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. Furthermore, two acceleration techniques based on the least-square minimization and two approximate symmetric stiffness matrices (i.e. the elastic stiffness matrix K _e and the stiffness matrix K _G 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 K _G 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.