ZHAO Bao-sheng, WANG Min-zhong. Equivalence of the Refined Theory and the Decomposed Theorem of an Elastic Plate[J]. Applied Mathematics and Mechanics, 2005, 26(4): 447-455.
Citation: ZHAO Bao-sheng, WANG Min-zhong. Equivalence of the Refined Theory and the Decomposed Theorem of an Elastic Plate[J]. Applied Mathematics and Mechanics, 2005, 26(4): 447-455.

Equivalence of the Refined Theory and the Decomposed Theorem of an Elastic Plate

  • Received Date: 2003-06-04
  • Rev Recd Date: 2004-12-03
  • Publish Date: 2005-04-15
  • A connection between Cheng's refined theory and Gregory's decomposed theorem is analyzed.The equivalence of the refined theory and the decomposed theorem is given.Using operator matrix determinant of partial differential equation,Cheng gained one equation,and he substituted the sum of the general integrals of three differential equations for the equation's solution.But he didn't prove the rationality of substitute.There,a whole proof for the refined theory from Papkovich-Neuber solution was given.At first expressions were obtained for all the displacements and stress components in term of the mid-plane displacement and its derivatives.Using Lur'e method and the theorem of appendix,the refined theory was given.At last,using basic mathematic method,the equivalence between Cheng's refined theory and Gregory's decomposed theorem was proved,i.e.,Cheng's bi-harmonic equation,shear equation and transcendental equation are equivalent to Gregory's interior state,shear state and Papkovich-Fadle state,respectively.
  • loading
  • [1]
    CHENG Shun.Elasticity theory of plates and a refined theory[J].Journal of Application Mechanics,1979,46(2):644—650.
    [2]
    Lur'e A I.Three-Dimensional Problems in the Theory of Elasticity[M].New York: Interscience, 1964,148—166.
    [3]
    王飞跃.横观各向同性板的弹性精化理论[J].上海力学,1985,6(2):10—21.
    [4]
    Gregory R D.The general form of the three-dimensional elastic field inside an isotropic plate with free faces[J].Journal of Elasticiy,1992,28(1):1—28. doi: 10.1007/BF00042522
    [5]
    Gregory R D.The semi-infinite strip x≥0,-1≤y≤1;completeness of the Papkovich-Fadle eigenfunctions when xx(0,y),yy(0,y) are prescribed[J].Journal of Elasticity,1980,10(1):57—80. doi: 10.1007/BF00043135
    [6]
    Gregory R D.The traction boundary value problems for the elastostatic semi-infinite strip; existence of solution, and completeness of the Papkovich-Fadle eigenfunctions[J].Journal of Elasticity,1980,10(3):295—327. doi: 10.1007/BF00127452
    [7]
    WANG Min-zhong,ZHAO Bao-sheng. The decomposed form of the three-dimensional elastic plate[J].Acta Mechanica,2003,166(3): 207—216. doi: 10.1007/s00707-003-0029-2
    [8]
    赵宝生,王敏中. 横观各向同性板的分解理论[J].力学学报,2004,36(1):57—63.
    [9]
    WANG Min-zhong,WANG Wei.Completeness and nonuniqueness of general solutions of transversely isotropic elasticity[J].International Journal of Solids and Structures,1995,32(3/4):501—513. doi: 10.1016/0020-7683(94)00114-C
    [10]
    WANG Wei,WANG Min-zhong. Constructivity and completeness of the general solutions in elasto~dynamics[J].Acta Mechanica,1992,91(1):209—214. doi: 10.1007/BF01194110
    [11]
    WANG Wei,SHI Ming-xing.Thick plate theory based on general solutions of elasticity[J].Acta Mechanica,1997,123(1):27—36. doi: 10.1007/BF01178398
  • 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 (2366) PDF downloads(836) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return