基于刚体准则的空间框架弹塑性非线性分析方法

基于刚体准则,采用二阶改进塑性铰模型,构建了空间弹塑性梁单元及其弹塑性刚度矩阵,建立了高效简洁的非线性增量迭代方法,可有效分析截面屈服产生的有限转动、二阶效应等柔性空间钢框架结构材料与几何非线性耦合效应。对于受初始力平衡的单元,随着单元的刚体转动与移动,其初始平衡力在当前状态下应保持大小不变,仅方向随单元做刚体转动,而实际结构的变形可以视为较大的刚体位移与较小的自然变形(弹性或非弹性)的组合。将此刚体准则植入增量迭代法,在预测阶段采用通过了刚体运动检验的弹塑性矩阵,从而合理确定迭代初始方向;在修正阶段使用刚体准则计算单元结点力,保证了计算精度。对三个典型柔性框架结构所做分析表明,本文方法能够准确预测结构的极限承载力值与塑性铰发展过程。对于空间框架结构,每根杆件仅需划分一个单元,极大提高了计算效率、降低了计算成本。与塑性区法、纤维元法以及考虑截面翘曲的修正切线刚度法等相比,本文提出的方法具有物理概念明确、单元划分少、刚度矩阵简单、分析过程简洁、计算精度与效率高等显著特点,适于工程应用。

Elasto-plastic nonlinear analysis method for spatial frame based on rigid body rule

Based on the rigid body rule and the second-order refined plastic hinge model, the spatial elasto-plastic beam element and its stiffness matrix are constructed in this paper. A highly efficient and simple nonlinear incremental iteration method is developed to effectively analyze the coupling effect of material and geometric nonlinearity of flexible spatial steel frame structures such as finite rotation and second-order effect caused by section yield. For the element equilibrium of initial force, the initial equilibrium force should keep numerical value unchanged with the rigid body rotation and movement of the element, and only its direction should rotate with the rigid body rotation. The deformation of the actual structure can be regarded as a combination of large rigid body displacement and small natural deformation (elastic or inelastic). In this paper, the rigid-body rule is implanted into the incremental iteration method, and the elasto-plastic matrix which satisfies the rigid body motion test is adopted in the predictor phase, so that the initial iteration direction can be reasonably determined. In the corrector phase, the rigid body rule is used to calculate the nodal force of the element to ensure the accuracy of calculation. The analysis of three typical flexible framed structures has shown that the proposed method can give the accurate prediction of the ultimate capacity and plastic hinge developments with only one element for each bar of the spatial framed structure. In such a way, the calculation efficiency is greatly enhanced and the cost is reduced. Compared with the plastic zone method, the fiber element method and the modified tangent stiffness method considering warping, the proposed method in this paper has the characteristics of clear physical concept, less element division, simple stiffness matrix and analysis process, high calculation accuracy and efficiency, and is suitable for engineering application.