柔性框架结构动力非线性分析的刚体准则法

大跨、高层等柔性结构，其动力响应往往表现出大位移、大转动等非线性特征。动力非线性问题的分析关键在于运动方程的高效稳定求解，以及单元大转动产生的结点力增量的有效计算。动力时程分析通常采用直接积分法，但对于强非线性动力问题，直接积分法难以兼顾计算精度与稳定性。该文基于几何非线性分析的刚体准则，针对杆件结构大转动小应变的非线性问题，提出了一种新型空间杆系结构动力非线性分析的刚体准则法。该方法采用满足刚体准则的空间非线性梁单元，结合HHT-α法求解结构运动方程，并将刚体准则植入动力增量方程的迭代求解过程以计算结点力增量。通过典型柔性框架算例结果表明，该文方法可以有效分析柔性框架结构的强动力非线性行为。与高精度单元相比，该文采用的单元刚度矩阵构造简明，计算过程简洁；与商业软件所用方法相比，单元数和迭代步少，精度高，适于工程应用。

RIGID BODY RULE METHOD FOR DYNAMIC NONLINEAR ANALYSIS METHOD OF FLEXIBLE FRAMED STRUCTURES

The dynamic response of flexible structures such as the large-span spatial structures and high-rise structures usually show nonlinear characteristics with large displacements and large rotations. The key problems of the dynamic nonlinear analysis are the stable calculation method for motion equations as well as the way to tackle the large rotations during the motion process. The direct integration method is widely used in the time domain analysis, which can hardly keep balance between the accuracy and stability of computation for the strong dynamic nonlinear problems. Herein, aiming to tackle the nonlinear problems of large displacements and small strain of framed structures, a novel dynamic nonlinear analysis method for a 3-D framed structure is proposed by using the rigid-body-rule (RBR). In the proposed method, the 3-D beam element satisfied the rigid body rule is adopted, while the equations of motion are solved by HHT-α method because of its advantages in stability and accuracy. The increments of nodal forces are tackled with the RBR that is rooted into the incremental-iterative process. The results of typical numerical examples show that the proposed method can effectively analyze the strong dynamic nonlinear behavior of flexible frame structures. Compared with the present high-precision element, the element stiffness matrix of proposed RBR-based beam element is simple and the calculation process was concise. Compared with the method used in commercial software, highly accurate results can be obtained using the proposed method with less elements and iteration steps, which is suitable for engineering application.