A weak-form quadrature element formulation for 3D beam elements used in nonlinear and postbuckling analysis of space frames

A weak-form quadrature element formulation is presented for the three-dimensional beam element for use in the geometrically nonlinear and postbuckling analysis of space frames. Starting from the virtual work equation of a beam in the linearized, incremental sense, the quadrature element method (QEM) is employed to derive the elastic stiffness, geometric stiffness, and induced moment matrices of the beam with due account taken of the large rotations in three-dimensional space. All the stiffness matrices are adopted in the incremental-iterative analysis using the generalized displacement control (GDC) method, with specific considerations for the predictor and corrector phases. By comparing the results obtained for all the benchmark problems studied with existing ones, it is demonstrated that the present formulation is capable of predicting large displacements and rotations, as well as the postbuckling paths of space frames. The present formulation is featured by the fact that it is simple, straightforward, and reliable.