| 基于集中浓度矩阵和精细积分法的氯离子时变扩散模型 |
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| 引用本文： | 余波,凌干展,范志宏,杨绿峰. 基于集中浓度矩阵和精细积分法的氯离子时变扩散模型[J]. 工程力学, 2021, 38(1): 174-182,204. DOI: 10.6052/j.issn.1000-4750.2020.03.0153 |
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| 作者姓名： | 余波 凌干展 范志宏 杨绿峰 |
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| 作者单位： | 广西大学土木建筑工程学院,广西,南宁 530004;广西大学工程防灾与结构安全教育部重点实验室,广西,南宁 530004;广西防灾减灾与工程安全重点实验室,广西,南宁 530004;广西大学土木建筑工程学院,广西,南宁 530004;中交四航工程研究院有限公司,广东,广州 510230 |
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| 基金项目： | 国家自然科学基金项目(51668008,51738004,51678165);广西杰出青年科学基金项目(2019GXNSFFA245004);广西自然科学基金项目(2018GXNSFAA281344)。 |
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| 摘 要： | 针对传统模型采用一致协调浓度矩阵和Taylor级数展开难以兼顾计算精度、效率和数值稳定性的缺陷，研究提出了一种基于集中浓度矩阵和精细积分法的氯离子时变扩散模型:通过引入等效扩散时间，将氯离子的时变扩散控制方程变换为等效常扩散控制方程；基于伽辽金加权余量法，建立了基于集中浓度矩阵的氯离子时变扩散有限元模型；结合Padé级数展开技术，提出了基于集中浓度矩阵和精细积分法的氯离子时变扩散模型；通过与传统有限元模型、解析模型和自然暴露试验数据的对比分析，验证了该模型的有效性。分析表明:与传统的一致协调浓度矩阵相比，采用集中浓度矩阵具有更高的计算精度，而且可以避免振荡和负值等数值不稳定性问题；与传统的Taylor级数展开相比，采用Padé级数展开只需较小的尺度因子就可以保证计算精度，计算效率大幅提高；该模型不仅可以同时兼顾计算精度、效率和数值稳定性，而且对空间离散网格和时间步长的依赖性相对较小。
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| 关 键 词： | 氯离子扩散 有限元模型 集中浓度矩阵 精细积分法 Padé级数展开 |
| 收稿时间： | 2020-03-11 |
TIME-DEPENDENT CHLORIDE DIFFUSION MODEL BASED ON LUMPED CONCENTRATION MATRIX AND PRECISE TIME-INTEGRATION METHOD |
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| YU Bo,LING Gan-zhan,FAN Zhi-hong,YANG Lu-feng. TIME-DEPENDENT CHLORIDE DIFFUSION MODEL BASED ON LUMPED CONCENTRATION MATRIX AND PRECISE TIME-INTEGRATION METHOD[J]. Engineering Mechanics, 2021, 38(1): 174-182,204. DOI: 10.6052/j.issn.1000-4750.2020.03.0153 |
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| Authors: | YU Bo LING Gan-zhan FAN Zhi-hong YANG Lu-feng |
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| Affiliation: | 1.School of Civil Engineering and Architecture, Guangxi University, Nanning, Guangxi 530004, China2.CCCC Fourth Harbor Engineering Research Institute Co., Ltd, Guangzhou, Guangdong 510230, China3.Key Laboratory of Engineering Disaster Prevention and Structural Safety of Ministry of Education, Nanning, Guangxi 530004, China4.Guangxi Key Laboratory of Disaster Prevention and Engineering Safety, Nanning, Guangxi 530004, China |
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| Abstract: | In order to overcome the disadvantages of traditional models which cannot balance the computational accuracy,efficiency and numerical stability by adopting the coordinated concentration matrix and the Taylor series expansion technology,a time-dependent chloride diffusion model was proposed based on the lumped concentration matrix and the precise time-integration method:The governing equation of time-varying chloride diffusion was transformed into that of equivalent constant chloride diffusion by introducing the equivalent diffusion time.a finite element model for time-varying chloride diffusion was established based on the lumped concentration matrix and the Galerkin weighted residual method.a time-dependent chloride diffusion model which is based on the lumped concentration matrix and the precise time-integration method was proposed by adopting the Padéseries expansion technology.The applicability of the proposed model was verified through a comparison among the traditional finite element model,analytical model and natural exposure field data.The analysis shows that:it is more accurate to adopt the lumped concentration matrix than to adopt the traditional coordinated concentration matrix since the former can solve the numerical stability problems such as oscillations and negative values.The computational accuracy and efficiency can be improved obviously by adopting the Padéseries expansion technology which requires only a small scale factor to guarantee the computational accuracy,compared with the traditional Taylor series expansion technology.The proposed model can not only balance the computational accuracy,efficiency and numerical stability,but also be insensitive to the meshed sizes of spatial grids and time steps. |
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| Keywords: | chloride diffusion finite element model lumped concentration matrix precise time-integration method Padéseries expansion |
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