大挠度直梁二类混合变量变分原理及其应用

陈英杰; 王超; 吕婷婷; 崔鹏

doi:10.6052/1000-0879-19-173

大挠度直梁二类混合变量变分原理及其应用

陈英杰^1), ,,
王超²⁾,
吕婷婷,
崔鹏

燕山大学建筑工程与力学学院,河北秦皇岛 066004

详细信息

通讯作者:
1) 陈英杰,教授,主要从事能量原理在工程中的应用,智能材料等方面的研究。E-mail: cyjysu@126.com

中图分类号: O343
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出版历程
- 收稿日期: 2019-05-04
- 发布日期: 2019-12-19

VARIATIONAL PRINCIPLES WITH DUAL MIXED VARIABLE AND APPLICATIONS FOR STRAIGHT BEAMS WITH LARGE DEFLECTION

School of Architectural Engineering and Mechanics, Yanshan University, Qinhuangdao 066004, Hebei, China

摘要

摘要: 本文在功的互等定理的基础上,利用位移和应力作为变分变量的二类混合变量的最小势能原理和最小势作用量原理来求解大挠度直梁变形稳定问题,将所得结果与有限元模拟结果进行对比分析,验证了给出的方法的可行性和计算结果的准确性。给出的方法简单灵活,结果准确,为解决大挠度直梁问题提供了新的解决途径,不仅具有一定的理论意义,而且可以直接应用于实际工程中。
- 功的互等定理 /
- 二类混合变量 /
- 最小势能原理 /
- 最小势作用量原理 /
- 大挠度直梁变形稳定
Abstract: Based on the work reciprocal theorem, the minimum potential energy principle and the principle of the minimum potential action of the dual mixed variable of the displacement and the stress are used to solve the problem of the deformation and the stability of a straight beam with large deflection. The results are compared with the finite element simulation results to verify the feasibility of the proposed method and the accuracy of the calculation results. The method is simple and flexible, and the result is accurate. It provides a new solution to solve the problem of a straight beam with large deflection. It can be directly applied to practical engineering problems.

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参考文献(11)

1 Timoshenko SP, Woinowsky-Krieger SW.Theroy of Plates and Shells. New York: McGraw-Hill, 1959

2 Timoshenko SP, Young DH.结构理论, 第2版. 北京: 清华大学出版社, 2002
Timoshenko SP, Young DH.Theory of Structures, 2nd edn. Beijing: Tsinghua University Press, 2002 (in Chinese)

3 董文堂, 孙锁泰. 解析电算法求解板壳大挠度微分方程组. 福州大学学报, 1994(4): 36-43
Dong Wentang, Sun Suotai.A solving method for differential equations of plates and shells with large deflection-analysis computation with computer. Journal of Fuzhou University, 1994(4): 36-43 (in Chinese)

4 李东. 修正迭代法在薄圆板非线性后屈曲分析中的应用. 应用数学和力学, 1991, 12(12): 1075-1080
Li Dong.Application of the modified iteration method to nonlinear post buckling analysis of thin circular plates. Applied Mathematics and Mechanics, 1991, 12(12): 1075-1080 (in Chinese)

5 张福范. 弹性薄板, 第2版. 北京: 科学出版社, 1984
Zhang Fufan. Elastic Sheet, 2nd edn. Beijing: Science Press, 1984 (in Chinese)

6 张福范. 均布荷载下悬臂矩形板的弯曲. 应用数学和力学, 1980(3): 349-362
Zhang Fufan.Bending of uniformly loaded cantilever rectangular plates. Applied Mathematics and Mechanics, 1980(3): 349-362 (in Chinese)

7 Betti E. Teoria della elasticita. Il Nuovo Cimento, 1872, 7-8(1): 357-367

8 付宝连. 修正的功的互等定理. 燕山大学学报, 2005(3): 189-195
Fu Baolian.Modified theorem of reciprocal works. Journal of Yanshan University, 2005(3): 189-195(in Chinese)

9 付宝连. 弹性力学中的能量原理及其应用. 北京: 科学出版社, 2004: 11-129
Fu Baolian.Principle of Energy in Elasticity and Its Application. Beijing: Science Press, 2004: 11-129 (in Chinese)

10 钱伟长. 弹性理论中广义变分原理的研究及其在有限元计算中的应用(续). 力学与实践, 1979, 1(2): 18-27
Qian Weichang.Research on generalized variational principle in elasticity theory and its application in finite element calculation. Mechanics and Practice, 1979, 1(2): 18-27 (in Chinese)

11 钱伟长. 变分法及有限元. 北京: 科学出版社, 1980
Qian Weichang.Variational Method and Finite Element. Beijing: Science Press, 1980 (in Chinese)

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