Quasistatic analysis of elastoplastic structures by the proper generalized decomposition in a space-time approach
Quasistatic analysis of elastoplastic structures by the proper generalized decomposition in a space-time approach
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DOI：
10.1016/j.mechrescom.2020.103500
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发表时间：
2020-03
影响因子：
2.4
通讯作者：
N. Shirafkan;F. Bamer;M. Stoffel;B. Markert
中科院分区：
文献类型：
--
作者：
N. Shirafkan;F. Bamer;M. Stoffel;B. Markert
在本文中，我们提出了时空公式使用适当的广义分解（PGD），以解决弹塑性结构在准静态载荷下。在这里，依赖于空间和时间的解是通过迭代地对富集求和直到获得收敛来构建的。因此，每个富集函数由空间和时间函数的并矢积表示，我们称之为空间和时间模式。所提出的策略被纳入一个有限元框架，导致两个耦合方程，一个在空间和一个在时间。这两个方程同时使用固定点算法求解。我们可视化和机械解释的空间和时间模式的演变建议的迭代方案。试验结构是由一个弹塑性框架几何形状的离散化受到外部循环力的历史。并与常规迭代法的计算结果进行了比较。结果表明，非弹性变形可以直接定位的时间函数的演变。然而，相应的空间模式显示出高度的相关性，包含全球的弹性和塑性变形模式，可以解释的正交基表示使用奇异值分解。
In this paper, we present the space-time formulation using the Proper Generalized Decomposition (PGD) to solve an elastoplastic structure under quasistatic loading. Here, the solution, dependent on space and time, is built by iteratively summing up enrichments until convergence is obtained. Thereby, each enrichment functional is represented by the dyadic product of spatial and temporal functions, which we call spatial and temporal modes. The proposed strategy is included into a finite element framework resulting in two coupled equations, one in space and one in time. Those two equations are solved simultaneously using the fixed-point algorithm. We visualize and mechanically interpret the evolution of the spatial and temporal modes within the proposed iterative scheme. The test structure is represented by the discretization of an elastoplastic frame geometry subjected to an external cyclic force history. The results are compared with the conventional iteration method. It is shown that inelastic deformation can be directly located by the evolution of the temporal functions. However, the corresponding spatial modes show a high correlation containing global elastic and plastic deformation patterns that can be interpreted by an orthonormal basis representation using the singular value decomposition.