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含孔洞有限板与加固板的连接问题的分区广义变分原理解法

陈宜亨 周德交 王平

陈宜亨, 周德交, 王平. 含孔洞有限板与加固板的连接问题的分区广义变分原理解法[J]. 应用数学和力学, 1987, 8(7): 649-660.
引用本文: 陈宜亨, 周德交, 王平. 含孔洞有限板与加固板的连接问题的分区广义变分原理解法[J]. 应用数学和力学, 1987, 8(7): 649-660.
Chen Yi-heng, Zhou De-jiao, Wang Ping. Solution of the Connection Problems between a Finite Holed Plate and a Stiffener by Using the Partitioning Concept of the Generalized Variational Method[J]. Applied Mathematics and Mechanics, 1987, 8(7): 649-660.
Citation: Chen Yi-heng, Zhou De-jiao, Wang Ping. Solution of the Connection Problems between a Finite Holed Plate and a Stiffener by Using the Partitioning Concept of the Generalized Variational Method[J]. Applied Mathematics and Mechanics, 1987, 8(7): 649-660.

含孔洞有限板与加固板的连接问题的分区广义变分原理解法

Solution of the Connection Problems between a Finite Holed Plate and a Stiffener by Using the Partitioning Concept of the Generalized Variational Method

  • 摘要: 本文提出了一种新的有限元解法,采用复变函数作为有限单元模式,结合运用分区广义变分原理,解决了经贴焊加固板后的含孔洞有限板应力集中系数的计算问题,得到了级数形式的解析解.计算实践表明,本方法成功地分析了加固板与含孔洞有限板在焊接线上的位移连续和内力平衡问题.由于仅需划分三个单元,故与常规有限元方法比较,本方法可大大节约计算机内存,提高精度,降低计算时间.应力集中系数和焊接线处应力的数值计算结果列于诸表之中,可供工程技术人员设计参考.
  • [1] Zhen,Y.H.,On a finite element method for solving Dirichlet's problem of Laplace's equation,Inter.J.Num.Meth.Engng.18,5(1982),687-700.
    [2] Washizu,K.,Variational Method in Elasticty and Plasticty,Pergamon Press,Oxford(1975).
    [3] 陈宜亨,两连域保角映射成环域的一种方法,应用数学和力学,4,6(1983),853-860.
    [4] Zhen,Y.H.,Solution of plane notch problems for a finite plate by the generalized variational method,Computer Methods in Applied Mechanics and Engineering 42,1(l984),57-70.
    [5] 龙驭球,弹性厚板的分区广义变分原理,应用数学和力学,4,2(1983),165-172.
    [6] 龙驭球,弹性力学的分区广义变分原理,上海力学,2,2(1981),1-9.
    [7] Muskhelishvili,N.I.,Some Basic Problems of Mathematical Theory of Elasticity,P.Noovdhoff Ltd,Groningen(1953).(in Russian).
    [8] 钱伟长,《变分法及有限元》,科学出版社(1980).
    [9] 钱伟长等,《弹性力学》,科学出版社(1956).
    [10] Chen Yi-heng,On the partitioning concept of the generalized variational method and a complex function finite element model for solving stiffened problems for a finite internally cracked plate.(to be published).
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出版历程
  • 收稿日期:  1985-06-13
  • 刊出日期:  1987-07-15

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