A Numerical Method for Predicting Critical Behavior of Elasto-plastic Frame with Elements Obeying Deteriorating Stress-strain Relation

在弹塑性框架极限或临界性能的梁柱有限元分析中，必须生成符合本构律的刚度矩阵。在这种分析中，钢构件的局部屈曲和混凝土材料的大变形将由符合弹-退化塑性应力-应变模型且具有适当长度的单元来估计。对于具有弹退化塑性单元的框架模型，传统的迭代生成一致刚度矩阵的方法往往存在循环过程的缺陷。提出了一种用于弹塑性框架静力平衡路径预测的一致刚度矩阵生成算法。该算法利用了比较框架刚度矩阵的特征向量。通过对杆的屈曲行为和门式刚架的倒塌行为的数值分析，验证了该算法的有效性。仿真结果表明，该算法能有效地生成一致刚度矩阵，并能有效地选择临界点附近的控制路径参数。然而，该算法尚未用于分析单元服从退化应力-应变关系的框架的临界行为。本研究证实了相似策略在这种情况下生成一致刚度矩阵的效果。该算法为执行数值分析提供了合理的控制路径参数选择。

In the beam-column FEM analysis of ultimate or critical behavior of elasto-plastic frames, the stiffness matrix consistent with the constitutive law must be generated. In such an analysis, local buckling of steel member and large deformation of concrete material will be estimated by elements which obey elastic-deteriorating plastic stress-strain model and which have an appropriate length. A conventional iterative procedure for generating consistent stiffness matrix of a frame model with elastic-deteriorating plastic elements frequently leads to a pitfall of cyclic process. An algorithm for generating consistent stiffness matrix has been presented for predicting the static equilibrium path of elastio-plastic frames by the head investigator. The algorithm utilizes an eigenvector of stiffness matrix of the comparison frame. In the numerical analyses of the buckling behaviors of bars and of the collapse behaviors of portal frames, the algorithm has been verified. These simulations demonstrate that the algorithm functions effectively for generating the consistent stiffness matrix and for sellecting the control path-parameter in the vicinity of critical point. However, the algorithm has not been utilized in analyzing the critical behavior of the frame with elements obeying deteriorating stress-strain relation. The effect of the similar strategy for generating consistent stiffness matrix in such case is confirmed in this study. The algorithm provides an apt selection of the control path-parameter for execution of numerical analysis.