加速对称刚度矩阵技术及其在岩土有限元分析中的应用

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 K e 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 K G 。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 K G 具有较好的计算性能，例如，加速 K G 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。

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

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.Furthe...