连续体力学中有限变形与转动的计算增量法

陈至达

连续体力学中有限变形与转动的计算增量法

陈至达

中国矿业学院北京研究生部

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出版历程
- 收稿日期: 1984-11-11
- 刊出日期: 1985-09-15

Incremental Formulation for Finite Strain and Finite Rotation of Continuum Mechanics

Chen Zhi-da

Beijing Graduate School, China Institute of Mining

摘要

摘要: 目前在非线性弹塑性力学计算中常用的经典非线性大变形理论由于内在的数学缺点,当变形量与转动很大时.往往误差达到不许可的程度.本文采用作者的有限变形力学理论表述了增量法.在作者与尚勇、谢和平联合研究的另二篇论文中,详细叙述这个新方法在工程中的应用,结果证明从微小变形过渡到大变形,计算结果总是可以满意地符合实验.

Abstract: Due to some confusions existing in the current coordinate description of large rotation and large strain of continuum mechanics, there are always undiscernible mistakes in the formulation of finite element method for large displacement problems. The object of this paper is to scrutinize some basic theoretical point of views in continuum mechanics of finite deformation by the author's geometrical field theory^[1][2], and to formulate fundamental equations of incremental displacement for finite element method by the energy principle of power type. The method described was used by Y. Shang^[9] and H. P. Xie^[10]. They obtained results which are in very good agreement with experiments of large deformation.

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参考文献(15)

[1]	陈至达,连续介质有限变形力学几何场论,No2(1979), 107-117.
[2]	陈至达,有理力学讲义,中国矿业学院,北京研究生部,修订本,(1983).
[3]	陈至达,杆、板、壳大变形理论,应用数学和力学讲座(讲义),(1982).
[4]	陈至达,钱氏定理在有限变形极矩弹性力学广义变分原理的应用,应用数学和力学2, 2(1981),191-196.
[5]	Argyris, J.H,J.St.Doltsinis, On the large strain inelastic analysis in natural formulations, part I: Quasistatic problems, Comp.Meths, Appl.Mech.Eng.,20(1979), 213-251.
[6]	Argyris, J, H,J, St.,Doltsinis, K, Straub, etc,Recent natural form ulations in nonlinear mechanics, Comp.Meths, Appl, Mech, Eng,32(1982),3-57.
[7]	Stones, G, G.,Cambridge Phil Soc, Trans,8, (1845).
[8]	Новожилов В.В.,非线性弹性力学(1948),朱兆祥译,科学出版社(1956).
[9]	尚勇,平面弹塑性大变形有限元分析法,中国矿业学院,工程力学专业硕士学泣论文,(1984).
[10]	谢和平,在重力场中连续体大变形分析及在地下工程中的应用、中国矿业学院,工程力学专业硕士学位论文,(1984)
[11]	Biot, M.A.Mechanics of Incremental Deformation, John wiley&Sons (1965),P.vi-vii.
[12]	陈至达,固体弹塑变形的热力学势函数及应力-应变关系,中国力学学会第一次塑性力学及极限设计讨论会,大连,(1963).
[13]	卞学错,董平,有限位移分析的变分公式,中译稿,译自High Speed cornpating of Elastic Structures, Tome I.
[14]	卞学错,增量有限单元法的变分原理中译稿,译自,.Franklin Inst,. 302(1976).
[15]	Chang, T, Y.and K.Sawamiphakdi, Nonlinear finite element analysis program for static and dynamic response of structures (1981).