Static and dynamic analysis of space frames using simple Timoshenko type elements

In this paper a finite element method for geometrically and materially non-linear analyses of space frames is described. Beams with both solid and thin-walled open cross-sections are considered. The equations of equilibrium are formulated using an updated incremental Lagrangian description. The elements developed can undergo large displacements and rotations, but the incremental rotations are assumed to be small. The material behaviour is described by elastoplastic, temperature-dependent elastoplastic and viscoplastic models with special reference to metals. Computationally, more economical formulations based on the relationship between stress resultants and generalized strain quantities are also presented. In the case of thin-walled beams the torsional behaviour is modelled using a two-parameter warping model, where the angle of twist and the axial variation of warping have independent approximations. This approach yields average warping shear strains directly from the displacement assumptions and no discrepancy between stress and strain fields exists.