Accurate shakedown analysis of 2D problems based on stabilization-free hybrid virtual elements

IF 6.9 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY
F.S. Liguori , A. Madeo , S. Marfia , E. Sacco , G. Garcea
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引用次数: 0

Abstract

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.
基于无稳定混合虚元的二维问题精确安定分析
安定分析需要精确地评估点向弹性应力,同时需要精确地表示弹塑性解,以便有效地捕获棘轮机制。然而,现有的离散化方法往往面临权衡:优化塑性性能的技术可能会损害弹性精度,反之亦然。基于无散度假设应力和多边形单元形状的混合虚拟单元法(HVEM)最近在线性弹性和增量弹塑性分析中都证明了其准确性。因此,本文介绍了一种基于hvem的安定分析公式。该方法基于Melan静力定理,利用HVEM的平衡应力插值。它的解是用一种完善的方法得到的,在这种方法中,安定乘数通过一系列安全值来评估,就像增量弹塑性中通常做的那样。该方法在典型的安定分析基准的数值测试活动中得到了验证。结果表明,与传统有限元相比,HVEM的计算效率有所提高,即使在粗网格离散化的情况下,其精度也很高。
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来源期刊
CiteScore
12.70
自引率
15.30%
发文量
719
审稿时长
44 days
期刊介绍: Computer Methods in Applied Mechanics and Engineering stands as a cornerstone in the realm of computational science and engineering. With a history spanning over five decades, the journal has been a key platform for disseminating papers on advanced mathematical modeling and numerical solutions. Interdisciplinary in nature, these contributions encompass mechanics, mathematics, computer science, and various scientific disciplines. The journal welcomes a broad range of computational methods addressing the simulation, analysis, and design of complex physical problems, making it a vital resource for researchers in the field.
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