滑移线解与最小上界解一致的证明

以矢量分析方法建立了平冲头压入半无限体连续速度场并证明其散度为零，由上界定理经参量积分，广义积分求得冲头单位压力通解后，以待定参数法求得通解最小上界值，证明了该值与Ｐｒａｎｄｔｌ按滑移线方法得到的解相一致。

A Direct Demonstration to Consistency of Slip Line Solution with Minimum Upper-Bound Solution

Vector analysis is applied to the continuous velocity and strain rate fields for a semi-infinitebody indented by a perfectly rough flat punch. The velocity vector expression is obtained with its divergenceproved as zero. Then, based on the upper-bound theorem,a general solution to unit indentation pressure isobtained through parametric integration and improper integral. Finally,with undetermined parameter used fthe minimum upper-bound solution is obtained,which is proved in line with the prandtl,s slip line solution.