论文标题
关于弹性分析中准静态增量问题的近端梯度方法的注释
A Note on a Family of Proximal Gradient Methods for Quasi-static Incremental Problems in Elastoplastic Analysis
论文作者
论文摘要
最近已经开发了加速的近端梯度方法，用于解决弹性塑料分析的准静态增量问题，并具有一些不同的收益标准。通过数值实验证明，这些方法可以超过计算可塑性中基于常规优化的方法。但是，在文献中，这些算法针对特定的收益标准进行了单独描述，因此没有将算法应用于其他收益标准的指南。这本简短的论文介绍了算法设计的一般形式，独立于特定形式的收益标准，该形式统一了现有的近端梯度方法。还对提出的一般算法的每个步骤都提供了明确的解释，以便每个更新规则都与基本的物理定律有关机械量链接。
Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria. It has been demonstrated through numerical experiments that these methods can outperform conventional optimization-based approaches in computational plasticity. However, in literature these algorithms are described individually for specific yield criteria, and hence there exists no guide for application of the algorithms to other yield criteria. This short paper presents a general form of algorithm design, independent of specific forms of yield criteria, that unifies the existing proximal gradient methods. Clear interpretation is also given to each step of the presented general algorithm so that each update rule is linked to the underlying physical laws in terms of mechanical quantities.
