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.