基于严格匀质化方法的砌体契合解构及其基本组元边界条件研究

发布时间：2018-02-27 04:29

  本文关键词： 砌体结构 匀质化理论 契合理论 RVE 边界条件　出处：《长沙理工大学》2014年硕士论文　论文类型：学位论文

【摘要】：砌体结构的受力性质和破坏机理较为复杂,通过物理和数学模式,建立系统的砌体结构分析理论是工程界非常关注的课题。匀质化方法是一种有效的多尺度计算方法,可以从细观层次上建立砌体的分析模型,为砌体结构精细化分析提供一种有效途径。本文运用基于契合理论的严格匀质化方法分析一顺一丁和全顺式两种砌筑模式砌体墙的内在契合及解构规律,得到各类基本组元及RVE单元；推导一顺一丁和全顺式两种砌体墙解构后的所有基本组元的边界条件。为建立RVE单元周期性边界条件及加载方式的选取提供理论依据,为砌体结构精细化分析奠定理论基础。本文的主要研究成果如下：(1)研究了平面应力假设下一顺一丁和全顺式两种砌筑模式砌体的内在契合规律,应用契合理论对一顺一丁和全顺式两类砌体进行周期性平面分割,并对分割后得到的各类基本组元进行解构分析。结果表明一顺一丁、全顺式砌体分别包含24、21种基本组元。一顺一丁砌筑模式的基本组元可以归为3大类,全顺式砌筑模式的基本组元可以归为4大类。研究为建立组元与其对应的RVE间的数学关系提供了依据。(2)以契合图形直观地描绘砌体在宏观均匀应力场中的变形特点,推出处于宏观均匀应力场中的砌体结构需要满足应力矢量连续和应变相容两个条件,为砌体严格匀质化过程在有限元软件中的实现及应用提供理论依据。(3)对基本组元与RVE之间契合关系及基本组元间的契合关系进行了数学描述,得出同一种RVE边界上的周期性和对称性可能不同,不同种RVE边界上的周期性和对称性可能相同。另外还推导了一顺一丁和全顺式共45类基本组元的边界条件,为砌体结构有限元分析中对RVE的边界条件的选用及加载方式的选取提供理论依据。
[Abstract]:The mechanical properties and failure mechanism of masonry structures are more complicated. It is a very concerned subject in engineering field to establish systematic theory of masonry structure analysis through physical and mathematical models. Homogenization method is an effective multi-scale calculation method. The analysis model of masonry can be established at the meso level. In this paper, a strict homogenization method based on fit theory is used to analyze the internal fit and deconstruction law of masonry wall with two masonry modes, I. e. All kinds of basic components and RVE elements are obtained, and the boundary conditions of all basic components after deconstruction of masonry walls are derived. The theoretical basis is provided for the establishment of periodic boundary conditions of RVE elements and the selection of loading modes. The main research results of this paper are as follows: 1) in this paper, we study the inherent fit law of masonry with two masonry modes under plane stress hypothesis. In this paper, the periodic plane segmentation of masonry is carried out by using coincidence theory, and the basic components obtained are analyzed. The results show that one line and one dichotomy are obtained. The whole masonry consists of 24 elements and 21 basic components. The basic components of the masonry model can be classified into three categories. The basic components of the complete sequence masonry model can be classified into four categories. The study provides a basis for establishing the mathematical relationship between the components and their corresponding RVE) and describes the deformation characteristics of masonry in macroscopic uniform stress field by using the fitting graph. It is concluded that masonry structures in macroscopic uniform stress field need to satisfy two conditions: stress vector continuity and strain compatibility. This paper provides a theoretical basis for the realization and application of the strict homogenization process of masonry in finite element software. It is concluded that the periodicity and symmetry on the same RVE boundary may be different, and the periodicity and symmetry on different RVE boundaries may be the same. It provides a theoretical basis for the selection of boundary conditions and loading modes of RVE in the finite element analysis of masonry structures.
【学位授予单位】：长沙理工大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TU364
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本文编号：1541133