柱坐标流函数解析半无限体压入

STREAM FUNCTION IN CYLINDRICAL COORDINATE SYSTEM TO SOLVE INDENTATION OF SEMI-INFINITE MEDIUM

对平冲头压入半无限体问题建立了柱坐标流函数速度场，证明了该速度场散度为零，旋度为剪切应变速度的２倍。采用上界定理对该速度场积分，变形力与滑移线法结果相一致，证明了流线为一族同心圆（曲线族滑移线），柱坐标流函数的解法比直角坐标的简化。

With stream function in cylindrical coordinates, a velocity field for indentation of semi-infinite medium by a flat punch is established. The divergence of the field has been shown to be zero and the vorticity be 2 times of the shear strain rate. Using upper-bound theorem and integrating, the result of the indentation force is the same as that by the slip line solution. It shows that the stream line is a family of concentric circles(curve slip lines) and solution by stream function in cylindrical coordinates is simplier than that in rectangular ones.