用MVM准则求解轴对称弹塑性问题

ELASTO-PLASTIC SOLUTION OF AN AXISYMMETRICAL PROBLEM BY MVM YIELD CRITERION

本文采用MVM 屈服准则,用相关联流动法则建立材料的本构关系.对于实际工程中常见的轴对称问题(平面应力、平面应变),进行弹塑性分析,给出求解问题的一组微分方程.采用Prager 假设,给出应力场和位移场.在分析中可以看出:对于平面应变问题,当v≠0.5时,求解应力场的问题是非静定的;当v=0.5或在平面应力问题中,求解应力的问题是静定的,方程组易于求解.通过数值计算考察SD 效应对结构的影响.结果表明,在压缩过程中,SD 效应增强了结构抵抗塑性变形的能力.

The constitutive relation is obtained by using the associative flow rule and MVM yield criterion.Aset of differential equations of the axisymmetrical(plane strain and plane stress)problem is also given byelasto-plastic analysis.Using Prager's assumption,the displacement fields and the stress fields can be ob-tained.It can be seen that for the plane strain,when v≠0.5,the problem for solving stress field isstatically indeferminate,but v=0.5 or for plane stress condition the stress field solution can be facillyobtained on account of equations are free from coupling.Through numerical calculations,the influenceof SD effect on the structure is discussed.The results show that the SD effect increases the capacity forresisting plastic deformation in compression process.