基于ANN的混凝土均匀化方法解析解

刘溢凡; 马小敏; 王志勇; 王志华

doi:10.21656/1000-0887.440106

基于ANN的混凝土均匀化方法解析解

doi: 10.21656/1000-0887.440106

刘溢凡^{1, 2,},
马小敏^{1, 2},
王志勇^{1, 2, ,},
王志华^{1, 2}

1.
太原理工大学机械与运载工程学院应用力学研究所，太原 030024
2.
材料强度与结构冲击山西省重点实验室，太原 030024

基金项目:

国家自然科学基金 12272257

国家自然科学基金 12202303

山西省基础研究计划 202203021211169

详细信息

作者简介:
刘溢凡(1999—)，男，硕士生(E-mail: liuyifan0019@link.tyut.edu.cn)

通讯作者:
王志勇(1982—)，男，副教授，博士，硕士生导师(通讯作者. E-mail: wangzhiyong@tyut.edu.cn)

中图分类号: TU37;TP39;O34
计量
- 文章访问数: 372
- HTML全文浏览量: 92
- PDF下载量: 39
- 被引次数: 0
出版历程
- 收稿日期: 2023-04-13
- 修回日期: 2023-12-18
- 刊出日期: 2024-05-01

Analytical Solution of the Concrete Homogenization Method Based on the ANN

LIU Yifan^{1, 2
,},
MA Xiaomin^{1, 2},
WANG Zhiyong^{1, 2
, ,},
WANG Zhihua^{1, 2}

1.
Institute of Applied Mechanics, College of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan 030024, P.R.China
2.
Shanxi Key Laboratory of Material Strength and Structural Impact, Taiyuan 030024, P.R.China

摘要

摘要: 通过自定义人工神经网络(artificial neural network，ANN)，借助其优秀的函数拟合功能，针对骨料/砂浆基质二相混凝土，求解间接均匀化理论中微分法的高度非线性耦合微分方程的解析解，得到了混凝土体积模量和剪切模量分别与骨料体积分数的函数关系，并与数值模拟的结果进行了对比. 结果表明，基于ANN的求解方法快速且具有更高的精度. 此外，通过解构ANN的方法给出了在细观力学参数不变的条件下由骨料体积分数、初始孔隙率直接计算骨料/砂浆基质/孔隙三相混凝土弹性模量的公式. 结果表明，对于不同骨料体积分数和初始孔隙率的混凝土样本，该公式均有较高的计算精度，同时避免了传统均匀化方法的复杂分析和大量假设，为复合材料均匀化方法研究提供了新思路.
- 人工神经网络 /
- 混凝土 /
- 均匀化 /
- 微分方程 /
- 弹性模量
Abstract: By means of the self-defined artificial neural network (ANN) and its excellent function fitting function, aimed at aggregate-mortar matrix 2-phase concrete, the analytical solutions of the highly nonlinear coupling differential equation of the differential method in the indirect homogenization theory were given, the functional relations between the volume modulus and the shear modulus of concrete and the volume fractions of aggregate were obtained respectively, and the results were compared with those of numerical simulation. The results show that, the method based on the ANN is fast and has higher precision. In addition, the method of deconstructing ANN provides the formula of calculating the elastic modulus of aggregate-mortar matrix-pore 3-phase concrete directly from aggregate volume fractions and initial porosities under constant meso-mechanical parameters. For concrete samples with different aggregate volume fractions and initial porosities, the formula has higher calculation accuracy, and avoids the complex analysis and many assumptions of the traditional homogenization method. The work provides a new idea of homogenization method for composite materials.
- artificial neural network /
- concrete /
- homogenization /
- differential equation /
- elasticity modulus

HTML全文

图 1 PYTHON绘制模型和有限元模型

Figure 1. The PYTHON drawing model and the finite element model

下载: 全尺寸图片幻灯片

图 2 部分不同骨料体积分数下混凝土细观模型样本

Figure 2. Some concrete meso-model samples with different aggregate volume fractions

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图 3 不同骨料体积分数下混凝土细观模型应力-应变曲线及有效性验证

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 3. The concrete meso-model stress-strain curves with different aggregate volume fractions and validity verification

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图 4 自定义ANN架构

Figure 4. The custom ANN architecture

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图 5 激活函数

Figure 5. The activation function

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图 6 训练过程的损失曲线

Figure 6. The loss curves of the training process

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图 7 ANN计算结果以及与其他方法对比

Figure 7. The ANN calculation results and the comparison with other methods

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图 8 不同骨料随机分布下的损伤和弹性模量

Figure 8. Damages and elastic moduli under different random distributions of aggregates

下载: 全尺寸图片幻灯片

图 9 有限元模型和PYTHON绘制模型

Figure 9. The finite element model and the PYTHON drawing model

下载: 全尺寸图片幻灯片

图 10 部分不同骨料体积分数和孔隙率下的混凝土细观模型样本

Figure 10. Some concrete meso-model samples with different aggregate volume fractions and porosity

下载: 全尺寸图片幻灯片

图 11 不同骨料体积分数和孔隙率下的混凝土细观模型应力-应变曲线

Figure 11. Some concrete meso-model stress-strain curves with different aggregate volume fractions and porosities

下载: 全尺寸图片幻灯片

图 12 BP神经网络解构流程

Figure 12. The deconstruction process of the BP neural network

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图 13 训练过程的损失曲线

Figure 13. The loss curves of the training process

下载: 全尺寸图片幻灯片

图 14 不同骨料体积分数下的弹性模量预测结果与数值模拟和试验对比

Figure 14. The prediction results of elastic moduli under different aggregate volume fractions compared with numerical simulation and experiment

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表 1 两种细观组分的力学参量

Table 1. Mechanical parameters of the 2 meso-components

	E/GPa	υ	f_c/MPa	Ψ/(°)	η/%	σ_b0/σ_c0
aggregate	43	0.23	-	-	-	-
mortar	25	0.2	35	38	0.1	1.16

下载: 导出CSV

表 2 数据集中各混凝土样本的弹性模量

Table 2. The elastic modulus of each concrete sample in the dataset

number	1	2	3	4	5	6	7
E/GPa	28.80	28.89	29.10	29.21	29.31	29.51	29.64

number	8	9	10	11	12	13	14
E/GPa	29.74	29.95	30.06	30.36	30.47	30.68	30.81

number	15	16	17	18	19	20	21
E/GPa	30.93	31.15	31.26	31.41	31.59	31.73	31.85

下载: 导出CSV

表 3 试验环境的硬件和软件参数

Table 3. Hardware and software parameters of the experimental environment

part	parameter
central processing unit	Inter Core i7-11800H CPU @ 2.3 GHz
memory	DDR4 memory 8 GB
graphics card	NIVIDA GeForce RTX3060
system	Windows 10
environment	PYTHON 3.9.7 Tensorfolw 2.8.0 Keras 2.0.6 Numpy 1.22.2

下载: 导出CSV

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