广义混合有限元分裂因子的优化方法

IF 2.5 3区 工程技术 Q2 MECHANICS
Weiming Guo, Guanghui Qing, Zhicheng Yong, Zhenyu Wang
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引用次数: 0

摘要

确定最优分裂因子是有效应用广义混合有限元的关键。在GME中,分裂因子调节了函数中应变和互补能的比例,直接影响数值解的精度。为了提高GME中畸变六面体单元的精度,提出了一种优化分裂因子的替代方法。用矩阵范数来量化变形单元与相应标准单元之间的系数矩阵偏差。因此,通过最小化偏差来获得分裂因子。该方法不是采用统一的分裂因子,而是为有限元模型中的每个单元确定个性化的分裂因子。用几个具有不同几何参数、边界条件和载荷的典型算例验证了所提出的方法。数值算例表明,与采用0.75的均匀分裂因子相比,个性化分裂因子显著提高了含畸变广义混合单元的数值精度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

An optimization method for the splitting factors of generalized mixed finite elements

An optimization method for the splitting factors of generalized mixed finite elements

Determining the optimal splitting factor is crucial for the efficient application of generalized mixed finite elements (GME). In GME, the splitting factor adjusts the proportion of strain and complementary energy in the functional, which directly affects the accuracy of the numerical solution. To improve the accuracy of distorted hexahedral elements in GME, an alternative method for optimizing the splitting factors is introduced. The deviation of the coefficient matrix between a distorted element and its corresponding standard element is quantified by the matrix norm. Accordingly, the splitting factor is obtained by minimizing the deviation. Rather than adopting a uniform splitting factor, the method determines individualized splitting factors for each element in the finite element model. Several representative examples with different geometric parameters, boundary conditions, and loads are used to validate the proposed method. Numerical examples demonstrate that, compared to adopting a uniform splitting factor of 0.75, the individualized splitting factors significantly improve the numerical accuracy of generalized mixed elements with distortion.

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来源期刊
CiteScore
4.40
自引率
10.70%
发文量
234
审稿时长
4-8 weeks
期刊介绍: Archive of Applied Mechanics serves as a platform to communicate original research of scholarly value in all branches of theoretical and applied mechanics, i.e., in solid and fluid mechanics, dynamics and vibrations. It focuses on continuum mechanics in general, structural mechanics, biomechanics, micro- and nano-mechanics as well as hydrodynamics. In particular, the following topics are emphasised: thermodynamics of materials, material modeling, multi-physics, mechanical properties of materials, homogenisation, phase transitions, fracture and damage mechanics, vibration, wave propagation experimental mechanics as well as machine learning techniques in the context of applied mechanics.
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