Fu Bao-lian. On the Method of Reciprocal Theorem to Find Solutions of the Plane Problems of Elasticity[J]. Applied Mathematics and Mechanics, 1989, 10(5): 437-446.
Citation: Fu Bao-lian. On the Method of Reciprocal Theorem to Find Solutions of the Plane Problems of Elasticity[J]. Applied Mathematics and Mechanics, 1989, 10(5): 437-446.

On the Method of Reciprocal Theorem to Find Solutions of the Plane Problems of Elasticity

  • Received Date: 1986-06-08
  • Publish Date: 1989-05-15
  • In this paper the method of reciprocal theorem is extended to find solutions of plane problems of elasticity of the rectangular plates with various edge conditions.First we give the basic solution of the plane problem of the rectangular plate with four edges built-in as the basic system and then find displacement expressions of the actual system by using the reciprocal theorem between the basic system and actual system with various edge conditions.When only displacement edge conditions exist,obtaining displacement expressions by means of the method of reciprocal theorem is actual.But in other conditions,when static force edge conditions or mixed ones exist,the obtained displacements are admissible.In order to find actual displacement,the minimum potential energy theorem must be applied.Calculations show that the method of reciprocal theorem is a simple,convenient and general one for the solution of plane problems of elasticity of the rectangular plates with various edge conditions.Evidently,it is a new method.
  • loading
  • [1]
    付宝连,一个求解位移方程的新方法,东北重型机械学院第三届学术报告会,(1981,1).
    [2]
    付宝连,应用功的互等定理求解具有复杂边界矩形板的挠曲面方程,应用数学和力学,3,3(1982),315-325.
    [3]
    付宝连,关于功的互等定理与迭加原理的等价性,应用数学和力学,6,9(1935),813-813.
    [4]
    付宝连,应用功的互等定理计算矩形弹性薄板的自然频率.应用数学和力学,6,11(1985).985-998.
    [5]
    付宝连,矩形弹性薄板固有频率的一个新算法,东北重型机械学院学报,2(1984,6).
    [6]
    付宝连,二对边简支另一边或两边为自由的矩形弹性薄板的固有频率,东北重型机械学院学报,1(1985,3).
    [7]
    付宝连,计算直梁横向振动自然频率的一个新方法,东北重型机械学院学报,3(1983,9).
    [8]
    钱伟长、叶开连《弹性力学》,科学出版社(1950,10).
    [9]
    徐芝纶,《弹性力学》(上册)(1979,1).
    [10]
    Timoshenko,S.and S.Woinowsky-Krieger,Theory of Plates and Shells,2nd edition.
  • 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 (2078) PDF downloads(691) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return