Rigid body rule method for dynamic nonlinear analysis method of flexible framed structures

被引：0
|
作者：
Chen Z.-H. [1 ,2 ]
Tao Y.-C. [3 ]
He M. [1 ]
机构：
[1] School of Civil Engineering, Chongqing University, Chongqing
[2] Key Lab. of New Technol. for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing
[3] College of Civil Engineering and Architecture, Zhejiang University, Hangzhou
来源：
Tao, Yu-Chen (taoyuchen1103@zju.edu.cn) | 1600年 / Tsinghua University卷 / 38期
关键词：
Direct integration method; Flexible framed structure; Geometric nonlinearity; HHT-α; method; Nonlinear dynamics; Rigid body rule;
D O I：
10.6052/j.issn.1000-4750.2020.10.0731
中图分类号：
学科分类号：
摘要：
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. © 2021, Engineering Mechanics Press. All right reserved.
引用
收藏
页码：57 / 65
页数：8
相关论文
共 18 条
  • [1] Bathe Klaus-Jurgen, Baig M M I., On a composite implicit time integration procedure for nonlinear dynamics, Computers & Structures, 83, 31, pp. 2513-2524, (2005)
  • [2] Bathe K J, Ramm E, Wilson E L., Finite element formulations for large deformation dynamic analysis, International Journal for Numerical Methods in Engineering, 9, 2, pp. 353-386, (1975)
  • [3] Remseth S N., Nonlinear static and dynamic analysis of framed structures, Computers & Structures, 10, 6, pp. 879-897, (1979)
  • [4] Cardona A, Geradin M., A beam finite element non-linear theory with finite rotations, International Journal for Numerical Methods in Engineering, 26, 11, pp. 2403-2438, (1988)
  • [5] Le T N, Battini J M, Hjiaj M., Efficient formulation for dynamics of corotational 2D beams, Computational Mechanics, 48, 2, pp. 153-161, (2011)
  • [6] Le T N, Battini J M, Hjiaj M., A consistent 3D corotational beam element for nonlinear dynamic analysis of flexible structures, Computer Methods in Applied Mechanics and Engineering, 269, 1, pp. 538-565, (2014)
  • [7] Du Ke, Teng Nan, Sun Jingjiang, Et al., A progressive collapse analytical model of RC frame structures based on corotational formulation for force-based fiber elements, Engineering Mechanics, 36, 3, pp. 95-104, (2019)
  • [8] Deng Jihua, Tan Jianping, Tan Ping, Et al., A geometric nonlinear plane beam element based on corotational formulation and on stability functions, Engineering Mechanics, 37, 11, pp. 28-35, (2020)
  • [9] Yang Y B, Chiou H T., Rigid body motion test for nonlinear analysis with beam elements, Journal of Engineering Mechanics, 113, 9, pp. 1404-1419, (1987)
  • [10] Yang Y B, Kuo S R., Theory & analysis of nonlinear framed structures, (1994)
12