Innovative high-order beam-column element for geometrically nonlinear analysis with one-element-per-member modelling method

Modern structural design requires the nonlinear characteristics within structural behaviors to be considered in analysis. Due to the limited deformation capacity of the conventional cubic Hermite beam-column element, a frame member has to be finely meshed into a number of the beam-column elements for nonlinear analysis, leading to a huge computational expense. Moreover, the tedious modeling process makes the use of advanced analysis approaches, such as the direct analysis method, impossible for complicated structures. In this paper, a fourth-order displacement function and an advanced beam-column element with 16 independent degrees of freedom are proposed for elastic geometrically nonlinear analysis. The element formulation is developed based on the compatibility conditions at the end and internal nodes. The potential energy function is adopted to derive the element stiffness matrices, and the matrices are presented in the Gauss integral form for easy programming. The verification examples presented in this paper demonstrate the significant deformation capacity of this innovative element. The one-element-per-member modeling method can accurately and effectively capture the structural buckling capacity and post-buckling behaviors. The proposed method can considerably reduce modeling and computational efforts in engineering practices.