土与结构的大变形单边接触研究

发布时间：2018-01-12 13:01

本文关键词：土与结构的大变形单边接触研究　出处：《湖南工业大学》2017年硕士论文　论文类型：学位论文

【摘要】：土与结构在接触过程中可能会发生大变形,把接触问题看成是简单的非线性问题已不能满足生产和科研需要。因此,在计算分析中一方面要考虑材料非线性的问题,另一方面要考虑几何非线性的问题。通过总结前人的研究成果,对土与结构相互作用的大变形问题,运用大变形有限元基本理论,建立了有初始间隙的接触单元模型和带剪切错动的接触单元模型,在土体本构模型中采用了Morh-Coulomb准则,并用VB语言编制了大变形有限元计算程序。本文具体工作内容如下:(1)简述了大变形有限元分析的基本理论,包括物体构形和运动的两种描述——Lagrange法和Euler法,介绍了变形梯度、应力和应变张量、大变形运动的微分方程和积分方程等基本理论;介绍了弹塑性本构方程基本理论,强调了应变空间表述的在材料中的普遍适用性。(2)给出了土体大变形的控制方程及其矩阵表达式。推导了二维情况土体物质描述下的大变形增量问题有限元格式;分析了土体与结构接触单元,提出了有初始间隙的接触面单元模型;提出了剪切错动带的计算模型,分析了薄层单元厚度与宽度之比对剪应力和相对剪切位移的影响,得到大变形情况下的接触面单元的劲度矩阵。(3)分析选用了混合法求解大变形接触计算,以期较大程度接近精确解;分别给出了有初始间隙的接触单元和带剪切破坏的接触单元的算法。结合两个算例,有初始间隙的接触单元在受压过程表现出了单元大变形的挤压过程;在带剪切错动的接触单元中讨论了不同厚度的薄层单元在不同水平应力下的变形情况,计算了接触面剪切应力和相对位移,并对计算结果出现偏差的原因作出了初步的讨论。
[Abstract]:Large deformation may occur in the process of contact between soil and structure, so that the contact problem can not be regarded as a simple nonlinear problem can no longer meet the needs of production and scientific research. On the one hand, the problem of material nonlinearity should be considered, on the other hand, the problem of geometric nonlinearity should be considered. Based on the large deformation finite element theory, the contact element model with initial clearance and the contact element model with shear dislocation are established. The Morh-Coulomb criterion is used in the soil constitutive model. The finite element analysis program of large deformation is compiled with VB language. The main work of this paper is as follows: (1) the basic theory of finite element analysis of large deformation is briefly described. The basic theories of deformation gradient, stress and strain Zhang Liang, differential equation and integral equation of large deformation motion are introduced. The basic theory of elastoplastic constitutive equation is introduced. The general applicability of strain space representation in materials is emphasized. The governing equation of large deformation of soil and its matrix expression are given, and the finite element scheme of large deformation increment problem is derived under the description of soil mass in two dimensions. The contact element between soil and structure is analyzed, and the contact surface element model with initial clearance is proposed. The calculation model of shear dislocation zone is proposed, and the influence of the ratio of thickness to width of thin layer element on shear stress and relative shear displacement is analyzed. The stiffness matrix of the contact surface element under large deformation is obtained. The hybrid method is used to solve the contact calculation of large deformation in order to approach the exact solution to a greater extent. The algorithms of contact element with initial gap and contact element with shear failure are given respectively. Combined with two examples, the contact element with initial gap shows the extrusion process of large deformation in compression process. In the contact element with shear dislocation, the deformation of thin layer element with different thickness under different horizontal stress is discussed, and the shear stress and relative displacement of contact surface are calculated. The reasons for the deviation of the calculation results are discussed preliminarily.
【学位授予单位】：湖南工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TU43;TU31

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