基于修正对称和反对称分解的三维数值流形元法应用推广  

Application and promotion of a modified symmetric and anti-symmetric decomposition-based three-dimensional numerical manifold method

作　　者：柯锦福 王水林[1,2] 郑宏 杨永涛[1,2] KE Jin-fu;WANG Shui-lin;ZHENG Hong;YANG Yong-tao(State Key Laboratory of Geomechanics and Geotechnical Engineering,Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,Wuhan,Hubei 430071,China;University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]中国科学院武汉岩土力学研究所岩土力学与工程国家重点实验室,湖北武汉430071 [2]中国科学院大学,北京100049

出　　处：《岩土力学》2020年第2期695-706,共12页Rock and Soil Mechanics

基　　金：国家重点基础研究发展计划项目(973计划)(No.2014CB047100)。

摘　　要：详细地介绍了基于修正对称和反对称分解(MSAD)的三维数值流形元法,并提出一个针对三维数值流形元法(3D NMM)中应用罚函数法施加位移约束和材料边界条件时罚系数的选取公式。在基于MSAD的三维数值流形元法中,引入了Bathe隐式时间积分方案,编写了基于统一强度理论和非关联流动法则的理想塑性本构模型,实现了三维弹塑性开挖问题模拟。将基于MSAD的三维数值流形元法应用到非线性动力学研究中,案例研究结果表明:Bathe隐式时间积分方案和基于MSAD的三维数值流形元法在处理大转动和长持续时间的非线性动力学问题时能够很好地保障模拟结果的稳定性,同时保证守恒体系动能和角动量的守恒。再次验证了MSAD理论,在模拟大转动问题时,MSAD具有很好的稳定性和较高的计算精度,能够合理地从变形梯度增量中分离出转动和应变,精确地更新转动应力,而不会产生错误体积膨胀问题。A detailed introduction to a modified symmetric and anti-symmetric decomposition(MSAD)based three-dimensional numerical manifold method(3D NMM)is given,and a formula to select the penalty factor of penalty method in 3D NMM is proposed.In the MSAD-based 3D NMM,a Bathe implicit time integration scheme is introduced,an ideal plastic constitutive model with the unified strength theory and non-associated flow rule is developed,and a simulation of a 3D elastic-plastic excavation problem is conducted.The MSAD-based 3D NMM is used to study nonlinear dynamics.The results show that:The Bathe implicit time integration scheme and the MSAD-based 3D NMM are able to ensure the stability of the simulation results for nonlinear dynamics problems with large rotation and long-time duration,and to maintain the conservation of kinetic energy and angular momentum for the conservative system.The MSAD theory is double-verified,in the simulation of large rotation problems,showing that it has good stability and high computational precision,and it is able to reasonably separate the rotation and strain apart from the incremental deformation gradient,and accurately update the rotational stress without causing the problem of false volume expansion.

关 键 词：修正对称和反对称分解(MSAD) 三维数值流形元法(3D NMM) 非线性动力学 Bathe隐式时间积分 罚系数选取公式 三维弹塑性开挖 

分 类 号：O241[理学—计算数学]