圆形平冲头压缩半无限体的上界理论解法

Upper Bound Theoretical Solution to the Indentation of Semi infinite Medium by a Round Flat Punch

建立了圆冲头压入半无限体的运动许可速度场；将变形区分为圆盘与圆环压缩两个区域，设定两个待定参数．结果表明，当冲头半径与变形区半径之比为１．５３，冲头半径与变形区高度之比为１．３６时，应力状态系数有最小上界值ｎσ＝２．８５．

The kinematically admissible velocity field for the indentation of semi infinite medium by a round flat punch has been established. The deforming zone is divided into two parts,solid and hollow disks. Using two undetermined parameters,the minimum upper bound value of stress state coefficient, n σ=2 85 ,is obtained when the retios of punch radius to deforming zone and deforming height are 1 53 and 1 36,respectively. With the method an upper bound analytical solution and the finest shape of the deforming zone with the minimum deformation force can be obtained.