Shakedown analyses require a precise evaluation of pointwise elastic stresses and, at the same time, an accurate representation of the elastoplastic solution for capturing the ratcheting mechanisms effectively. However, existing discretization methods often face a trade-off: techniques that optimize plasticity performance may compromise elastic accuracy, and vice versa. The Hybrid Virtual Element Method (HVEM), based on divergence-free assumed-stresses and polygonal element shapes, has recently proven accuracy in both linear elastic and incremental elastoplastic analyses. For this reason, this work introduces an HVEM-based formulation for shakedown analysis. The proposed approach is based on Melan’s static theorem, leveraging the equilibrated stress interpolation of HVEM. Its solution is obtained using a well-established method in which the shakedown multiplier is evaluated through a sequence of safe values, as commonly done in incremental elastoplasticity. The proposed approach is validated in a numerical testing campaign consisting in typical benchmark for shakedown analysis. The results highlight the enhanced computational efficiency of HVEM compared to traditional finite elements, and its high accuracy even with coarse mesh discretizations.

中文翻译：

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基于无稳定混合虚拟元素的 2D 问题准确整定分析

安定分析需要精确评估逐点弹性应力，同时准确表示弹塑性解决方案，以有效捕获棘轮机构。然而，现有的离散化方法经常面临权衡：优化塑性性能的技术可能会损害弹性精度，反之亦然。基于无发散的假设应力和多边形单元形状的混合虚拟单元方法 （HVEM） 最近在线弹性和增量弹塑性分析中都证明了准确性。出于这个原因，这项工作引入了一种基于 HVEM 的算法进行安定分析。所提出的方法基于 Melan 静态定理，利用 HVEM 的平衡应力插值。它的解是使用一种成熟的方法获得的，其中安定乘数通过一系列安全值进行评估，就像在增量弹塑性中所做的那样。所提出的方法在数值测试活动中得到了验证，该活动包括用于安定分析的典型基准。结果突出了与传统有限元相比，HVEM 的计算效率更高，即使在粗网格离散化的情况下也能保持高精度。