区间运算和静力区间有限元

郭书祥; 吕震宙

区间运算和静力区间有限元

郭书祥¹,
吕震宙²

1.
空军工程大学工程学院力学教研室, 西安, 710038;
2.
西北工业大学飞机工程系, 西安, 710072

基金项目: 国家自然科学基金资助项目(5957504059775032)

详细信息

作者简介:
郭书祥(1964- ),男,陕西商州人,讲师,博士.

中图分类号: TB115;O242.29
计量
- 文章访问数: 2385
- HTML全文浏览量: 147
- PDF下载量: 683
- 被引次数: 0
出版历程
- 收稿日期: 1999-04-20
- 修回日期: 2001-07-03
- 刊出日期: 2001-12-15

Interval Arithmetic and Static Interval Finite Element Method

GUO Shu-xiang¹,
LÜ Zhen-zhou²

1.
Faculty of Mechanics, Engineering Institute, Air Force Engineering University, Xi'an 710038, P. R. China;
2.
Department of Aircraft Engineering, Northwestern Polytechnical University, Xi'an 710072, P. R. China

摘要

摘要: 用均值和离差两参数表征区间变量的不确定性,根据区间运算规则,论证了区间变量的运算特性.将区间分析和有限元方法相结合,提出了非概率不确定结构的一种区间有限元分析方法.将区间有限元静力控制方程中n自由度不确定位移场特征参数的求解归结为求解一2n阶线性方程组.实例分析表明文中方法是有效和可行的.
- 区间运算 /
- 区间变量 /
- 有限元方法 /
- 区间有限元
Abstract: When the uncertainties of structures may be bounded in intervals, through some suitable discretization, interval finite element method can be constructed by combining the interval analysis with the traditional finite element method(FEM). The two parameters, median and deviation, were used to represent the uncertainties of interval variables. Based on the arithmetic rules of intervals, some properties and arithmetic rules of interval variables were demonstrated. Combining the procedure of interval analysis with FEM, a static linear interval finite element method was presented to solve the non-random uncertain structures. The solving of the characteristic parameters of n -freedom uncertain displacement field of the static governing equation was transformed into 2n-order linear equations. It is shown by a numerical example that the proposed method is practical and effective.
- interval variable /
- interval arithmetic /
- finite element method /
- interval finite element method

HTML全文

参考文献(10)

[1]	郭书祥,冯元生,吕震宙.随机有限元方法和结构可靠性[J].力学进展,2000,30(3):343-350.
[2]	龚勃文, 林赐云. 一种个性化城市多目标最短路径随机优化算法[J]. 中国科技论文, 2016,11(7): 828-834.(GONG Bowen, LIN Ciyun. A stochastic optimization algorithm of the shortest path under multi-criteria for urban roads[J]. China Sciencepaper,2016,11(7): 828-834.(in Chinese))
[3]	Elishakoff I.Essay on uncertainties in elastic and visco elastic s tructures:from A M Freudenthal's criticisms to modern convex modeling[J].Computers & Structures,1995,56(6):871-895.
[4]	Ben-Haim Y,Elishakoff I.Convex Models of Uncertainty in Applied Mechanics[M].Amsterdam:Elsevier Science,1990.
[5]	Ben-Haim Y.Convex models of uncertainty in radial pulse buckling of shells[J].Journal of Applied Mechanics,1993,60(3):683-688.
[6]	Elishakoff I,Elisseeff P,Glegg S A L.Non-probabilistic,convex-theoretic modeling of scatter in material properties[J].AIAA Journal,1994,32(4):843-849.
[7]	Qiu Z,Elishakoff I.Anti-optimization of structures with large uncertain-but-non-random parameters viainterval analysis[J].Computer Methods in Applied Mechanics and Engineering,1998,152(3-4):361-372.
[8]	Koylouglu H U,Cakmak A S,Nielsen S R K.Intervalalgebr a to deal with pattern loading and structural uncertainties[J].Journal of Engineering Mechanics,1995,121(11):1149-1157.
[9]	Rao S S,Berke L.Analysis of uncertain structural system using in terval analysis[J].AIAA Journal,1997,35(4):727-735.
[10]	Alefeld G,Claudio D.The basic properties of interval arithmetric,its software realizations and some applications[J].Computers & Structures,1998,67(1/3):3-8.