Highly Efficient Pretwisted Element for Buckling Analysis of Pretwisted Members Under Various Loading Conditions

This paper is aimed at formulating a highly efficient pretwisted beam element for the buckling analysis of linearly pretwisted columns under various end loads. First, a torsional (or convected) coordinate system for the pretwisted beam of rectangular cross-sections is defined, in addition to the fixed coordinate system. Based on the updated Lagrangian framework, the strain-displacement relationship and displacement transformation in the deformed configuration are obtained. Then the principle of virtual work in incremental form is employed to derive the elastic and geometric stiffness matrices for the pretwisted element. In the numerical examples, the efficiency and robustness of the pretwisted beam elements are demonstrated via comparison with the solutions obtained by ABAQUS shell elements and conventional straight beam elements. It was shown that the presence of pretwisting can significantly increase the critical load of the columns under compression or bending, as well as of the arches under in-plane loads, while it will adversely reduce the stability resistance under torsional loads. Due to its relatively high computational efficiency with respect to the shell elements, the pretwisted element should find applications in simulation of blades encountered in wind turbines or rotors industry and pretwisted members in buildings and bridges, in dealing with the initial stress or deformation effects.