Dual‐based adaptive FEM for inelastic problems with standard FE implementations
Dual‐based adaptive FEM for inelastic problems with standard FE implementations
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DOI：
10.1002/nme.5156
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发表时间：
2016-07
影响因子：
2.9
通讯作者：
Kai‐Uwe Widany;R. Mahnken
中科院分区：
文献类型：
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作者：
Kai‐Uwe Widany;R. Mahnken
面向目标的误差估计允许在空间和时间上针对任意量细化网格。所需的对偶问题，需要解决通常需要弱公式和Galerkin方法在空间和时间建立。不幸的是，这显然不会导致固体力学的标准有限元实现的结构。这些问题的特征在于节点（例如位移）和积分点（例如内部变量）处的变量组合，并且由于局部解耦和全局耦合方程，因此使用两级牛顿法求解。因此，我们提出了一种方法来近似的对偶问题，同时保持这些结构。原始和对偶问题是来自多场制定。在时间和空间上的离散化与适当的形状函数和重排产生所需的结果。详细介绍了实际实施以及在弹塑性中的应用。数值算例验证了该方法的有效性。版权所有© 2015约翰威利父子有限公司.
Goal‐oriented error estimation allows to refine meshes in space and time with respect to arbitrary quantities. The required dual problems that need to be solved usually require weak formulations and the Galerkin method in space and time to be established. Unfortunately, this does not obviously leads to structures of standard finite element implementations for solid mechanics. These are characterized by a combination of variables at nodes (e.g. displacements) and at integration points (e.g. internal variables) and are solved with a two‐level Newton method because of local uncoupled and global coupled equations. Therefore, we propose an approach to approximate the dual problem while maintaining these structures. The primal and the dual problems are derived from a multifield formulation. Discretization in time and space with appropriate shape functions and rearrangement yields the desired result. Details on practical implementation as well as applications to elasto‐plasticity are given. Numerical examples demonstrate the effectiveness of the procedure. Copyright © 2015 John Wiley & Sons, Ltd.