous authors on elastic materials. In the limiting case, when the thickness of the strip becomes small in comparison to the overall length, the micropolar beam equations are developed. Because buckling analysis requires the consideration of geometric nonlinearity, nonlinear micropolar equations are derived using a variational procedure, which also results in variationally consistent boundary conditions. Due to the complexity of micropolar theory, its application has been limited to linear analysis with a few exceptions.