基于p型自适应有限元法的混凝土骨料模型数值模拟  

NUMERICAL SIMULATION FOR CONCRETE AGGREGATE MODELS BASED ON THE p-VERSION ADAPTIVE FEM METHOD

作　　者：陈恒 肖映雄[1] 郭瑞奇[1] CHEN Heng;XIAO Ying-xiong;GUO Rui-qi(Civil Engineering and Mechanics College, Xiangtan University, Xiangtan, Hunan 411105, China)

机构地区：[1]湘潭大学土木工程与力学学院

出　　处：《工程力学》2019年第B06期158-164,共7页Engineering Mechanics

基　　金：国家自然科学基金项目(10972191);湖南省教育厅资助科研项目(15A183)

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.

关 键 词：骨料模型 p型自适应有限元 分区分级 局部误差控制 数值模拟 

分 类 号：O343.3[理学—固体力学]