有强化弹塑性含圆孔单向受拉板的渐近解

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The Asymptotic Analytical Solution of the Strain-Hardening Elastoplastic Plate Containing a Circular Hole under Simple Tension

摘要: 本文运用有强化弹塑性平面问题的一般渐近解,以解决有强化弹塑性含圆孔的无限大板在单向受拉下的应力分布问题.文中求得了二次近似解的应力分量的解析表达式,并与其他作者的数值计算^[4]和实验结果^[5]进行了比较,结果颇为符合.最后,作者还就Neuber公式的正确性进行了考查.

Abstract: In this paper the general asymptotic analytical solution of plane problem of elasto-plasticity with strain-hardening[2] is used in solving the problem of an infinitely large plate containing a circular hole under simple tension, and the analytical expressions of stress components of the first two approximations are given, These results are compared with the numerical and the experimental results given by other authors[4,5], and a good agreement is obtained. At the end of this paper the authors inspect the correctness of Neuber's formula[9] for this problem.

[1]	钱伟长.固定圆薄板在均布荷载下的大挠度问题.中国物理学报,7. 2, 102-113.
[2]	顾求林,有强化弹塑性平而问题的一般渐近解,力学学报.1(1982).
[3]	Gu Qiu-lin,The Asymptotic Solution and Experiment of a Strain-Hardening Elas-to-Plastic Plate Containing an Elliptical Hole under Tension,Contributed Paper at 9th U.S.National Congress of Applied Mechanics,Paper No,149,(1982).
[4]	Xie Zhi-cheng,Wang Rei-wu,Yang Xue-zhong and Chian Zhen-dong,The Perturbation Finite Element Method for Solving Problems with Nonlinear Materials,Proceedings of the International Conference on Finite Element Methods,(1982).
[5]	Thomson,R.A.and M.M.Frcht,Further Work on Plane Elasto-Plastic Stress Distributions,International Symposium on Photoelasticity,(1962)
[6]	Timoshenko,S.,Theory of Elasticity,(1951).
[7]	Мусхелишвили,Н.И.,Некоmoрые Оснобные Забачu Маmeмаmuческоu Теорuu Уnрuосmu(1954).
[8]	周春田,带有缺陷板在单向拉伸时弹塑性应力应变场的测定,清华大学学报(待发表).
[9]	Neuber,H.,Theory of stress-concentration for shear strained prismatical bodies in the arbitrary nonlinear stress-strain law,J.Appl,Mech.28,(1961).