理想塑性轴对称问题的一般方程
On the General Equations of Axisymmetric Problems of Ideal Plasticity
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摘要: 本文引用速度势函数,将理想塑性轴对称问题化为二个非线性的偏微分方程,根据导得的方程讨论了Haar-Kármán假设对于Mises屈服准则及与其相关联的流动法则的协调性问题。Abstract: In this paper, introducing a velocity potential, we reduce the fundamental equations of axisymmetric problems of ideal plasticity to two nonlinear partical differential equations. Front these equations we discuss compatibility of Harr-Kármán hypothesis with von Mises yield criterion and the associated flow law.
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[1] Symonds, P. S., On the general equations of problems of axial symmetry in the theorg of plasticity, Quar. Appl. Math., 6, 4(1949), 448-452. [2] 林鸿荪,轴对称塑性变形问题(英译名:On the problem of axial-symmetric plastic deformation),物理学报.10.2(1954).89-104. [3] Аннин В.Д.,Одно оочнее решеие осесимметричной зддачи идеалвной пластичности,Журнал Прuклабноu механuкu u Технuческоu Фuзuкu,14,2(1973),171-172. [4] Haar, A., and Th. von Kármán, Zur Theorie der Spannungs-zustande in plastischen, Math. Phy. Klasse,(1909), 204-218. [5] Hill, R., The Mathematical Theory of Plasticity, Oxford Clarenden Press,(1950). [6] Shield, R. T., On the plastic flow of metals under conditions of axial symmetry, Proc. Roy. Rec., A233,(1955), 267-287. -
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