论文部分内容阅读
Mohr-Coulomb屈服面的边界角点奇异性问题,使得屈服面在这些部位的微分出现不连续现象,给数值分析带来了诸多困难,针对此问题,平滑及非平滑处理方法得以应用,其中,非平滑处理方法中的回代求导法和塑性应变增量求和法等因易于实现而应用较多。这些方法精度的研究多相对于某些典型算例而进行的,而对于塑性应变的发展遵循何规律,非平滑处理方法对塑性应变产生何影响,如何评价这种影响效应等等问题尚未在理论上被深入研究。为此,在传统塑性位势理论的框架内对塑性剪应变的发展规律,以及通过非平滑处理后塑性剪应变的发展规律进行了理论研究。研究发现,在角点奇异性屈服面的非平滑处理方法中,最终推导出的塑性剪应变出现不连续现象。通过对这一现象进行的理论研究和定量分析,结果表明:非平滑处理对塑性应变存在影响效应(即不连续效应),故对于具体问题,应具体分析这些方法的影响效应,具体评估其计算结果的可靠性和对相应问题的适用性,以便正确选择所采用的处理方法。
The problem of the singularity of the boundary corner of the Mohr-Coulomb yielding surface leads to the discontinuity of the differential surface of the yield surface in these parts, which brings many difficulties for the numerical analysis. For this problem, the smoothing and non-smoothing methods are applied, The non-smoothing method of back to the derivative method and the plastic strain increment sum method and so easy to implement due to more applications. The accuracy of these methods is mostly relative to some typical examples. However, how the non-smoothing method affects the plastic strain and how to evaluate the effect have not been discussed in theory On in-depth study. Therefore, the development of plastic shear strain in the framework of the traditional plastic potential theory and the development of plastic shear strain after non-smooth processing are theoretically studied. It is found that the discontinuity of plastic shear strain finally deduced in the non-smooth treatment of corner singularity yield surface. Through the theoretical and quantitative analysis of this phenomenon, the results show that non-smooth processing has an effect on the plastic strain (ie, discontinuous effect), so for specific problems, the impact of these methods should be analyzed in detail to evaluate the calculation The reliability of the results and the suitability of the corresponding questions so that the correct method of treatment can be chosen.