• CN:11-2187/TH
  • ISSN:0577-6686

›› 2011, Vol. 47 ›› Issue (24): 69-73.

• 论文 • 上一篇    下一篇



  1. 燕山大学机械工程学院;燕山大学亚稳材料制备技术与科学国家重点实验室
  • 发布日期:2011-12-20

Displacement Solution of Axisymmetrical Plane Stress Problem in Plastic State

LI Weimin;QIU Ping;LUO Junting   

  1. College of Mechanical Engineering, Yanshan University State Key Laboratory of Metastable Materials Science and Technology, Yanshan University
  • Published:2011-12-20

摘要: 由于数学手段上的限制,解析求解一直是固体力学中一条难以逾越的鸿沟。从轴对称问题的应力平衡微分方程、几何方程与Levy-Mises增量理论出发,采用位移法分析轴对称平面应力问题,以位移增量的形式给出塑性状态下轴对称平面应力问题位移解的通解。研究结果表明,塑性状态下轴对称平面应力问题中,位移解的结果与材料属性无关。按照研究结果,利用位移和应力混合边界条件,分析发电机护环液压胀形过程中坯料高度及外径的变化规律,建立以增量形式表述的计算护环内径、外径及高度变化的递推公式。所得结果与相关文献的试验数据相比具有较高的精度:外径相对误差为0.09%,高度相对误差为1.178%,完全能够满足实际工程的需要。

关键词: 发电机护环, 塑性状态, 位移法, 液压胀形, 轴对称平面应力问题, 扁疤宽度, 车辆-轨道耦合系统动力学模型, 车轮扁疤三维模型, 冲击振动, 轮轨接触几何关系

Abstract: Because of the restrictions on mathematical method, analytical solution has been an insuperable barrier in the solid mechanics. From the differential equation of stress equilibrium, geometry equations and the Levy-Mises incremental theory of plasticity, axisymmetrical plane stress problem is analyzed using displacement method. The general solution of displacement for the axisymmetrical plane stress problem in plastic state is given in the form of displacement increment. The research results indicate that displacement solution of axisymmetrical plane stress problem in plastic state has no dependence on the material properties. According to this result, height and diameter variation of generator retaining ring in hydroforming process is analyzed in the combined boundary condition of displacement and stress. And recurrence formula to calculate outer diameter, inner diameter and height of protective-ring is established. Comparing with the experimental data from related literature, the calculation’s results have high precision:The relative error is 0.09% in external diameter and 1.178% in height. It is fully able to meet the actual needs of practical engineering.

Key words: Axisymmetrical plane stress problem, Displacement method, Hydroforming, Plastic state, Turbogenerator’s protective-ring, contact geometry, flat width, impact and vibration, vehicle/rail coupling system dynamics model, three dimensional wheel flat model