A rational elasto-plastic spatially curved thin-walled beam element

Torsion is one of the primary actions in members curved in space, and so an accurate spatially curved-beam element needs to be able to predict the elasto-plastic torsional behaviour of such members correctly. However, there are two major difficulties in most existing finite thin-walled beam elements, such as in ABAQUS and ANSYS, which may lead to incorrect predictions of the elasto-plastic behaviour of members curved in space. Firstly, the integration sample point scheme cannot capture the shear strain and stress information resulting from uniform torsion. Secondly, the higher-order twists are ignored which leads to loss of the significant effects of Wagner moments on the large twist torsional behaviour. In addition, the initial geometric imperfections and residual stresses are significant for the elasto-plastic behaviour of members curved in space. Many existing finite thin-walled beam element models do not provide facilities to deal with initial geometric imperfections. Although ABAQUS and ANSYS have facilities for the input of residual stresses as initial stresses, they cannot describe the complicated distribution patterns of residual stresses in thin-walled members. Furthermore, external loads and elastic restraints may be applied remote from shear centres or centroids. The effects of the load (and restraint) positions are important, but are not considered in many beam elements. This paper presents an elasto-plastic spatially curved element with arbitrary thin-walled cross-sections that can correctly capture the uniform shear strain and stress information for integration, and includes initial geometric imperfections, residual stresses and the effects of the load and restraint positions. The element also includes elastic restraints and supports, which have to be modelled separately as spring elements in some other finite thin-walled beam elements. Comparisons with existing experimental and analytical results show that the elasto-plastic spatially curved-beam element is accurate and efficient.