LUO Jian-hui, LIU Guang-dong. Research on an Orthogonal Relationship for Orthotropic Elasticity[J]. Applied Mathematics and Mechanics, 2005, 26(5): 621-624.
Citation: LUO Jian-hui, LIU Guang-dong. Research on an Orthogonal Relationship for Orthotropic Elasticity[J]. Applied Mathematics and Mechanics, 2005, 26(5): 621-624.

Research on an Orthogonal Relationship for Orthotropic Elasticity

  • Received Date: 2003-04-01
  • Rev Recd Date: 2005-01-25
  • Publish Date: 2005-05-15
  • The new orthogonal relationship is generalized for orthotropic elasticity of three-dimensions. The thought of how dual vectors are constructed in a new orthogonal relationship for theory of elasticity is generalized into orthotropic problems. A new dual vector is presented by the dual vector of the symplectic systematic methodology for elasticity that is over again sorted. A dual differential equation is directly obtained by using a mixed variables method. A dual differential matrix to be derived possesses a peculiarity of which principal diagonal sub-matrixes are zero matrixes. As a result of the peculiarity of the dual differential matrix, two independently and symmetrically orthogonal sub-relationships are discovered for orthotropic elasticity of three-dimensions. The dual differential equation is solved by a method of separation of variable. Based on the integral form of orthotropic elasticity a new orthogonal relationship is proved by using some identical equations. The new orthogonal relationship not only includes the symplectic orthogonal relationship but is also simpler. The physical significance of the new orthogonal relationship is the symmetry representation about an axis z for solutions of the dual equation. The symplectic orthogonal relationship is a generalized relationship but it may be appeared in a strong form with narrow sense in certain condition. This theoretical achievement will provide new effective tools for the research on analytical and finite element solutions to orthotropic elasticity of three-dimensions.
  • loading
  • [1]
    钟万勰.条形域平面弹性问题与哈密尔顿体系[J].大连理工大学学报,1991,31(4):373—384.
    [2]
    钟万勰.分离变量法与哈密顿体系[J].计算结构力学及其应用,1991,8(3):229—240.
    [3]
    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.
    [4]
    罗建辉,刘光栋.各向同性平面弹性力学求解新体系正交关系的研究[J].计算力学学报,2003,20(2):199—203.
    [5]
    钟万勰.互等定理与共轭辛正交关系[J].力学学报,1992,24(4):432—437.
    [6]
    ZHONG Wan-xie,Williams F W. Physical interpretation of the symplectic orthogonality of the eigensolutions of a Hamiltonian or symplectic matrix[J].Computers & Structures,1993,49(4):749—750.
    [7]
    ZHONG Wan-xie, Williams F W.On the direct solution of wave propagation for repetitive structures[J].Journal Sound & Vibration,1995,181(3):485—501.
    [8]
    钟万勰,姚伟岸.多层层合板圣维南问题的解析解[J].力学学报,1997,25(5):617—626.
    [9]
    姚伟岸, 钟万勰.辛弹性力学[M].北京:高等教育出版社,2002.
    [10]
    罗建辉,刘光栋,尚守平.弹性力学求解体系的研究[J]. 应用数学和力学,2003,24(7):755—763.
  • 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 (2248) PDF downloads(715) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return