线性蠕变平面问题中的摄动有限元方法

邬瑞锋; 杨海天

线性蠕变平面问题中的摄动有限元方法

大连工学院

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出版历程
- 收稿日期: 1985-04-09
- 刊出日期: 1988-01-15

The Perturbation Finite Element Method for Solving the Plane Problem in Consideration of Linear Creep

Dalian Institute of Technology, Dalian

摘要

摘要: 本文提出一种利用摄动有限元求解线性蠕变问题的方法(PFMC).它可用于平面蠕变问题,诸如钢筋混凝土梁,预应力混凝土梁,钢筋混凝土圆筒或位于弹性或粘弹性介质中的钢筋混凝土隧洞及地下建筑等.本方法不采用一般增量法中关于在一个时段内各物理量保持不变的假设,提高了分析精度,加大了计算步长,减少了机器存储,提高了运算效率.本文构造了包含钢筋在内的四节点四边形等参单元的有限元摄动格式.并给出五个算例,与解析解相比,有令人满意的精度.

Abstract: In this paper, a method(PFMC) for solving plane problem of linear creep is presented by using perturbation finite element. It can be used in plane problem in consideration of creep, such as reinforced concrete beam, presiressed concrete beam, reinforced concrete cylinder and reinforced concrete tunnel in elastic or visco-elastic medium, as well as underground building and so on.In the presented method, the assumption made in the general increment method that variables remain constant in a divided time interval is not taken. The accuracy is improved and the length of time step becomes larger. The computer storage can be reduced and the calculating efficiency can be increased.Perturbation finite element formulae for four-node quadrilateral isoparametric element including reinforcement are established and five numerical examples are given. As contrasted with the analytical solution, the accuracy is satisfactory.

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参考文献(10)

[1]	Zienkiewicz,O.C.,The Finite Element Method in Engineering Science,London(1971).
[2]	Bazant,Z.P.and F.H.Wittmann,Creep and Shinkage in Concrete Structure(1982).
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[7]	谢志成等,在材料非线性问题中的摄动有限元法,应用数学和力学,4,1(1983),123-134.
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[9]	谢志成等,摄动有限元方法解一般轴对称壳几何非线性问题,应用数学和力学,5,5(1984),709-722
[10]	У Жуй-фын(邬瑞锋)Неустановившаяся ползучестъ составной цилиндрической трубы в удругой среде,Изэ.АН АРМ.ССР,Серця Фцз.Мам.Наук,Том Ⅻ ВЫП.3(1959).