Post-Buckling Analysis of Edge Cracked Columns Under Axial Compression Loads

In this paper, post-buckling analysis of an edge cracked cantilever column subjected to non-follower axial compression loads are studied by using the total Lagrangian Timoshenko column element approximation. The cross-section of the column is circular. The cracked column is modeled as an assembly of two sub-column connected through a massless elastic rotational spring. In the case of columns subjected to compression loads, load rise causes compressible forces end therefore buckling and post-buckling phenomena occurs. It is known that post-buckling problems are geometrically nonlinear problems. The considered highly non-linear problem is solved considering full geometric nonlinearity by using incremental displacement-based finite element method in conjunction with Newton–Raphson iteration method. There is no restriction on the magnitudes of deflections and rotations in contradistinction to von-Karman strain–displacement relations of the column. The columns considered in numerical examples are made of lower-carbon steel. In the study, the effect of the cracks on the deflections, rotational angles, post-buckling configuration and Cauchy stresses of the columns are illustrated in detail in post-buckling case. The difference between cracked case and intact case is investigated in detail.

Three-Dimensional Elasticity Solution for the Buckling of Sandwich Columns

A study of the buckling of a sandwich column, based on the three dimensional theory of elasticity, and a comparison with the simple Euler or transverse shear correction Engesser / Haringx / Timoshenko column buckling formulas, is presented. All three phases of the sandwich structure (two face sheets and the core) are assumed to be orthotropic and the column is in the form of a hollow circular cylinder. The Euler or Engesser / Haringx / Timoshenko loads are based on the equivalent axial modulus. Representative results show the significance of the effect of transverse shear in these sandwich structures.