二维非线性动力问题的显式双网格虚元法

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering Pub Date : 2025-03-11 DOI:10.1016/j.cma.2025.117893

Ruopu Zhou, Zhixin Zeng, Xiong Zhang

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引用次数: 0

摘要

提出了一种新的求解二维非线性动力问题的显式双网格虚元法。该方法采用欧拉背景网格求解虚拟元法的动量方程，显著提高了虚拟元法的空间稳定性和时间稳定性。首先建立了一维问题的显式临界时间步长公式，然后将其推广到二维问题，考虑了顶点位置和相邻单元相互作用的影响。针对接触现象，提出了一种基于背景网格的拉格朗日乘子接触法。通过数值算例验证了该方法在非线性动力学问题中的有效性。

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Explicit Dual-Mesh virtual element method for 2D nonlinear dynamic problems

A novel explicit Dual-Mesh virtual element method (DM-VEM) for two dimensional nonlinear dynamic problems is proposed. The DM-VEM employs an Eulerian background grid to solve the momentum equation of the virtual element method (VEM), which significantly improves the spatial stability and the temporal stability of the VEM. An explicit critical time step formula is first developed for one dimensional problems and then extended to two dimensional problems, which takes the effect of vertex position and neighboring cell interaction into consideration. An efficient Lagrangian multiplier contact method based on the background grid is also proposed to deal with contact phenomena. Several numerical examples are studied to verify the proposed explicit DM-VEM in nonlinear dynamic problems.

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来源期刊

Computer Methods in Applied Mechanics and Engineering 工程技术-工程：综合

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.