解析厚件压缩问题的积分中值定理

Analytical Solution of Thick Slab's Punch Indentation by Integral Mean Value Theorem

本文运用积分中值定理得到厚件压缩滑移线场单位压力计算的显式,并得到近似解为 p/2k=2.53,与数值计算结果(p/2k=2.54)相对误差仅为0.39％,这一结果不仅从理论上验证了传统数值解的可靠性,而且大大简化了计算步骤。

Applying the integral mean value theorem to the analytical solution of thickslab's punch indentation, an explicit formula is given to the unit pressure in slipline field with an approximate solution of p/2k=2.53. The relative error of thisapproximate value to its numerical solution (2. 54) is found only 0.39%. Not onlythe theoretical reliability of conventional numerical solution but the simplifica-tion of calculation are provided by this method.