本文關(guān)鍵詞： 砌體結(jié)構(gòu) 勻質(zhì)化理論 契合理論 RVE 邊界條件　出處：《長沙理工大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

【摘要】：砌體結(jié)構(gòu)的受力性質(zhì)和破壞機(jī)理較為復(fù)雜,通過物理和數(shù)學(xué)模式,建立系統(tǒng)的砌體結(jié)構(gòu)分析理論是工程界非常關(guān)注的課題。勻質(zhì)化方法是一種有效的多尺度計(jì)算方法,可以從細(xì)觀層次上建立砌體的分析模型,為砌體結(jié)構(gòu)精細(xì)化分析提供一種有效途徑。本文運(yùn)用基于契合理論的嚴(yán)格勻質(zhì)化方法分析一順一丁和全順式兩種砌筑模式砌體墻的內(nèi)在契合及解構(gòu)規(guī)律,得到各類基本組元及RVE單元；推導(dǎo)一順一丁和全順式兩種砌體墻解構(gòu)后的所有基本組元的邊界條件。為建立RVE單元周期性邊界條件及加載方式的選取提供理論依據(jù),為砌體結(jié)構(gòu)精細(xì)化分析奠定理論基礎(chǔ)。本文的主要研究成果如下：(1)研究了平面應(yīng)力假設(shè)下一順一丁和全順式兩種砌筑模式砌體的內(nèi)在契合規(guī)律,應(yīng)用契合理論對一順一丁和全順式兩類砌體進(jìn)行周期性平面分割,并對分割后得到的各類基本組元進(jìn)行解構(gòu)分析。結(jié)果表明一順一丁、全順式砌體分別包含24、21種基本組元。一順一丁砌筑模式的基本組元可以歸為3大類,全順式砌筑模式的基本組元可以歸為4大類。研究為建立組元與其對應(yīng)的RVE間的數(shù)學(xué)關(guān)系提供了依據(jù)。(2)以契合圖形直觀地描繪砌體在宏觀均勻應(yīng)力場中的變形特點(diǎn),推出處于宏觀均勻應(yīng)力場中的砌體結(jié)構(gòu)需要滿足應(yīng)力矢量連續(xù)和應(yīng)變相容兩個(gè)條件,為砌體嚴(yán)格勻質(zhì)化過程在有限元軟件中的實(shí)現(xiàn)及應(yīng)用提供理論依據(jù)。(3)對基本組元與RVE之間契合關(guān)系及基本組元間的契合關(guān)系進(jìn)行了數(shù)學(xué)描述,得出同一種RVE邊界上的周期性和對稱性可能不同,不同種RVE邊界上的周期性和對稱性可能相同。另外還推導(dǎo)了一順一丁和全順式共45類基本組元的邊界條件,為砌體結(jié)構(gòu)有限元分析中對RVE的邊界條件的選用及加載方式的選取提供理論依據(jù)。
[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.
【學(xué)位授予單位】：長沙理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：TU364
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本文編號(hào)：1541133