Establishment and finite element mesh of 3D mesoscopic stochastic models of concrete
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摘要: 将混凝土假定为由骨料和砂浆组成的两相复合材料, 研究了球形、椭球形和两者混合体的边界和干涉判断数学条件; 设计了球形、椭球形骨料随机投放算法, 并利用MATLAB编制相应程序, 生成了混凝土细观层次三维随机几何模型; 采用相邻骨料颗粒中心距判断球形骨料的干涉关系, 利用一个椭球上任一点与另一个椭球形心连线构成的直线段上的任一点与该椭球的关系判断椭球形骨料的干涉关系, 将两椭球之间的干涉关系转化为一点与椭球的关系; 基于MATLAB平台开发了mat2scr2017程序, 将MATLAB中的图形文件数据读入SCR脚本文件中, 将mat2scr 2017程序生成的随机骨料模型转化为AutoCAD图形文件, 并导入有限元软件COMSOL Multiphysics中剖分混凝土几何模型有限元网格。研究结果表明: 建立的随机骨料模型的骨料体积率可达到50%, 骨料粒径和投放位置均满足随机性要求; 椭球形随机骨料投放算法简单、高效, 且能保证椭球自身倾角的随机性; 模型适用于任意级配混凝土的生成, 对连续级配混凝土骨料的逐级随机投放保证了各级配骨料的体积率; 实现了MATLAB图形向AutoCAD图形的转换, 极大地提高了混凝土随机骨料模型的通用性; 所建混凝土模型网格剖分满足骨料、砂浆交界处网格一致性要求, 满足有限元分析的需要。Abstract: The concrete was assumed to be a two-phase composite material of aggregate and mortar.The mathematical boundary conditions and interference judgment of spherical and ellipsoid aggregates and their mixtures were studied, respectively.A stochastic packing algorithm was designed for the spherical and ellipsoid aggregate, and a corresponding program was compiled using MATLAB to realize the generation of a three-dimensional mesoscopic stochastic geometric model of concrete.The interference relationship of spherical aggregates was judged by the center distance between adjacent aggregate particles.The interference between ellipsoidal aggregates was judged by the relationship between any point on an ellipsoid and a point on the straight-line segment formed by the connection of any point on an ellipsoid and the center of another ellipsoid.Thus, the interference relationship between two ellipsoids was simplified as the relationshipbetween an ellipsoid and a point.A program named mat2 scr 2017 was developed on MATLAB to read the graphic file data from MATLAB into SCR script file.The stochastic aggregate model built with mat2 scr 2017 program was transformed into an AutoCAD graphics file and input into the COMSOL Multiphysics software.The finite element mesh of concrete geometric model was carried out through COMSOL Multiphysics.Research result shows that the volume ratio of the stochastic aggregate model can reach 50%, and the aggregate size and packed position meet the randomness requirements.The ellipsoid random aggregate packing algorithm is simple and efficient, and can guarantee the randomness of dip angle of ellipsoid.The model is applicable to the generation of arbitrarily graded concrete, and the continuously graded concrete aggregates are packed according to different gradations, thus ensuring the volume ratio of the aggregates at all levels.The conversion of MATLAB graphics to AutoCAD graphics is realized, and the generality of stochastic concrete model is greatly enhanced.The mesh generation of the concrete model meets the requirement of grid consistency at the interface of aggregate and mortar, and the needs for finite element analysis.
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Key words:
- bridge engineering /
- concrete /
- stochastic aggregate /
- packing algorithm /
- MATLAB /
- mesh generation
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图 1 随机骨料颗粒生成和投放流程
Figure 1. Generating and packing process of random aggregate particles
图 2 150mm×150mm×150mm单粒级配球形随机骨料几何模型
Figure 2. Geometric model of 150mm×150mm×150mm spherical aggregate with single grain gradation
图 3 150mm×150mm×150mm连续级配球形随机骨料几何模型
Figure 3. Geometric model of 150mm×150mm×150mm spherical aggregate with continuous gradation
图 6 150mm×150mm×150mm单粒级配椭球形随机骨料几何模型
Figure 6. Geometric model of 150mm×150mm×150mm ellipsoidal aggregate with single grain gradation
图 7 150mm×150mm×150mm连续级配椭球形随机骨料几何模型
Figure 7. Geometric model of 150mm×150mm×150mm ellipsoidal aggregate with continuous gradation
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