基于p型自适应有限元法的混凝土骨料模型数值模拟
|
摘要
混凝土骨料模型是由骨料、砂浆基体以及界面层组成的三相复合材料。由于骨料形状的复杂性及各相材料性质差异悬殊,需要采用自适应有限元方法进行有效数值计算与模拟。p型自适应有限元法通过自适应提高基函数的阶次来改善各骨料界面处数值解精度,具有对网格质量要求不高、前处理工作量较少以及阶谱性等优点。该文首先基于ANSYS软件生成了含量可达60%以上的几种复杂形态的二维骨料几何模型;然后,设计和分析了一种基于"分区分级"局部误差控制的p型自适应有限元法,并将其应用于几类典型骨料模型的线性及非线性有限元分析中。数值结果表明,该文设计的p型自适应有限元法对求解混凝土骨料模型是非常有效的,可大大提高各骨料界面处数值解的计算精度,为进行混凝土材料的相关力学性能分析提供了一种高效计算方法。
The concrete aggregate model is a type of three-phase composite material consisting of aggregate,mortar matrix and interface layers. Due to the complexity of the aggregate shape and the disparity in material properties of each phase, the adaptive finite element method is needed to improve the efficiency of the corresponding numerical computation and simulation. The p-version finite element method(FEM) can improve the accuracy of numerical solutions by adaptively increasing the order of the basis functions for those elements near each aggregate interface. This method is of such advantages as less limits on the grid quality, less pre-processing work and the hierarchical feature, etc. In this paper, some geometrical models with different aggregate shapes in two dimensions are firstly generated in ANSYS. Moreover, the corresponding aggregate content can reach approximately 60%. A special p-version adaptive FEM method is then designed and analyzed based on the local error control by using subdomains and grading. The resulting method is applied to the linear and nonlinear finite element analyses of several typical aggregate models. The numerical results show that this method is very efficient for the solution of the aggregate models and the computation accuracy of the numerical solutions near the aggregate interfaces can be greatly improved. A highly efficient computational method is provided for further analyzing the relevant mechanical properties of concrete materials.
The concrete aggregate model is a type of three-phase composite material consisting of aggregate,mortar matrix and interface layers. Due to the complexity of the aggregate shape and the disparity in material properties of each phase, the adaptive finite element method is needed to improve the efficiency of the corresponding numerical computation and simulation. The p-version finite element method(FEM) can improve the accuracy of numerical solutions by adaptively increasing the order of the basis functions for those elements near each aggregate interface. This method is of such advantages as less limits on the grid quality, less pre-processing work and the hierarchical feature, etc. In this paper, some geometrical models with different aggregate shapes in two dimensions are firstly generated in ANSYS. Moreover, the corresponding aggregate content can reach approximately 60%. A special p-version adaptive FEM method is then designed and analyzed based on the local error control by using subdomains and grading. The resulting method is applied to the linear and nonlinear finite element analyses of several typical aggregate models. The numerical results show that this method is very efficient for the solution of the aggregate models and the computation accuracy of the numerical solutions near the aggregate interfaces can be greatly improved. A highly efficient computational method is provided for further analyzing the relevant mechanical properties of concrete materials.
引文
[1]马怀发,陈厚群,黎保琨.混凝土细观力学研究进展及评述[J].中国水利水电科学研究院学报,2004,2(2):124-130.Ma Huaifa,Chen Houqun,Li Baokun.Review on micro-mechanics studies of concrete[J].Journal of China Institute of Water,2004,2(2):124-130.(in Chinese)
[2]宋来忠,沈涛,余波.混凝土二维参数化骨料模型的创建方法[J].工程力学,2013,30(10):5-13.Song Laizhong,Shen Tao,Yu Bo.The approach to establishing a 2D parameterized aggregate model for concrete simulation[J].Engineering Mechanics,2013,30(10):5-13.(in Chinese)
[3]Roelfstra P E,Sadouki H,Wittmann F H.Le beton numerique[J].Mater Constr,1985.
[4]高政国,刘光廷.二维混凝土随机骨料模型研究[J].清华大学学报(自然科学版),2003,43(5):710-714.Gao Zhengguo,Liu Guangting.Two-dimensional random aggregate structure for concrete[J].Journal of Tsinghua University(Science&Technology),2003,43(5):710-714.(in Chinese)
[5]宋晓刚,杨智春.一种新的混凝土圆形骨料投放数值模拟方法[J].工程力学,2010,27(1):154-159.Song Xiaogang,Yang Zhichun.A new method to simulate round concrete aggregate generation[J].Engineering Mechanics,2010,27(1):154-159.(in Chinese)
[6]Siamak Shahbazi,Iraj Rasoolan.Meso-scale finite element modeling of non-homogeneous three-phase concrete[J].Case Studies in Construction Materials,2017,6:29-42.
[7]Ma H F,Xu W X,Li Y C.Random aggregate model for mesoscopic structures and mechanical analysis of fully-graded concrete[J].Computers and Structures,2016,177:103-113.
[8]刘海峰,韩莉.基于随机骨料模型混凝土动态性能数值模拟[J].应用力学学报,2017,34(1):162-168.Liu Haifeng,Han Li.Numerical simulation of dynamic properties of concrete on the basis of random aggregate model[J].Chinese Journal of Applied Mechanics,2017,34(1):162-168.(in Chinese)
[9]Szabo B.Mesh design for the p-version of the finite element method[J].Computer Methods in Applied Mechanics and Engineering,1986,55(1/2):181-197.
[10]王彪,肖映雄,李真有.求解弱不连续问题的p型自适应有限元方法[J].固体力学学报,2016,37(1):59-73.Wang Biao,Xiao Yingxiong,Li Zhenyou.The p-version finite element method for modeling weak discontinuity problems[J].Chinese Journal of Solid Mechanics,2016,37(1):59-73.(in Chinese)
[11]Babuska I,Szabo B A,Katz I N.The p-version of the finite element method[J].Siam Journal on Numerical Analysis,1981,18(3):515-545.
[12]Wiberg N E,Li X D,Abdulwahab F.Adaptive finite element procedures in elasticity and plasticity[J].Engineering with Computers,1996,12(2):120-141.
[13]费文平,张林,谢和平.p型自适应有限单元法及其在岩土工程中的应用[J].岩土力学,2004,25(11):1727-1732.Fei Wenping,Zhang Lin,Xie Heping.A p-version adaptive finite element method and its application to rock and soil engineering[J].Rock and Soil Mechanics,2004,25(11):1727-1732.(in Chinese)
[14]郭瑞奇,肖映雄,唐现琼.一种快速生成三维混凝土骨料模型的混合实现方法[J].土木建筑与环境工程,2017,39(5):100-107.Guo Ruiqi,Xiao Yingxiong,Tang Xianqiong.A fast hybrid realization method for three-dimensional concrete aggregate models[J].Journal of Civil,Architectural&Environmental Engineering,2017,39(5):100-107.(in Chinese)
[15]许桂生,陈胜宏.含排水孔渗流场的p型自适应复合单元法分析[J].岩石力学与工程学报,2006,25(5):969-973.Xu Guisheng,Chen Shenghong.Seepage analysis considering drainage holes by p-version adaptive composite element method[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(5):969-973.(in Chinese)
[16]Stoykov S,Ribeiro P.Vibration analysis of rotating 3Dbeams by the p-version finite element method[J].Finite Elements in Analysis and Design,2013,65:76-88.
[2]宋来忠,沈涛,余波.混凝土二维参数化骨料模型的创建方法[J].工程力学,2013,30(10):5-13.Song Laizhong,Shen Tao,Yu Bo.The approach to establishing a 2D parameterized aggregate model for concrete simulation[J].Engineering Mechanics,2013,30(10):5-13.(in Chinese)
[3]Roelfstra P E,Sadouki H,Wittmann F H.Le beton numerique[J].Mater Constr,1985.
[4]高政国,刘光廷.二维混凝土随机骨料模型研究[J].清华大学学报(自然科学版),2003,43(5):710-714.Gao Zhengguo,Liu Guangting.Two-dimensional random aggregate structure for concrete[J].Journal of Tsinghua University(Science&Technology),2003,43(5):710-714.(in Chinese)
[5]宋晓刚,杨智春.一种新的混凝土圆形骨料投放数值模拟方法[J].工程力学,2010,27(1):154-159.Song Xiaogang,Yang Zhichun.A new method to simulate round concrete aggregate generation[J].Engineering Mechanics,2010,27(1):154-159.(in Chinese)
[6]Siamak Shahbazi,Iraj Rasoolan.Meso-scale finite element modeling of non-homogeneous three-phase concrete[J].Case Studies in Construction Materials,2017,6:29-42.
[7]Ma H F,Xu W X,Li Y C.Random aggregate model for mesoscopic structures and mechanical analysis of fully-graded concrete[J].Computers and Structures,2016,177:103-113.
[8]刘海峰,韩莉.基于随机骨料模型混凝土动态性能数值模拟[J].应用力学学报,2017,34(1):162-168.Liu Haifeng,Han Li.Numerical simulation of dynamic properties of concrete on the basis of random aggregate model[J].Chinese Journal of Applied Mechanics,2017,34(1):162-168.(in Chinese)
[9]Szabo B.Mesh design for the p-version of the finite element method[J].Computer Methods in Applied Mechanics and Engineering,1986,55(1/2):181-197.
[10]王彪,肖映雄,李真有.求解弱不连续问题的p型自适应有限元方法[J].固体力学学报,2016,37(1):59-73.Wang Biao,Xiao Yingxiong,Li Zhenyou.The p-version finite element method for modeling weak discontinuity problems[J].Chinese Journal of Solid Mechanics,2016,37(1):59-73.(in Chinese)
[11]Babuska I,Szabo B A,Katz I N.The p-version of the finite element method[J].Siam Journal on Numerical Analysis,1981,18(3):515-545.
[12]Wiberg N E,Li X D,Abdulwahab F.Adaptive finite element procedures in elasticity and plasticity[J].Engineering with Computers,1996,12(2):120-141.
[13]费文平,张林,谢和平.p型自适应有限单元法及其在岩土工程中的应用[J].岩土力学,2004,25(11):1727-1732.Fei Wenping,Zhang Lin,Xie Heping.A p-version adaptive finite element method and its application to rock and soil engineering[J].Rock and Soil Mechanics,2004,25(11):1727-1732.(in Chinese)
[14]郭瑞奇,肖映雄,唐现琼.一种快速生成三维混凝土骨料模型的混合实现方法[J].土木建筑与环境工程,2017,39(5):100-107.Guo Ruiqi,Xiao Yingxiong,Tang Xianqiong.A fast hybrid realization method for three-dimensional concrete aggregate models[J].Journal of Civil,Architectural&Environmental Engineering,2017,39(5):100-107.(in Chinese)
[15]许桂生,陈胜宏.含排水孔渗流场的p型自适应复合单元法分析[J].岩石力学与工程学报,2006,25(5):969-973.Xu Guisheng,Chen Shenghong.Seepage analysis considering drainage holes by p-version adaptive composite element method[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(5):969-973.(in Chinese)
[16]Stoykov S,Ribeiro P.Vibration analysis of rotating 3Dbeams by the p-version finite element method[J].Finite Elements in Analysis and Design,2013,65:76-88.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |