Three dimensional automatic refinement method for transient small strain elastoplastic finite element computations

摘要

In this paper, the refinement strategy based on the “Non-Linear Localized Full MultiGrid” solver originally published in Int. J. Numer. Meth. Engng 84(8):947–971 (2010) for 2-D structural problems is extended to 3-D simulations. In this context, some extra information concerning the refinement strategy and the behavior of the error indicators are given. The adaptive strategy is dedicated to the accurate modeling of elastoplastic materials with isotropic hardening in transient dynamics. A multigrid solver with local mesh refinement is used to reduce the amount of computational work needed to achieve an accurate calculation at each time step. The locally refined grids are automatically constructed, depending on the user prescribed accuracy. The discretization error is estimated by a dedicated error indicator within the multigrid method. In contrast to other adaptive procedures, where grids are erased when new ones are generated, the previous solutions are used recursively to reduce the computing time on the new mesh. Moreover, the adaptive strategy needs no costly coarsening method as the mesh is reassessed at each time step. The multigrid strategy improves the convergence rate of the non-linear solver while ensuring the information transfer between the different meshes. It accounts for the influence of localized non-linearities on the whole structure. All the steps needed to achieve the adaptive strategy are automatically performed within the solver such that the calculation does not depend on user experience. This paper presents three-dimensional results using the adaptive multigrid strategy on elastoplastic structures in transient dynamics and in a linear geometrical framework. Isoparametric cubic elements with energy and plastic work error indicators are used during the calculation.