塑性流动理论的变分不等式模式及其优化解  

THE VARIATIONAL INEQUALITY FORMULATION FOR THE FLOW THEORY IN PLASTICITY AND ITS OPTIMUM SOLUTION

作　　者：郭小明[1] 佘颖禾[1] 

机构地区：[1]东南大学

出　　处：《上海力学》1993年第1期48-55,共8页Chinese Quarterly Mechanics

摘　　要：本文研究与塑性流动理论相等价的变分不等式泛函形式,此类形式比现有的能量形式描述更为简洁,便于数值计算,并具有可靠的数学依据,文章还证明了其广义塑性势形式具有线性和凸性性质。在进行有限元离散后,采用变分不等式二次规划解,不需要传统求解弹塑性问题的迭代过程,迭代次数比传统方法少得多,而且具有足够的精度,其效果优于传统的非线性问题解法。In this paper,the flow theory in plasticity is put into the variational inequa-lity formulation By so doing,the constraint conditions of constitutive eqnationsmay be relaxed and the computation becomes more convenient than to follow thetraditional energy method,and it also has reliable mathematical basis.It is alsoproved that the extremal form of the variational inequality has linear and convexcharacter.The finite element discretc forms of the present formulation is deduced andthe Variational Inequality Quadratic Programming is used for the numerical calcu-lation.Instcad of conventional iterative methods,the nonlinear problems now can besolved by the Variational Inequality Quadratic Programming which shows greatadvantage in accuracy and convenient over the commonly used methods.

关 键 词：塑性流动 变分不等式 

分 类 号：O351[理学—流体力学]