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用于复合材料热传导分析的Voronoi单元有限元法

Voronoi cell finite element method for heat conduction analysis of composite materials.

作者信息

Chen Siqi, Hu Changhao, Tian Jingjie, Tan Dawen, Gong Yuqiang, Xia Fan, Ning Shaoqing, Zhang Rui

机构信息

Faculty of Civil Engineering and Mechanics, Kunming University of Science and Technology, Kunming, 650500, China.

Xiluodu Hydropower Plant, China Yangtze Power Co., Ltd., Zhaotong, 657000, China.

出版信息

Sci Rep. 2024 May 27;14(1):12083. doi: 10.1038/s41598-024-61263-4.

DOI:10.1038/s41598-024-61263-4
PMID:38802453
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC11130315/
Abstract

In this paper, Voronoi cell finite element method (VCFEM) based on assumed flux hybrid formulation has been presented for heat conduction problem of particle reinforced composites material. The heat fluxes satisfying a priori internal thermal balance are directly approximated independently in the matrix and the inclusion respectively. The temperatures on element boundary and matrix-inclusion interface are interpolated by nodal temperature. The thermal balance on the interelement boundary and matrix-inclusion interface is relaxed and introduced into the functional by taking the temperature as Lagrange multiplier. In this way, a functional containing two variables of heat flux and temperature is proposed. Full field heat flux and effective thermal conductivity are obtained. Feasibility and effectiveness of the proposed approach are verified through several numerical examples.

摘要

本文针对颗粒增强复合材料的热传导问题，提出了基于假定通量混合公式的Voronoi元有限元法（VCFEM）。分别在基体和夹杂中直接独立地近似满足先验内部热平衡的热通量。单元边界和基体-夹杂界面上的温度由节点温度插值得到。通过将温度作为拉格朗日乘子，松弛单元间边界和基体-夹杂界面上的热平衡并将其引入泛函中。通过这种方式，提出了一个包含热通量和温度两个变量的泛函。得到了全场热通量和有效热导率。通过几个数值算例验证了所提方法的可行性和有效性。

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