Second-order flexibility-based model for nonlinear inelastic analysis of 3D semi-rigid steel frameworks

This paper presents an efficient computer method for large deflection distributed plasticity analysis of 3D semi-rigid steel frameworks. A novel second-order inelastic flexibility-based element has been developed by combining the Maxwell-Mohr rule and the second-order force based functions for computation of the generalized displacements. The proposed model allows explicit and efficient modelling of the initial geometric imperfections and residual stresses and is intended to model the combined effects of nonlinear geometrical and gradual spread-of-plasticity by using only one beam-column element per physical member. At the cross-sectional level the proposed method addresses computational efficiency through the use of path integral approach to numerical integration of the cross-sectional nonlinear characteristics and residual stresses, enabling in this way the accurate geometrical specifications and precise modelling of cross-sections. The combined effects of material, geometric and connection behavior nonlinearity sources have been implemented in a general nonlinear static purpose computer program. Several computational examples are given to validate the effectiveness of the proposed method.