素混凝土中裂缝开裂的扩展有限元数值模拟

发布时间：2018-04-15 22:15

本文选题：扩展有限元法 + 单元子域划分　；参考：《哈尔滨工业大学》2017年硕士论文

【摘要】：在实际工程结构中,结构由于受力强度超过自身抗拉强度会产生裂缝,并且材料本身也经常存在各种缺陷如裂纹、夹杂、空洞等等,这些都会影响结构的受力性能,因此有必要对存在裂纹的结构进行受力分析,确保工程结构的正常使用。传统有限元方法是一种典型且经常使用的数值模拟方法,但是在模拟带裂纹结构时存在瓶颈,这主要是因为传统扩展有限元方法划分网格时要求与裂纹边重合,裂纹扩展的不确定性极大地增加了计算上的难度和时间。扩展有限元是在传统有限元方法的基础上发展而来的,其在处理裂纹时可以独立于网格划分,在处理裂纹模型时显示了极大的优越性,被认为是处理裂纹时最有效的数值方法。本文在matlab平台上,利用扩展有限元法对裂纹发生分叉、交叉时的情形进行了模拟,实现了对含粘聚力裂纹的动态扩展的数值模拟,主要研究内容和结论如下:(1)在单位分解法的基础上,详细阐述了扩展有限元法的基本原理,介绍了如何利用水平集法表征裂缝的几何信息。推导了扩展有限元法中,当裂纹界面不存在相互作用力以及存在粘聚力时的积分弱形式和离散方程,得到了两种情形下的刚度矩阵表达式。(2)在静态裂缝算例中(即线弹性断裂模型),提出了单元、节点编码形式和改进的单元子域划分方案,对静态裂纹模型的计算流程进行了梳理,对静态单一裂纹、分叉裂纹、交叉裂纹模型进行了数值模拟,得到了模型的变形图以及顶部节点竖向位移与节点之间的关系。(3)在动态裂纹扩展模型中,本文提出了一种界面粘聚力本构模型,该模型可以同时考虑裂纹界面法向应力和切向应力的影响,并且提出了一种改进的数值积分方案,使得积分点的划分大大简化。在此基础上提出了裂纹动态扩展的计算流程。对单边切口三点支撑梁进行了数值模拟,分析了裂纹扩展路径、荷载-CMOD关系曲线、荷载-加载点竖向位移曲线等等,结果表明数值分析和实验结果拟合程度较好。对影响数值分析的几个参数如扩展步长设置、裂纹尖端影响半径大小等进行了分析,提出了合适的取值范围。
[Abstract]:In the actual engineering structure, the structure will produce cracks because the stress intensity exceeds its own tensile strength, and the material itself often has various defects such as cracks, inclusions, voids, etc., all of which will affect the mechanical performance of the structure.Therefore, it is necessary to analyze the stress of the structures with cracks to ensure the normal use of engineering structures.The traditional finite element method is a typical and often used numerical simulation method, but there is a bottleneck in simulating the structure with cracks, which is mainly due to the coincidence between the traditional extended finite element method and the crack edge in meshing.The uncertainty of crack propagation greatly increases the computational difficulty and time.The extended finite element method is developed on the basis of the traditional finite element method. It can be separated from the mesh when dealing with the crack. It shows great superiority in dealing with the crack model and is considered to be the most effective numerical method in dealing with the crack.In this paper, the propagation finite element method is used to simulate the dynamic propagation of crack with cohesive force on matlab platform.The main contents and conclusions are as follows: (1) based on the unit decomposition method, the basic principle of extended finite element method (EFEM) is described in detail, and how to use the horizontal set method to characterize the geometric information of cracks is introduced.In the extended finite element method, the integral weak form and discrete equation are derived when there is no interaction at the crack interface and there is cohesion.In this paper, the expression of stiffness matrix in two cases is obtained. In the static crack example (linear elastic fracture model), the element, the node coding form and the improved subdomain partition scheme of the element are proposed.The calculation flow of static crack model is combed, and the static single crack, bifurcation crack and cross crack model are numerically simulated.The deformation diagram of the model and the relationship between the vertical displacement of the top node and the joint are obtained. In the dynamic crack growth model, a constitutive model of the interface cohesion force is proposed in this paper.The influence of normal stress and tangential stress on crack interface can be considered in this model, and an improved numerical integration scheme is proposed, which simplifies the division of integral points.On this basis, the calculation flow of crack dynamic propagation is presented.Numerical simulation of three-point beam with one-sided notch is carried out, crack propagation path, load-CMOD relation curve, vertical displacement curve of load-loading point and so on are analyzed. The results show that the numerical analysis and experimental results fit well.Several parameters affecting numerical analysis, such as the setting of propagation step size and the influence radius of crack tip, are analyzed, and the appropriate range of values is put forward.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TU755.7

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