|Table of Contents|

Research on CR formulation of large rotational symmetric plane beam element(PDF)

长安大学学报（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

Issue:
2023年4期
Page:
60-67
Research Field:
桥梁与隧道工程
Publishing date:

Info

Title:
Research on CR formulation of large rotational symmetric plane beam element
Author(s):
DENG Ji-hua1; 2;  CHEN Li-qiang1;  TIAN Zhong-chu1;  TAN Ping3
(1. School of Civil Engineering, Changsha University of Science and Technology, Changsha 410114, Hunan, China; 2. Ministry of Education Key Laboratory of Safety Control of Bridge Engineering, Changsha University ofScience & Technology, Changsha 410114, Hunan, China; 3. Earthquake Engineering Research &Test Center, Guangzhou University, Guangzhou 510405, Guangdong, China)
Keywords:
[HQ]Key words:bridge engineering;  plane beam element;  co-rotational method;  geometric nonlinearity;  symmetric tangent stiffness matrix;  virtual work principle
PACS:
U441
DOI:
10.19721/j.cnki.1671-8879.2023.04.007
Abstract:
According to the shortage of tangent stiffness matrix asymmetry of nonlinear plane beam element by using co-rotational method in former studies, researches were carried out to reasonably select the origin and coordinate axis direction of the plane beam element co-rotation coordinate system. Firstly, the origin was set at the average value point of the left and right element node coordinates, and the x-axis was always in the connecting direction from the left node to the right. The coordinate system moved with the rigid body rotation and translation of the node, and the element node coordinates and displacement were calculated on the basis of deducting the element rigid displacement. Secondly, based on the principle of equal virtual work in structural coordinate system and co-rotating coordinate system as well as the principle of geometric consistency, the symmetrical tangent stiffness matrix and the node resistance algorithm of plane beam elements under the condition of large rotation and small strain were established. Combined with the solution method of nonlinear equations which unifies the load increment method and displacement increment method, the corresponding calculation program was developed. The cantilever beam and William's toggle frame with bending moment at the beam end were calculated and compared. The results show that for the former example, the beam is divided into 20 elements, and load increment method is adopted by 10 uniform loading levels. The numerical solution obtained is in good agreement with the analytical solution and the difference between the two is less than 0.0001, which can be negligible even when the cantilever beam is bent into a circle. As for the latter example, each frame member is homogeneously divided into 10 elements. The extreme point of load-displacement curve can be successfully passed through after transforming the solution method of nonlinear equations to displacement increment method and the calculated value is basically consistent with William's test. The research results can provide a powerful tool for the nonlinear analysis of plane beam structures.9 figs, 24 refs.

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Last Update: 2023-08-20