北京航空航天大学学报 ›› 2018, Vol. 44 ›› Issue (6): 1273-1282.doi: 10.13700/j.bh.1001-5965.2017.0400

• 论文 • 上一篇    下一篇

基于Eshelby-Stroh公式各向异性弹性体接触问题研究

颜灯灯1, 李成刚1, 申景金2, 王艳1, 王春明1, 宋伟山1   

  1. 1. 南京航空航天大学 机电学院, 南京 210016;
    2. 南京邮电大学 自动化学院, 南京 210023
  • 收稿日期:2017-06-12 出版日期:2018-06-20 发布日期:2018-06-28
  • 通讯作者: 李成刚.E-mail:lichenggang@nuaa.edu.cn E-mail:lichenggang@nuaa.edu.cn
  • 作者简介:颜灯灯 男,硕士研究生。主要研究方向:触觉传感器;李成刚 男,博士,副教授,硕士生导师。主要研究方向:工业机器人技术、并联机器人与传感器技术;申景金 男,博士,讲师,硕士生导师。主要研究方向:生物材料本构关系、接触力学、机器人分析与控制。
  • 基金资助:
    江苏省自然科学基金(BK20141414)

Study on contact problem of anisotropic elastic body based on Eshelby-Stroh formalism

YAN Dengdeng1, LI Chenggang1, SHEN Jingjin2, WANG Yan1, WANG Chunming1, SONG Weishan1   

  1. 1. School of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;
    2. School of Automation, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
  • Received:2017-06-12 Online:2018-06-20 Published:2018-06-28

摘要: 针对线性各向异性弹性体小变形接触问题,将弹性体按是否与刚体压头发生接触进行划分,基于Eshelby-Stroh公式求解各个部分的位移函数和应力函数,进一步通过应力函数积分得到载荷值。考虑到求解结果存在交接处应力突变和非接触区域应力不近似于零的问题,采用整体位移约束法和线性叠加原理,通过迭代方式使位移函数和应力函数逼近理想解,解决了圆柱压头和倒圆角楔形压头与弹性体的接触问题。基于圆柱压头求得的载荷值接近弹性半空间法的求解结果,当级数总项数为400时,计算结果的相对误差仅为0.52%。基于圆柱压头和倒圆角楔形压头求得的载荷值与ABAQUS仿真结果较为吻合:圆柱压头载荷值的相对误差为0.67%;倒圆角楔形压头,对6个不同的圆角值进行计算,载荷的相对误差都小于2%。

关键词: 各向异性, 弹性体, 圆柱压头, 倒圆角楔形, 线性叠加, 整体位移约束法

Abstract: In order to solve infinitesimal deformation contact problem of a linear anisotropic elastic body, the elastic body is divided into several parts, according to the contact condition between the rigid body and the indenter. Based on Eshelby-Stroh formalism, the displacement function and stress function of each part are solved, and the load is obtained by integrating the stress function. Considering the stress mutation at junction and nonzero stress on the top of noncontact region, both whole displacement constraint method and linear superposition principle are used for getting ideal displacement function and stress function based on iteration. The contact problem between the cylindrical indenter and bounded elastic body and the contact problem between the rounded wedge indenter and elastic body are solved. The load results based on cylinder indenter are close to the results of elastic half space method. When the quantity of series is 400, the computing relative error is only 0.52%. The computed load results based on cylindrical indenter and rounded wedge indenter agree well with those of ABAQUS simulation. The relative error of cylindrical indenter load is 0.67%, and 6 rounded wedge indenters are computed with all the relative errors of load less than 2%.

Key words: anisotropic, elastic body, cylindrical indenter, rounded wedge, linear superposition, whole displacement constraint method

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