Effect of higher order constitutive terms on the elastic buckling of thin-walled rods

• Summarizes a geometrically exact 7-DOF rod model with cross-sectional warping.
• Develops an elastic constitutive equation with higher-order strain terms.
• Proposes a simple warping function for thin-walled cross-sections.
• Shows the effects on the buckling and post-buckling behavior of beams and columns.

In this paper we revisit an elastic constitutive equation proposed in two previous works and extend it in order to include all higher-order terms on the deformations. Our purpose is to assess the influence of these terms on the elastic buckling of thin-walled rods. The resulting material model was incorporated into a geometrically exact rod formulation and implemented into a nonlinear finite element code. By means of simple numerical examples we show that the higher order terms may play a significant role on the values of the buckling loads and on the post-buckling behavior of thin-walled beams and columns.