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三维线弹性力学修正的功的互等定理及其应用

付宝连

付宝连. 三维线弹性力学修正的功的互等定理及其应用[J]. 应用数学和力学, 2015, 36(5): 523-538. doi: 10.3879/j.issn.1000-0887.2015.05.008
引用本文: 付宝连. 三维线弹性力学修正的功的互等定理及其应用[J]. 应用数学和力学, 2015, 36(5): 523-538. doi: 10.3879/j.issn.1000-0887.2015.05.008
FU Bao-lian. Corrected Reciprocal Theorem for 3D Linear Elasticity and Its Application[J]. Applied Mathematics and Mechanics, 2015, 36(5): 523-538. doi: 10.3879/j.issn.1000-0887.2015.05.008
Citation: FU Bao-lian. Corrected Reciprocal Theorem for 3D Linear Elasticity and Its Application[J]. Applied Mathematics and Mechanics, 2015, 36(5): 523-538. doi: 10.3879/j.issn.1000-0887.2015.05.008

三维线弹性力学修正的功的互等定理及其应用

doi: 10.3879/j.issn.1000-0887.2015.05.008
详细信息
    作者简介:

    付宝连(1934—),男,辽宁辽阳人,教授(E-mail: ysufubaolian@163.com).

  • 中图分类号: O343.2;TU311

Corrected Reciprocal Theorem for 3D Linear Elasticity and Its Application

  • 摘要: 该研究发现,三维线弹性力学Betti(贝蒂)功的互等定理命题中的两个主要前提,“一个弹性体”和“两组力的作用”是相互矛盾的,因为两组力的任意一组力都可能改变已知的弹性体为另外一个弹性体.这一矛盾导致Betti功的互等定理是一个具有逻辑错误的定理.基于对这一矛盾的分析,提出了修正的功的互等定理,在这一定理中,给出了功的互等定理的正确命题.此外,该修正的功的互等定理为功的互等法提供理论基础,该法是结构分析的一个新颖的和强有力的方法.
  • [1] Betti E. Teoria Della elasticita’[J].Nuovo Cimento,1872,7/8(1): 69-97.
    [2] 付宝连. 关于功的互等定理与叠加原理的等价性[J]. 应用数学和力学, 1985,6(9): 813-818.(FU Bao-lian. On equivalent of the reciprocal theorem to superposition principles[J].Applied Mathematics and Mechanics,1985,6(9): 813-818.(in Chinese))
    [3] 付宝连. 广义倒易定理及其应用[J]. 应用数学和力学, 2002,23(2): 188-194.(FU Bao-lian. Generalized reciprocal theorem and its applications[J].Applied Mathematics and Mechanics,2002,23(2): 188-194.(in Chinese))
    [4] 付宝连. 应用功的互等定理求解具有复杂边界条件的矩形板的挠曲面方程[J]. 应用数学和力学, 1982,3(3): 315-325.(FU Bao-lian. Applications of reciprocal theorem to solving the equations of deflection surface of rectangular plates with various edge conditions[J].Applied Mathematics and Mechanics,1982,3(3): 315-325.(in Chinese))
    [5] 付宝连, 李农. 弹性矩形薄板受迫振动的功的互等定理法(Ⅰ)——四边固定的矩形板和三边固定的矩形板[J]. 应用数学和力学, 1989,10(8): 693-714.(FU Bao-lian, LI Nong. The method of the reciprocal theorem of forced vibration for the elastic thin rectangular plates(Ⅰ)—rectangular plates with four clamped edges and with three clamped edges[J]. Applied Mathematics and Mechanics,1989, 1〖STHZ〗0(8): 693-714.(in Chinese))
    [6] 付宝连, 李农. 弹性矩形薄板受迫振动的功的互等定理法(Ⅱ)——两邻边固定的矩形板[J]. 应用数学和力学, 1990,11(11): 977-988.(FU Bao-lian, LI Nong. The method of the reciprocal theorem of forced vibration for the elastic thin rectangular plates(Ⅱ)—rectangular plates with two adjacent clamped edges[J].Applied Mathematics and Mechanics,1990,11(11): 977-988.(in Chinese))
    [7] 付宝连, 李农. 弹性矩形薄板受迫振动的功的互等定理法(Ⅲ)——悬臂矩形板[J]. 应用数学和力学, 1991,12(7): 613-620.(FU Bao-lian, LI Nong. The method of the reciprocal theorem of forced vibration for the elastic thin rectangular plates(Ⅲ)—cantilever rectangular plates[J].Applied Mathematics and Mechanics,1991,12(7): 613-620.(in Chinese))
    [8] 付宝连. 应用功的互等定理法求立方体的位移解[J]. 应用数学和力学, 1989,10(4): 297-308.(FU Bao-lian. Application of the method of the reciprocal theorem to finding displacement solutions of cubes[J].Applied Mathematics and Mechanics,1989,10(4): 297-308.(in Chinese))
    [9] 付宝连. 关于求解弹性力学平面问题的功的互等定理法[J]. 应用数学和力学, 1989,10(5): 437-446.(FU Bao-lian. On the method of reciprocal theorem to finding solutions of the plane problems of elasticity[J].Applied Mathematics and Mechanics,1989,10(5): 437-446.(in Chinese))
    [10] 付宝连. 弯曲薄板的修正的功的互等定理及其应用[J]. 应用数学和力学, 2014,35(11): 1197-1209.(FU Bao-lian. Corrected reciprocal theorem of works for bending thin plates and its application[J].Applied Mathematics and Mechanics,2014,35(11): 1197-1209.(in Chinese))
    [11] Love A E H.Treatise on the Mathematical Theory of Elasticity [M]. 4th ed. New York: Dover Publication, 1944.
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    [14] 钱伟长, 叶开沅. 弹性力学[M]. 北京: 科学出版社, 1980.(CHIEN Wei-zang, YEH Kai-yuan.Mechanics of Elasticity [M]. Beijing: Science Press, 1980.(in Chinese))
    [15] 付宝连. 弯曲薄板功的互等新理论[M]. 北京: 科学出版社, 2003.(FU Bao-lian.New Theory of the Reciprocal Theorem of Bending of Thin Plates [M]. Beijing: Science Press, 2003.(in Chinese))
    [16] 付宝连. 弹性力学混合变量的变分原理及其应用[M]. 北京: 国防工业出版社, 2010.(FU Bao-lian.Variational Principles With Mixed Variables in Elasticity and Their Applications[M]. Beijing: National Defense Industry Press, 2010.(in Chinese))
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出版历程
  • 收稿日期:  2014-11-17
  • 修回日期:  2015-02-07
  • 刊出日期:  2015-05-15

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