关于《关于修正的功的互等定理的讨论》的讨论

付宝连

关于《关于修正的功的互等定理的讨论》的讨论

付宝连

燕山大学建筑工程与力学学院, 河北秦皇岛 066004

详细信息

作者简介:
付宝连(1934—)，男，教授(E-mail: ysufubaolian@163.com)

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- 文章访问数: 88
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- 被引次数: 0
出版历程
- 收稿日期: 2023-06-19
- 修回日期: 2023-07-03
- 刊出日期: 2024-12-01

On Discussion of Discussion on the Modified Reciprocal Theorem of Works

FU Baolian

School of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao, Hebei 066004, P.R.China

摘要

摘要: 阅读完《关于修正的功的互等定理的讨论》(以下简称《讨论》)之后，对《讨论》有下述两个主要判断：① 《讨论》作者对Betti功的互等定理的命题的理解是不完整和不准确的；② 《讨论》作者认为“修正的功的互等定理实际上是Betti功的互等定理另一种表现形式”这一判断是错误的.——题记

Abstract: After reading Discussion on the Modified Reciprocal Theorem of Works (Discussion for short), there are 2 main judgments about Discussion: ① the understanding of the proposition for the reciprocal theorem of Betti's works is incomplete and inaccurate; ② the assertion that the corrected reciprocal theorem of works is actually another manifestation of Betti's reciprocal theorem, is wrong.

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图 1 悬臂梁1

Figure 1. Cantilever beam1

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图 2 悬臂梁2

Figure 2. Cantilever beam2

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参考文献(17)

[1]	付宝连. 弯曲薄板功的互等新理论[M]. 北京: 科学出版社, 2003. FU Baolian. A New Theory of Reciprocal Work for Bending Thin Plates[M]. Beijing: Science Press, 2003. (in Chinese)
[2]	付宝连. 弹性力学中的能量原理及其应用[M]. 北京: 科学出版社, 2004. FU Baolian. The Principle of Energy in Elasticity and Its Application[M]. Beijing: Science Press, 2004. (in Chinese)
[3]	付宝连. 弯曲矩形板的广义位移原理[M]. 北京: 科学出版社, 2006. FU Baolian. The Generalized Displacement Principle of Bending Rectangular Plate[M]. Beijing: Science Press, 2006. (in Chinese)
[4]	付宝连. 功的互等理论及其应用[M]. 北京: 科学出版社, 2007. FU Baolian. The Reciprocal Theory of Work and Its Application[M]. Beijing: Science Press, 2007. (in Chinese)
[5]	付宝连. 弹性力学混合变量的变分原理及其应用[M]. 北京: 科学出版社, 2010. FU Baolian. The Variational Principle of Mixed Variables in Elasticity and Its Application[M]. Beijing: Science Press, 2010. (in Chinese)
[6]	付宝连. 弯曲厚矩形板功的互等定理及其应用[M]. 北京: 科学出版社, 2014. FU Baolian. Reciprocity Theorem of Bending Thick Rectangular Plate Work and Its Application[M]. Beijing: Science Press, 2014. (in Chinese)
[7]	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. ZHONG Wanxie. New System for Solving Elastic Mechanics[M]. Dalian: Dalian University of Technology Press, 1995. (in Chinese)
[8]	付宝连. 有限位移理论线弹性动力学二类和三类混合变量的最小势作用量原理和驻值余作用量原理及其应用[J]. 应用数学和力学, 2017, 38(12): 1359-1376. doi: 10.21656/1000-0887.380005 FU Baolian. Principles of minimum potential action and stationary complementary action with dual and triple mixed variables for linear elastodynamics of finite displacement theory and the application[J]. Applied Mathematics and Mechanics, 2017, 38(12): 1359-1376. (in Chinese) doi: 10.21656/1000-0887.380005
[9]	付宝连. 有限位移理论线弹性力学二类和三类混合变量的变分原理及其应用[J]. 应用数学和力学, 2017, 38(11): 1251-1268. doi: 10.21656/1000-0887.380004 FU Baolian. Variational principles for dual and triple mixed variables of linear elasticity with finite displacements and the application[J]. Applied Mathematics and Mechanics, 2017, 38(11): 1251-1268. (in Chinese) doi: 10.21656/1000-0887.380004
[10]	付宝连. 有限位移理论的功的互等定理及其应用[J]. 应用数学和力学, 2015, 36(10): 1019-1034. doi: 10.3879/j.issn.1000-0887.2015.10.002 FU Baolian. The reciprocal theorem for the finite displacement theory and its application[J]. Applied Mathematics and Mechanics, 2015, 36(10): 1019-1034. (in Chinese) doi: 10.3879/j.issn.1000-0887.2015.10.002
[11]	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 Baolian. Corrected reciprocal theorem for 3D linear elasticity and its application[J]. Applied Mathematics and Mechanics, 2015, 36(5): 523-538. (in Chinese) doi: 10.3879/j.issn.1000-0887.2015.05.008
[12]	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. doi: 10.3879/j.issn.1000-0887.2014.11.003 FU Baolian. Corrected reciprocal theorem of works for bending thin plates and its application[J]. Applied Mathematics and Mechanics, 2014, 35(11): 1197-1209. (in Chinese) doi: 10.3879/j.issn.1000-0887.2014.11.003
[13]	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 Baolian. Modified theorem of reciprocal works[J]. Journal of Yanshan University, 2005, 29(3): 189-195. (in Chinese)
[14]	付宝连. 有限变形非线性的变形能原理及功的互等定理与变分原理的关系[J]. 燕山大学学报, 2002, 26(1): 4-6. FU Baolian. Relations between deformation energy theorem and reciprocal theorem and variational principles in non-linear elasticity with finite displacements[J]. Journal of Yanshan University, 2002, 26(1): 4-6. (in Chinese)
[15]	付宝连. 应用功的互等定理法求解立方体的位移解[J]. 应用数学和力学, 1989, 10(4): 297-308. http://www.applmathmech.cn/article/id/3652 FU Baolian. 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) http://www.applmathmech.cn/article/id/3652
[16]	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. http://www.applmathmech.cn/article/id/4565 FU Baolian. 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)) http://www.applmathmech.cn/article/id/4565
[17]	徐小明, 杨迪雄. 关于修正的功的互等定理的讨论[J]. 应用数学和力学, 2016, 37(9): 993-998. doi: 10.21656/1000-0887.370021 XU Xiaoming, YANG Dixiong. Discussion on the modified reciprocal theorem of works[J]. Applied Mathematics and Mechanics, 2016, 37(9): 993-998. (in Chinese) doi: 10.21656/1000-0887.370021