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力学与实践 ›› 2019, Vol. 41 ›› Issue (6): 681-687.doi: 10.6052/1000-0879-19-173

• 应用研究 • 上一篇    下一篇

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   

  1. 燕山大学建筑工程与力学学院,河北秦皇岛 066004
  • 收稿日期:2019-05-05 发布日期:2019-12-27
  • 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; 2) E-mail: 1451517490@qq.com

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

CHEN Yingjie1), WANG Chao2), LÜ Tingting, CUI Peng   

  1. School of Architectural Engineering and Mechanics, Yanshan University, Qinhuangdao 066004, Hebei, China
  • Received:2019-05-05 Published:2019-12-27

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。

关键词: 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.

Key words: work reciprocal theorem, dual mixed variable, minimum potential energy principle, principle of minimum potential action, deformation and stability of straight beam with large deflection

中图分类号: 

  • O343