扩展有限元及其在混凝土结构中的应用研究

发布时间：2018-01-11 13:32

本文关键词：扩展有限元及其在混凝土结构中的应用研究　出处：《昆明理工大学》2015年博士论文　论文类型：学位论文

【摘要】：混凝土是由骨料、水泥浆体等按一定配比制备而成的多相复合材料,受其相间特有的结构特性影响,混凝土材料受力后易于通过相间的损伤演化而导致开裂。因此混凝土开裂机制与断裂问题一直是土木水利学科领域的一个重要研究课题。然而,由于问题的复杂性,迄今为止该学科领域未能完善地建立起描述混凝土服役期损伤演化的力学模型,既能预测裂缝模式、裂缝宽度以及裂缝发展状况,又能模拟混凝土结构受力开裂破坏的响应形式。为此,研究建立相应的计算模型来描述和解释混凝土开裂和破坏力学行为便成了本学科领域研究的热点。本文在扩展有限元(X-FEM)框架体系内,系统研究了混凝土材料开裂及裂缝扩展导致的断裂问题,其内容可分为两个主要部分。首先基于X-FEM的基础理论,研究了二维、三维断裂问题的应力强度因子求解方法。其次,建立起混凝土材料及结构开裂的理论方法,实现了混凝土结构起裂和裂缝开展的数值模拟。具体工作内容如下：(1)基于单位分解法原理,系统地建立了X-FEM位移计算模式,将虚拟裂缝扩展法与X-FEM相结合,利用X-FEM中裂纹独立于有限元网格的重要特性,提出了通过求解应变能释放率来获取应力强度因子的直接刚度计算法。与传统方法相比,这种方法省去了大量的后处理工作,提高了计算效率,且编程和数值实现过程都较为简单容易。(2)推演了使用X-FEM通过回路积分方法进行三维断裂问题应力强度因子计算的完整理论和方法。针对三维弯曲裂前问题用水平集方法计算存在的问题,分析了有限元计算网格对计算精度敏感性的影响,提出了使用裂前正交网格来改善计算精度的有效方法。(3)研究了黏聚裂缝模型使用的材料软化曲线对混凝土结构的力学性能影响,揭示了初始断裂能和拉伸强度与常规尺寸试件(或大多数实际结构)峰值荷载之间的内在关系,为在缺乏足够材料软化信息条件下分析计算混凝土结构实际工程断裂问题提供了计算依据。(4)通过引入局部平均方法计算裂前应力应变场,构建了用X-FEM进行混凝土结构断裂分析的数值计算模型。该模型不仅可以有效模拟传统断裂分析中的预设裂缝问题,而且可以较好地处理无裂缝预置的开裂问题,并能同时计算多条裂缝的开展,实现复合型断裂问题裂缝连续任意开展的数值模拟。(5)利用建立的X-FEM模型与其它结构模型单元耦合分析计算了某混凝土带裂大坝,预测了大坝裂缝潜在的开展轨迹,评估了加固方案的可行性和大坝的安全现状,得出了具有实际工程意义的重要结论。
[Abstract]:Concrete is a kind of multiphase composite material, which is made of aggregate, cement paste and so on. It is influenced by its unique structure characteristics. Concrete materials are prone to crack through interphase damage evolution after loading. Therefore, the cracking mechanism and fracture of concrete has been an important research topic in the field of civil water conservancy. Due to the complexity of the problem, the mechanical model describing the damage evolution of concrete service period has not been established in this field, which can predict the crack mode, crack width and crack development. It can also simulate the response form of concrete structure under stress cracking and failure. It has become a hot topic in this field to study and establish the corresponding calculation model to describe and explain the cracking and failure mechanical behavior of concrete. This paper is in the framework of extended finite element method (FEM). The fracture problem caused by cracking and crack propagation of concrete material is studied systematically, which can be divided into two main parts. Firstly, based on the basic theory of X-FEM, two-dimensional analysis is carried out. The method of solving the stress intensity factor of three-dimensional fracture problem. Secondly, the theoretical method of crack of concrete material and structure is established. Numerical simulation of crack initiation and crack development of concrete structure is realized. The detailed work is as follows: 1) based on the principle of unit decomposition, the X-FEM displacement calculation model is established systematically. The virtual crack propagation method is combined with X-FEM, and the important characteristic of crack independence from finite element mesh in X-FEM is used. A direct stiffness calculation method is proposed to calculate the stress intensity factor by solving the strain energy release rate. Compared with the traditional method, this method saves a lot of post-processing work and improves the calculation efficiency. And both programming and numerical implementation are simple and easy. The complete theory and method of calculating stress intensity factor of three dimensional fracture problem by using X-FEM through loop integral method are deduced. The problems existing in calculating the stress intensity factor of three dimensional bending crack problem by level set method are deduced. The effect of finite element mesh on accuracy sensitivity is analyzed. An effective method to improve the calculation accuracy by using pre-crack orthogonal grid is proposed. The influence of the material softening curve used in the cohesive crack model on the mechanical properties of concrete structures is studied. The relationship between the initial fracture energy and tensile strength and the peak loads of conventional size specimens (or most of the actual structures) is revealed. It provides a basis for analyzing and calculating the fracture problem of concrete structure under the condition of lack of material softening information.) the local average method is introduced to calculate the pre-crack stress and strain field. A numerical model for fracture analysis of concrete structures using X-FEM is constructed, which can not only simulate the preset crack problem in traditional fracture analysis effectively. And it can deal with the crack problem without crack preset, and can calculate the development of multiple cracks at the same time. Numerical simulation of continuous and arbitrary crack development in complex mode fracture problem. 5) A concrete dam with crack is calculated by using the element coupling analysis of X-FEM model and other structural models. The potential track of dam crack is predicted, the feasibility of reinforcement scheme and the present situation of dam safety are evaluated, and an important conclusion of practical engineering significance is obtained.
【学位授予单位】：昆明理工大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TU37

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