Second-Order Elasto-Plastic Analysis of Frames by Differential Quadrature Element Method

A new differential quadrature element model is presented for the second-order elasto-plastic analysis of frames in this study. The new model is based on the differential quadrature method (DQM) and the finite-cut technique. Firstly the basic equilibrium differential equations of members, the compatibility conditions of joints and the equilibrium equations of joints for the second-order analysis of frames are established. The differential quadrature method is used to discretize the basic equations and then the stiffness equations of the whole structure can be derived. While the corresponding boundary conditions are considered, the mechanical behavior of frames can be obtained. The yielding development along the axis of the member can be taken into consideration by selecting several discrete points and simultaneously the yielding development across the section can be considered using the layered approach. The full historical second-order elasto-plastic analysis is achieved by the incremental iterative algorithm. According to the new model derived in this paper, the interrelated structural calculating program is worked out. The results of numerical examples demonstrate the validity of the differential quadrature element model (DQEM). The new model can be used in the second-order elasto-plastic analysis of arbitrary frames.