In this study, the unusual stress fluctuation in the smoothed finite element method (SFEM) for 2D elastoplastic problems is investigated. The governing equation of the 2D elastoplastic problem based on SFEM is presented. The mysterious stress fluctuations from different SFEM approaches are explored. It is demonstrated that conventional finite element method might experience the same symptom. It is found that the stress noises only occur for cases consisting of elements with linear shape functions. Three strategies, including use of higher-order elements, modification of interpolation techniques, and evenly distributed mesh division are proposed to prevent mysterious stress fluctuations. All of them could considerably minimize the strange stress noises.

中文翻译：

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二维弹塑性问题光滑有限元法中的应力波动

在这项研究中，研究了二维弹塑性问题的平滑有限元法 (SFEM) 中的异常应力波动。提出了基于SFEM的二维弹塑性问题的控制方程。探索了来自不同 SFEM 方法的神秘应力波动。事实证明，传统的有限元方法可能会遇到相同的症状。发现应力噪声只发生在由具有线性形状函数的单元组成的情况下。提出了三种策略，包括使用高阶单元、修改插值技术和均匀分布的网格划分，以防止神秘的应力波动。它们都可以大大减少奇怪的压力噪音。