A Note on the Legendre Series Solution of the Biharmonic Equation for Cylindrical Problems

被引：6
|
作者：
Strozzi, Antonio [1 ]
机构：
[1] Univ Modena, I-41125 Modena, Italy
来源：
JOURNAL OF ELASTICITY | 2012年 / 108卷 / 01期
关键词：
Biharmonic equation; Cylindrical problems; Stress function; Series solution; Legendre polynomials;
D O I：
10.1007/s10659-011-9353-2
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
The solution of cylindrical problems is addressed. A series solution is considered of the biharmonic equation, in which the series terms of the stress function I broken vertical bar are expressions based upon Legendre polynomials and logarithmically singular functions. An explicit form of a polynomial supplementing each logarithmically singular part of the series solution is obtained.
引用
收藏
页码：119 / 123
页数：5
相关论文
共 50 条
  • [31] ON THE BOUNDARY-INTRINSIC PROBLEMS FOR THE BIHARMONIC EQUATION
    ATAKHODZHAEV, MA
    DOKLADY AKADEMII NAUK, 1992, 325 (05) : 893 - 896
  • [32] A NOTE ON THE REFLECTION PRINCIPLE FOR THE BIHARMONIC EQUATION AND THE STOKES SYSTEM
    FARWIG, R
    ACTA APPLICANDAE MATHEMATICAE, 1994, 37 (1-2) : 41 - 51
  • [33] Numerical solution of the biharmonic equation by conformal mapping
    Chan, Raymond H.
    Delillo, Thomas K.
    Horn, Mark A.
    SIAM Journal of Scientific Computing, 1997, 18 (06): : 1571 - 1582
  • [34] Regularized Solution of the Cauchy Problem for the Biharmonic Equation
    Tran Nhat Luan
    Tran Thi Khieu
    Tra Quoc Khanh
    Bulletin of the Malaysian Mathematical Sciences Society, 2020, 43 : 757 - 782
  • [35] REGULARIZED SOLUTION FOR A BIHARMONIC EQUATION WITH DISCRETE DATA
    Tran Ngoc Thach
    Nguyen Huy Tuan
    O'Regan, Donal
    EVOLUTION EQUATIONS AND CONTROL THEORY, 2020, 9 (02): : 341 - 358
  • [36] Highly accurate numerical solution of a biharmonic equation
    Numer Methods Partial Differential Equations, 4 (375):
  • [37] Regularized Solution of the Cauchy Problem for the Biharmonic Equation
    Tran Nhat Luan
    Tran Thi Khieu
    Tra Quoc Khanh
    BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2020, 43 (01) : 757 - 782
  • [38] On the solution of a complicated biharmonic equation in a hydroelasticity problem
    Kononov Y.M.
    Journal of Mathematical Sciences, 2023, 274 (3) : 340 - 351
  • [39] The numerical solution of the biharmonic equation by conformal mapping
    Chan, RH
    Delillo, TK
    Horn, MA
    SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1997, 18 (06): : 1571 - 1582
  • [40] Uniquely Solvable Problems for Abstract Legendre Equation
    Glushak A.V.
    Russian Mathematics, 2018, 62 (7) : 1 - 12
12345