关于修正的功的互等定理的讨论

徐小明; 杨迪雄

doi:10.21656/1000-0887.370021

关于修正的功的互等定理的讨论

doi: 10.21656/1000-0887.370021

大连理工大学工程力学系;工业装备结构分析国家重点实验室(大连理工大学), 辽宁大连 116024

详细信息

作者简介:
徐小明（1986—），男，博士生（E-mail: xxm@mail.dlut.edu.cn);杨迪雄（1970—），男，教授，博士，博士生导师（通讯作者. E-mail: yangdx@dlut.edu.cn）.

中图分类号: O343.2; TU311
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出版历程
- 收稿日期: 2016-01-15
- 刊出日期: 2016-09-15

Discussion on the Modified Reciprocal Theorem of Works

State Key Laboratory of Structural Analysis for Industrial Equipment(Dalian University of Technology); Department of Engineering Mechanics,Dalian University of Technology, Dalian, Liaoning 116024, P.R.China

摘要

摘要: 以线弹性直梁系统为例，对Betti-Maxwell功的互等定理与修正的功的互等定理进行了比较研究.研究发现处于真实状态的两个不同的直梁系统均可等效地转化为同一直梁受两组不同外力作用的系统，进而揭示了修正的功的互等定理中“两个不相同的线弹性体”即为位移和力的边界条件相互等效的同一个结构.所以，“修正的功的互等定理”实际上仍是Betti-Maxwell功的互等定理的另一种表现形式.
- Betti-Maxwell功的互等定理 /
- 修正的功的互等定理 /
- 倒易功 /
- 直梁 /
- 线弹性系统
Abstract: A comparative study was demonstrated between the BettiMaxwell reciprocal theorem of works and the modified reciprocal theorem of works in view of linearelastic beam systems. It is indicated that 2 different beam systems under the real equilibrium states can be equivalently transformed into an identical beam system subjected to 2 sets of different external forces. Moreover, it is revealed that the ‘2 different linear elastic bodies’ in the modified reciprocal theorem of works are the same structure with equivalent boundary conditions of displacements and forces. Consequently, the modified reciprocal theorem of works is actually an alternative representation of the BettiMaxwell reciprocal theorem of works.
- Betti-Maxwell reciprocal theorem of works /
- modified reciprocal theorem of works /
- reciprocal work /
- straight beam /
- linear-elastic system

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参考文献(9)

[1]	Betti E. Teoria della elasticita’[J]. Nuovo Cimento,1872,7/8(1): 69-97.
[2]	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))
[3]	龙驭球, 包世华, 袁驷. 结构力学[M]. 第3版. 北京: 高等教育出版社, 2012.(LONG Yu-qiu, BAO Shi-hua, YUAN Si. Structural Mechanics [M]. 3rd ed. Beijing: Higher Education Press, 2012.(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 the reciprocal theorem to solving the equations of the deflection surface of the rectangular plates with various edge conditions[J]. Applied Mathematics and Mechanics,1982,3(3): 315-325.(in Chinese))
[5]	付宝连, 谭文锋. 求解厚矩形板弯曲问题的功的互等定理法[J]. 应用数学和力学, 1995,16(4): 367-379.(FU Bao-lian, TAN Wen-feng. Reciprocal theorem method for solving the problems of bending of thick rectangular plates[J]. Applied Mathematics and Mechanics,1995,16(4): 367-379.(in Chinese))
[6]	付宝连. 功的互等理论及其应用[M]. 北京: 国防工业出版社, 2007.(FU Bao-lian. Reciprocal Theory of Works and Its Applications [M]. Beijing: National Defence Industry Press, 2007.(in Chinese))
[7]	付宝连. 修正的功的互等定理[J]. 燕山大学学报, 2005,29(3): 189-195.(FU Bao-lian. Modified theorem of reciprocal works[J]. Journal of Yanshan University,2005,29(3): 189-195.(in Chinese))
[8]	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))
[9]	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.(FU Bao-lian. Corrected reciprocal theorem for 3D linear elasticity and its application[J]. Applied Mathematics and Mechanics,2015,36(5): 523-538.(in Chinese))