屈服条件由应力张量的二次齐次函数与一次齐次函数之和来表达的极限分析定理
Theorems on the Limit Analysis Dealing with the Yield Condition Expressed by the Sum of the Homogeneous Linear Form of Stress Tensor and the Homogeneous Quadratic Form of Stress Tensor
-
摘要: 本文建立了由应力张量σij的二次齐次函数与一次齐次函数的和来表达其屈服条件的刚理想塑性体的极限分析变分原理,它可用于岩土力学的极限分析问题,并把屈服条件为应力张量σij 的二次齐次函数或一次齐次函数来表达的情况作为其特例.Abstract: In this paper a generalized variational principle on the limit analysis dealing with the yield condition expressed by the sum of the homogeneous linear form of stress tensor and the homogeneous quadratic form of stress tensor is suggested.This variational principle can be applied to the limit analysis in rock mechanics and it takes the situation, in which the yield condition is expressed by the homogeneous linear form of stress tensor or the homogeneous quadratic form of stress tensor, as its special case.
-
[1] 胡海昌,论弹性体力学与受范性体力学中的-般变分原理物理学报,10,3(1954) [2] Reissner,E.,On the variational theorem in elasticity,J.Math.Phys.29,(1950). [3] 解伯民,关于弹塑性棍合体的变分原理及其运用,力学学报,1,3(1957). [4] 钱伟长,弹性理论中广义变分原理的研究及其在有限元计算中的应用,力学与实践,1-2(1979). [5] 钱令希等,论固体力学中的极限分析并建议-个-般变分原理,力学学报,6,4(1963). [6] Mura,T.and S.L.Lee,Application of variational principle of limit analysis,Quart.Appl.Math.Vol.21,No.3,(1963). [7] 王仁、黄文彬、曲圣年、赵祖武、梅占馨、王长兴等,对“论固体力学中的极限分析并建议-个-般变分原理”-文的讨论,力学学报,8,1(1965). [8] 薛大为,建议-组关于极限分析的定理,科学通报,20(1975). [9] 薛大为,-个关于大变形的极限分析定理,科学通报(1980年数学物理化学专辑),25(1980). [10] 赵彭年,三种型式极限曲线的极限平衡条件的统-表达式,地下工程,(1981) [11] 钱伟长,《变分法及有限元》(上册),科学出版社,(1980). [12] Wai-fah Chen,Limit Analysis and Soil Plasticity,(1975). -
计量
- 文章访问数: 1874
- HTML全文浏览量: 93
- PDF下载量: 521
- 被引次数: 0
下载:
渝公网安备50010802005915号