平面钢框架弹塑性大变形简化分析方法

Simplified Analysis of Elasto-plastic Plane Steel Frames with Large Displacement

提出了用准有限区域法来分析平面钢框架弹塑性大变形．根据采用内力形式描述的截面屈服面方程，首先推导了截面的一致切线弹塑性刚度矩阵，然后沿杆长积分得到梁柱单元的刚度矩阵．由于屈服面方程大都存在奇异点，提出加权法以获得奇异点处的截面刚度矩阵．采用协同旋转法处理大变形，采用Ｓｉｍｏ提出的算法使截面的内力组合保持在屈服面上．最后给出一个算例说明准有限区域法的有效性．

A quasi - plastic - zone method for analysis of elasto - plastic plane steel frames with large displacements is described in the paper. The consistent tangent stiffness matrix of a cross section is derived according to the yield surface equation in terms of stress resultants, then stiffness matrix of the beam (column) element is attained by a numerical integration method. Because there exist some singular points on yield surfaces, the weighting method is proposed to attain stiffness matrix of the cross section at the singular points. The co-rotational formulation is adopted to deal with he deformation, and algorithm proposed by Simo is used to keep the combination of stress resultants on the yield surface. A numerical example is presented to demonstrate the accuracy and efficiency of the proposed method.