统一强度理论角点奇异性的统一处理  

UNIFIED MANNER TO ELIMINATE THE CORNER SINGULARITY OF UNIFIED STRENGTH THEORY

作　　者：俞茂宏[1] 昝月稳[1] 李建春[1] 

机构地区：[1]西安交通大学建筑工程与力学学院,西安710049

出　　处：《岩石力学与工程学报》2000年第z1期849-852,共4页Chinese Journal of Rock Mechanics and Engineering

摘　　要：统一强度理论于 1991年发表以来 ,在国内外得到进一步深入研究和推广应用。在统一强度理论推广为塑性应力应变本构关系时会遇到角点奇异性问题 ,即分段线性屈服面交点或相交角隅的塑性应变增量的方向和大小的唯一性问题。本文采用一种矢量平均的统一处理方法 ,合理而简便地解决了角点奇异性问题。它具有简明的物理和数学概念 ,合理的结果 ,并可以统一处理 ,较国外对 Mohr- Coulomb理论的角点处理方法更为合理和适用。The unified strength theory is completely a new system of yield and failure of materials under the complex stress state. It embraces many well established criteria as its special or asymptotic cases, such as the Tresca (1864), the Mises (1913), and the Mohr Coulomb (lower bound,1900), as well as the twin shear strength theory ( upper bound, Yu 1985). The unified strength theory forms an entire spectrum of convex and non convex criteria, which can be used to describe many kinds of engineering materials. It has been studied and applied in the researches of applied mechanics and analyses of engineering structures. Various criteria of the unified strength theory are the piecewise linear criteria. The forms of limit surface of the unified strength theory are angular. A single smooth surface can be developed to approximate to all the piecewise linear criteria of the unified strength theory. However, the non linear mathematical expressions of the smooth curves are difficult for application to analytic solution of plastic analysis of structures. The piecewise linear expressions of the unified strength theory are convenient for analytic solution of the plastic problems. The singularity at the corners of the unified strength theory has been overcome by using a simple and unified manner. It is convenient for computational implementation.

关 键 词：破坏准则 统一强度理论 角点 奇异性 塑性应变增量 

分 类 号：O[理学] 346