上海交通大学学报

上海交通大学学报（自然版） ›› 2011, Vol. 45 ›› Issue (10): 1469-1474.

• 物理学 • 上一篇    下一篇

大变形弹塑性梁的刚柔耦合动力学特性

石望，刘锦阳   

  1. (上海交通大学 船舶海洋与建筑工程学院， 上海 200240)
  • 收稿日期:2010-05-25 出版日期:2011-10-31 发布日期:2011-10-31
  • 基金资助:

    国家自然科学基金 (10872126)，高等学校博士学科点专项科研基金（20100073110007）资助项目

Investigation on Rigid-Flexible Coupling Dynamics for Elasto-Plastic Beam with Large Deformation

 SHI  Wang, LIU  Jin-Yang   

  1. (School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiaotong University, Shanghai 200240, China)
  • Received:2010-05-25 Online:2011-10-31 Published:2011-10-31

摘要： 研究了大变形弹塑性梁的刚柔耦合动力学特性.从弹塑性梁的非线性本构关系和非线性应变位移关系出发，给出了曲率的精确表达式；基于绝对节点坐标法，用虚功原理建立了大变形弹塑性梁的动力学变分方程；用有限元法对梁进行离散，建立了大变形弹塑性梁的刚柔耦合动力学方程.对重力作用下的柔性单摆进行数值仿真.结果表明，弹塑性梁的横向变形呈现平均值大和振幅衰减的特征，计算结果较基于小变形理论的一次近似模型稳定，适用于大变形问题.
 

关键词: 大变形, 弹塑性梁, 非线性本构关系, 动力学

Abstract: Rigid-flexible coupling dynamic performance of an elastoplastic beam with large deformation was investigated. Based on nonlinear constitutive relation and nonlinear strain-displacement relationship, and using exact expression of curvature, dynamics variational equations for an elasto-plastic beam with large deformation were established using virtual work principle and absolute nodal coordinate formulation. Finite element method was used for discretization, and then rigid-flexible coupling dynamic equations were established. The simulations of a single pendulum under gravity show that elasto-plastic strain leads to the increase of the absolute value of the average transverse deformation and the decrease of transverse vibration amplitude. Furthermore, the comparison of the present nonlinear formulation with oneorder approximate dynamic model based on the theory of small deformation shows that the present result is stable for large deformation problem.

Key words: large deformation, elastoplastic beam, nonlinear constitutive relation, dynamics

中图分类号: