[1]周太全,李兆霞,贾军波.弹塑性损伤分析的参变量变分原理[J].东南大学学报(自然科学版),2001,31(5):67-71.[doi:10.3969/j.issn.1001-0505.2001.05.015]
 Zhou Taiquan,Li Zhaoxia,Jia Junbo.Parametric Variational Principle for Coupled Elasto-Plasticity Damage Problem Analysis[J].Journal of Southeast University (Natural Science Edition),2001,31(5):67-71.[doi:10.3969/j.issn.1001-0505.2001.05.015]
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弹塑性损伤分析的参变量变分原理()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
31
期数:
2001年第5期
页码:
67-71
栏目:
数学、物理学、力学
出版日期:
2001-09-20

文章信息/Info

Title:
Parametric Variational Principle for Coupled Elasto-Plasticity Damage Problem Analysis
作者:
周太全 李兆霞 贾军波
东南大学土木工程学院, 南京 210096
Author(s):
Zhou Taiquan Li Zhaoxia Jia Junbo
College of Civil Engineering, Southeast University, Nanjing 210096, China)
关键词:
弹塑性耦合损伤 参变量变分原理 势能泛函极值 数值方法
Keywords:
elasto-plasticity damage parametric variational principle minimum of potential function numerical method
分类号:
O344.3
DOI:
10.3969/j.issn.1001-0505.2001.05.015
摘要:
参变量变分原理采用了现代控制理论中的极值变分思想,将本构关系化为状态方程控制着泛函的变分,是一种有效的求解非线性问题的方法.本文在弹塑性损伤基本方程基础上构造了弹塑性损伤分析的势能泛函,对损伤演化方程和加载函数作了近似处理,导出了状态方程,指出求解弹塑性损伤问题归结为求解在状态方程控制下的势能泛函极值问题,由此建立了弹塑性损伤分析的参变量变分原理; 变分原理物理意义明确,并给出了参变量变分原理实施的有限元列式,易于计算机编程实现.文中对一算例进行了数值计算,计算结果表明该方法是求解弹塑性耦合损伤问题的有效方法.
Abstract:
The parametric variational principle adopts the maximum variational idea in the modern control theory and uses state equations deduced from the constitutive laws to control the functional variation, which is an effective solution to the nonlinear equations. Based on the fundamental equations of elasto-plasticity coupled damage, the article constructs the potential functional of elasto-plasticity and deduces the state equations with some approximation of damage evolution equation and load functions. It is verified that the solution of elasto-plasticity damage problem can be deduced to solve problem of the potential energy function minimum under the restriction of state equations. Thus the parametric variational principle for coupled damage is brought forth. The variational principle has the virtue of definite physical meaning and the finite element equations are presented in the article to facilitate the application of parametric variatioal principle, which is easy to program on computer.Using the method mentioned in the article, a numerical calculation is carried out and the calculation result shows that the method is efficient for solving ealsto-plasticity damage problems.

参考文献/References:

[1] 臧峰刚,陈大鹏,周本宽.损伤问题的本构方程、变分泛函及有限元列式.西南交通大学学报,1997,32(4):395~400
[2] 楼志文.损伤力学基础.西安:西安交通大学出版社,1991.56~58
[3] 钟万勰.参变量变分原理及其在工程中的应用.北京:科学出版社,1997.21~30
[4] 马景槐.弹塑性损伤结构耦合分析的虚功原理和线性互补解法.应用数学和力学,2000,21(2):164~170

备注/Memo

备注/Memo:
作者简介:周太全,男,1976年生,博士研究生.
更新日期/Last Update: 2001-09-20