加速对称刚度矩阵技术及其在岩土有限元分析中的应用  

Accelerated symmetric stiffness matrix technique and its applications in geotechnical finite element analysis

作　　者：陈曦[1] 程勇刚[2] 

机构地区：[1]北京交通大学土木建筑工程学院,北京100044 [2]武汉大学水资源与水电工程科学国家重点实验室,湖北武汉430072

出　　处：《岩土工程学报》2011年第8期1216-1221,共6页Chinese Journal of Geotechnical Engineering

基　　金：教育部留学回国人员科研启动基金资助项目(教外司留[2010]1561号);中央高校基本科研业务费专项资金资助项目(2011JB-M070)

摘　　要：非关联塑性岩土工程问题的有限元离散会产生非对称刚度矩阵,对于大规模岩土工程问题,大量非对称线性方程组的求解会显著增加内存需求和计算耗时。基于加速初始刚度法的思想,提出了加速对称刚度矩阵技术来求解具有非关联塑性模型的岩土工程问题。进一步评价和比较了两个基于最小二乘法的加速技术以及两个近似对称刚度矩阵,即弹性刚度矩阵Ke和投影到塑性势面的具有关联塑性流的等效材料的刚度矩阵KG。通过一个二维孔洞扩张算例和一个二维边坡算例,评价和比较了这些加速刚度矩阵技术和Newton-Raphson迭代法。数值结果表明加速KG具有较好的计算性能,例如,加速KG技术只需要对称线性求解器,收敛速度较快,计算耗时有时会少于Newton-Raphson迭代法。Finite element discretization of non-associated plastic geotechnical problems may result in non-symmetric stiffness matrices,and solving the nonsymmetric linear systems of equations arising from large-scale geotechnical problems may significantly increase the computer memory storage requirement and the computer runtime.Based on the accelerated initial stiffness matrix technique,the accelerated symmetric stiffness matrix techniques are proposed to solve the non-associated plastic geotechnical problems.Furthermore,two acceleration techniques based on the least-square minimization and two approximate symmetric stiffness matrices（i.e.the elastic stiffness matrix Ke and the stiffness matrix KG obtained from an equivalent material with associated plastic flow by mapping the yield surface to the plastic potential surface） are assessed and compared.By using a 2-D cavity expansion example and a 2-D slope example,the accelerated symmetric stiffness matrix techniques and the Newton-Raphson iteration are evaluated and compared,and numerical results show that the accelerated KG techniques possess better computational performances.For example,they only resort to symmetric linear solvers,and have faster convergence rates,and the consumed computer runtime may be less than that of the Newton-Raphson iteration.

关 键 词：非关联塑性流 非对称刚度矩阵 加速对称刚度 初始刚度 最小二乘法 剪切强度折减法 

分 类 号：TD853.34[矿业工程—金属矿开采]