2006 Volume 47 Issue 546 Pages 622-626
We have investigated efficient iterative methods for solving a large sparse system of linear equations in elastic-plastic finite element analysis applying the multigrid (MG) method. In this study, we extend this method to the shell structure. For a combination of shell elements and an iterative solver such as an ordinary conjugate gradient (CG) method, it is well known that convergency tends to degrade. The MG method, which we adopt here, is combined with the CG method. This finite element system including the solid-degenerated shell element displays greatly improved convergency. Furthermore we also adapt it to the contact problem. In the latter half of this paper, we show numerical results for plate bending and V-bending analyses. In a series of plate bending analyses, our new solver requires less computing time than the direct solver does, for a fairly large-scale model. For the largest model, which has about 380,000 degrees of freedom, the direct solver is not applicable due to the insufficient memory capacity of the computer (PC) used in this research, whereas our new solver is able to obtain a converged solution. The new solver has obvious advantages in computing time and memory usage over the standard direct solvers.
