平面刚架弹塑性大位移分析的多刚体离散元法

Multi rigid body discrete element method of large displacement elasto plastic analysis for plane frames

本文基于多刚体－弹簧系统模型，给出了求解平面刚架结构弹塑性、大位移极限承载力分析的多刚体离散元法。文中首先推导了多刚体离散元法在总体坐标下的切线刚度阵，建立多刚体离散元法的增量平衡方程；而后推导了多刚体离散元的弹塑性弹簧系数矩阵，建立了多刚体离散元内力屈服面塑性铰法的增量求解格式，成功地进行了平面钢框架的弹塑性、大位移极限承载力分析。计算结果与其他数值方法或实验结果吻合良好。

This paper presents a multi rigid body discrete element method based on the rigid body Spring model to solve the ultimate carrying load capacity of frame structures involving large displacement and elasto plasticity.At first, the tangential stiffness matrix of rigid body element is derived under global coordinate system and the incremental equilibrium equation is established. Then, the elasto plastic spring coefficient matrix of rigid body element is developed in terms of the plastic incremental theory and a incremental numerical formulation of multi rigid body element method is formed by implementing plastic hinge method of internal force plastic interaction surface. The formulation is successfully applied to the ultimate carrying load capacity of plane steel frames involving large displacement and elasto plasticity.Results obtained from this approach agree with independent published numerical or test results, which maked multi rigid body element method more appealing to ultimate carrying load capacity analysis.