DOI: 10.11908/j.issn.0253-374x.20076

作者:

作者单位: 1.同济大学 道路与交通工程教育部重点实验室，上海 201804;2.同济大学 上海市轨道交通结构耐久与系统安全重点实验室，上海 201804;3.新城控股集团股份有限公司上海第二分公司，上海 201800;4.麦克马斯特大学 土木工程系， 汉密尔顿 L8S4L7


作者简介: 代 宁（1989—），男，博士生，主要研究方向为土体动力学特性及本构关系。 E-mail:1710512@tongji.edu.cn


通讯作者: 耿大将(1988—), 男，工学博士，主要研究方向为土体本构模型及数值实现。 E-mail:1410704@tongji.edu.cn

中图分类号: TU431


基金项目: 国家自然科学基金（51761135109）；国家留学基金委项目（201906260113）




Application of Conjugate Gradient Method in Numerical Implementation of Elasto-plastic Model
Author:

Affiliation: 1.Key Laboratory of Road and Traffic Engineering of the Ministry of Education， Tongji University， Shanghai 201804，China;2.Shanghai Key Laboratory of Rail Infrastructure Durability and System Safety， Tongji University， Shanghai 201804，China;3.Shanghai Second Branch of Seazen Holdings Co.， Ltd.， Shanghai 201800， China;4.Department of Civil Engineering， McMaster University， Hamilton L8S4L7， Canada


Fund Project:




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摘要:基于Jacobian矩阵的奇异和不收敛特性，分析了弹塑性本构模型的组成和算法。将牛顿?最近点投影法（Newton?CPPM）隐式算法中高度非线性方程组的求解问题转化为求最小值问题，通过采用共轭梯度法求解该最小值来实现对传统隐式算法的改进。最后，以考虑软土结构性的Saniclay模型为例，在单元体分析计算的基础上，考虑不同的应变路径和初始应力状态，对传统隐式算法和改进隐式算法在计算收敛性、计算精度和计算效率方面进行对比，并通过工程算例检验传统隐式算法和改进隐式算法之间的差异。结果表明：相较于传统隐式算法，改进隐式算法能够有效提高计算效率和收敛性。



Abstract:Based on the singularity and non-convergence characteristics of the Jacobian matrix， the composition and the algorithm of the elasto-plastic constitutive model were comprehensively analyzed. The problem of solving the highly nonlinear equations in Newton-closest point projection method（Newton-CPPM） implicit algorithm was transformed into a seeking minimum value problem by the conjugate gradient method， and the improvement of traditional implicit method was eventually accomplished. Finally， according to the calculations of single unit， the Saniclay model considering the structural properties of soft soils was set as an example， which is involved in different strain paths and initial stress states. In this process， the calculation convergence， the accuracy and the efficiency between traditional implicit algorithm and improved implicit algorithm were separately compared. In addition， the differences between traditional and improved implicit algorithm were examined by engineering example. Results show that， compared with the traditional implicit algorithm， the improved implicit algorithm can effectively improve the computational efficiency and convergence.





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