YAO Wei-an, ZHANG Bing-ru. Paradox Solution on Elastic Wedge Dissimilar Materials[J]. Applied Mathematics and Mechanics, 2003, 24(8): 849-856.
Citation: YAO Wei-an, ZHANG Bing-ru. Paradox Solution on Elastic Wedge Dissimilar Materials[J]. Applied Mathematics and Mechanics, 2003, 24(8): 849-856.

Paradox Solution on Elastic Wedge Dissimilar Materials

  • Received Date: 2001-12-03
  • Rev Recd Date: 2003-04-18
  • Publish Date: 2003-08-15
  • According to the Hellinger Reissner variational principle and introducing proper transformation of variables,the problem on elastic wedge dissimilar materials can be led to Hamiltonian system,so the solution of the problem can be got by employing the separation of variables method and symplectic eigenfunction expansion under symplectic space,which consists of original variables and their dual variables.The eigenvalue -1 is a special one of all symplectic eigenvalue for Hamiltonian system in polar coordinate.In general,the eigenvalue 1 is a single eigenvalue,and the classical solution ofan elastic wedge dissimilar materials subjected to a unit concentrated couple at the vertex is got directly by solving the eigenfunction vector for eigenvalue 1.But the eigenvalue 1 becomes a double eigenvalue when the vertex angles and modulus of the materials satisfy certain definite relationships and the classical solution for the stress distribution becomes infinite at this moment,that is,the paradox should occur.Here the Jordan form eigenfunction vector for eigenvalue 1 exists,and solution of the paradox on elastic wedge dissimilar materials subjected to a unit concentrated couple at the vertex is obtained directly by solving this special Jordan form eigenfunction.The result shows again that the solutions of the special paradox on elastic wedge in the classical theory of elasticity are just Jordan form solutions in symplectic space under Hamiltonian system.
  • loading
  • [1]
    Sternberg E,Koiter W T.The wedge under a concentrated couple: a paradox in the two-dimensional theory of elasticity[J].Journal of Applied Mechanics,1958,25:575-581.
    [2]
    Dundurs J,Markenscoff X.The Sternberg-Koiter conclusion and other anomalies of the concentrated couple[J].Journal of Applied Mechanics,1989,56(2):240-245.
    [3]
    Markenscoff X.Some remarks on the wedge paradox and saint-Venant's principle[J].Journal of Applied Mechnics,1994,61(3):519-523.
    [4]
    Dempsey J P.The wedge subjected to tractions: a paradox re-resolved[J].Journal of Elasticity,1981,11(1):1-10.
    [5]
    Ting T C T.The wedge subjected to tractions:a paradox re-examined[J].Journal of Elasticity,1984,14(3):235-247.
    [6]
    王敏中.受一般载荷的楔:佯谬的解决[J].力学学报,1986,18(3): 242-252.
    [7]
    丁皓江,彭南陵,李育.受rn分布载荷的楔:佯谬的解决[J].力学学报,1997,29(1):62-73.
    [8]
    姚伟岸.极坐标哈密顿体系约当型与弹性楔的佯谬解[J].力学学报,2001,33(1):79-86.
    [9]
    钟万勰.弹性力学求解新体系[M].大连:大连理工大学出版社,1995,117-146.
    [10]
    钟万勰.弹性平面扇形域问题及哈密顿体系[J].应用数学和力学,1994,15(12):1057-1066.
    [11]
    张洪武,李云鹏,钟万勰.双材料楔结合点的奇性分析[J].大连理工大学学报,1995,35(6):776-782.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (2266) PDF downloads(557) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return