弯曲薄板的修正的功的互等定理及其应用

付宝连

doi:10.3879/j.issn.1000-0887.2014.11.003

弯曲薄板的修正的功的互等定理及其应用

doi: 10.3879/j.issn.1000-0887.2014.11.003

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，辽宁辽阳人，教授（E-mail: ysufubaolian@163.com）.

中图分类号: TU311
计量
- 文章访问数: 1310
- HTML全文浏览量: 102
- PDF下载量: 898
- 被引次数: 0
出版历程
- 收稿日期: 2014-03-07
- 修回日期: 2014-07-07
- 刊出日期: 2014-11-18

Corrected Reciprocal Theorem of Works for Bending Thin Plates and Its Application

FU Bao-lian

College of Architectural Engineering and Mechanics, Yanshan University,Qinhuangdao, Hebei 066004, P.R.China

摘要

摘要: 研究发现，弯曲薄板Betti(贝蒂)的功的互等定理命题中的两个主要前提，“一个弯曲薄板”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以改变“一个弯曲薄板”成为另外一个弯曲薄板.这一矛盾导致弯曲薄板Betti的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，在该定理中，给出了弯曲薄板的功的互等定理的正确命题.同时，该修正的功的互等定理为功的互等法提供了理论基础，功的互等法是结构分析的一个新颖的和强有力的方法.
- Betti的功的互等定理 /
- 修正的功的互等定理 /
- 一个弯曲薄板 /
- 两组力的作用
Abstract: It was discovered that the 2 main premises in the proposition of Betti’s reciprocal theorem of works for bending thin plates, ‘1 bending thin plate’ and ‘action of 2 sets of forces’, were contradictory to each other because any one of the 2 sets of forces might change ‘1 bending thin plate’ to a different one. The contradiction results in the fact that Betti’s reciprocal theorem of works for bending thin plates is one with error in logic. Based on the analysis of the contradiction, a corrected reciprocal theorem was proposed, in which the correct proposition of the reciprocal theorem for bending thin plates was given. The corrected reciprocal theorem provides a theoretical foundation for the reciprocal method of work, which makes a novel and powerful way to the analysis of bending plates.
- Betti’s reciprocal theorem of works /
- corrected reciprocal theorem of works /
- 1 bending thin plate /
- action of 2 sets of forces

HTML全文

参考文献(26)

[1]	Maxwell J C. On calculation of the equilibrium and stiffness of frames[J]. Philosophical Magazine Series 4,1864,27(182): 294-299.
[2]	Betti E. Teoria Della elasticita’[J]. Nuovo Cimento,1872,7/8(1): 69-97.
[3]	Тимошенко С П.Сопротивление МатериаловⅠ[M]. Москва: Ннаука, 1965: 297.(Timoshenko S P. Strength of Materials Part Ⅰ [M]. 3rd ed. Pricenton New Jersey, Toronto, New York, London: D Van Nostrand Company, Inc. 1965: 297.(in Russian))
[4]	Lamb H. On reciprocal theorems in dynamics[J]. Proceedings of the London Mathematical Society,1887,1(1): 144-151.
[5]	Aндреев Н Н. Теорема взаимностн в теорий колебаний и акустике[J].Физ Словарь,1936,1: 458-459.(Andleev N N. Reciprocal theorem in theory of vibration and sound[J]. Phy Dictionary,1936,1: 458-459. (in Russian))
[6]	胡海昌. 论弹性动力学中的倒易定理及它的一些应用[J]. 力学学报, 1957,1(1): 63-71.(HU Hai-chang. On reciprocal theorem in elasto-dynamics and its some applications[J]. Mechanica Sinica,1957,1(1): 63-71.(in Chinese))
[7]	Payton R G. An application of the dynamic Betti-Rayleigh reciprocal theorem to moving point load in elastic media[J]. Quarterly of Applied Mathematics,1964,21(4): 299-313.
[8]	Iesan D. On reciprocal theorems and variational theorems in linear elasto-dynamicis[J]. Bulletin de l’Academie des Sciences, Serie des Sciences Techniques,1974,22: 273-281.
[9]	Айнола Л Я. К теореме взаимности для динамических задач теории упргости[J]. Прикладная Математика и Mеханика,1967,31(1): 176-182.(Ainora L Y. On reciprocal theorem for dynamic problems of elasticity[J]. Journal of Applied Mathematics and Mechanics,1967,31(1): 176-182.(in Russian))
[10]	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))
[11]	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))
[12]	付宝连. 求解位移方程的一个新方法[C]//东北重型机械学院第三届科学报告会,1981,3: 45-56.(FU Bao-lian. A new approach for solving displacement equations[C]// Third Scientific Report Conference of Northeast Heavy Machinery Institute,1981,3: 45-56.(in Chinese))
[13]	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））
[14]	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,1989,10 (8): 693-714. （in Chinese））
[15]	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））
[16]	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））
[17]	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））
[18]	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））
[19]	Love A E H. Treatise on the Mathematical Theory of Elasticity[M]. 4th ed. New York: Dover Publication, 1944.
[20]	Timoshenko S P, Goodier J N. Theory of Elasticity[M]. 3rd ed. McGraw-Hill Book Company, 1970.
[21]	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. Mechanies of Elasticity [M]. Beijing: Science Press, 1980.(in Chinese))
[22]	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 Wan-xie. A New Systematic Methodology for Theory of Elasticity[M]. Dalian: Dalian University of Technology Press, 1995.(in Chinese)）
[23]	Fung Y C. Foundation of Solid Mechanics [M]. New Jersey: Prentice-Hall, Inc Englewood Cliffs, 1965.
[24]	Wang Chi-teh. Applied Elasticity[M]. McGRaw-Hill Publishing Company LTD ,1956.
[25]	胡海昌. 弹性力学的变分原理及其应用[M]. 北京: 科学出版社, 1981.（HU Hai-chang. Variational Principles in Elastic Mechanics and Its Applications[M]. Beijing: Science Press, 1981.(in Chinese)
[26]	张福范. 弹性薄板[M]. 第2版. 北京: 科学出版社, 1984.（ZHANG Fu-fan. Elastic Thin Plats[M]. 2nd ed. Beijing: Science Press, 1984.(in Chinese)）