基于割线刚度的钢筋混凝土三维非线性有限元分析

发布时间：2018-04-05 04:25

本文选题：钢筋混凝土　切入点：三维非线性有限元　出处：《重庆大学》2014年硕士论文

【摘要】：钢筋混凝土结构在受力时表现出了复杂的非线性性能，随着计算机性能的不断提高，有限元法作为强大的数值模拟手段被各国学者广泛应用于钢筋混凝土的非线性分析中，以期能够比较好地模拟钢筋混凝土的受力非线性特性。本文以本研究组前期二维非线性有限元分析为基础，参考了多伦多大学Vecchio研究团队的分析思路，建立了采用割线刚度迭代法基于修正斜压场理论的钢筋混凝土三维非线性有限元分析算法。主要完成了如下几方面工作： ①建立了适合于修正斜压场理论的三维单元模型。修正斜压场理论认为开裂的钢筋混凝土是一种正交各向异性的裂缝均匀分布的连续固体介质，通过试验可以量测到该“新材料”的平均应力和平均应变之间的关系。采用修正斜压场理论进行三维有限元分析时，就需要采用与之相适应的单元模型，用修正斜压场理论描述单元平均应力与平均应变之间的关系。 ②完善了三维位移加载控制计算方法。钢筋混凝土结构非线性有限元分析和结构试验一样，在加载控制方式上有力加载和位移加载两种。通过力加载模式，可以得到钢筋混凝土结构力变形关系的“上升段”曲线。而通过位移加载模式却可以得到结构力变形关系的全过程曲线。因此，采用位移加载可以对钢筋混凝土结构受力后期性能进行深入研究。 ③提出了解决割线刚度迭代数值问题的计算起点平移算法。本文的非线性有限元分析采用的是割线刚度迭代法，鉴于钢筋混凝土本构模型的复杂性，在进行三维有限元分析时，不可避免地会遇到割线刚度异常产生的数值问题，只有解决这些数值问题，才能得到合理的分析结果。 ④解决了三维滞回分析历史变量继承问题。在进行钢筋混凝土三维滞回分析时，需要采用钢筋混凝土的滞回本构模型。滞回模型中需要存储大量的历史变量，，对于三个方向的三套历史变量，就存在着历史变量的继承问题。在钢筋混凝土三维滞回有限元分析时，该问题直接影响着分析结果的稳定性和正确性。通过本文的研究工作，主要取得了如下成果： ①基于本文提出的有限元分析算法和单元模型，编制了钢筋混凝土非线性有限元程序。 ②运用本文的程序对弯扭组合受力的梁、剪切板和带翼缘的剪力墙进行了单调和滞回分析，取得了良好的模拟效果，同时验证了本文程序的有效性。
[Abstract]:Reinforced concrete structures exhibit complex nonlinear performance when subjected to force. With the continuous improvement of computer performance, finite element method is widely used in nonlinear analysis of reinforced concrete as a powerful means of numerical simulation.It is expected that the nonlinear behavior of reinforced concrete can be well simulated.In this paper, based on the two-dimensional nonlinear finite element analysis of our research group, we refer to the analysis ideas of the Vecchio research team of the University of Toronto.Based on the modified baroclinic field theory, a 3D nonlinear finite element analysis algorithm for reinforced concrete is established using the Secant stiffness iteration method.The main achievements are as follows:1. A three-dimensional element model suitable for modified baroclinic field theory is established.The modified baroclinic theory holds that the cracked reinforced concrete is a kind of orthotropic continuous solid medium with uniform distribution of cracks. The relationship between the average stress and the average strain of the "new material" can be measured by experiments.When the modified baroclinic theory is used for 3D finite element analysis, it is necessary to use the element model to describe the relationship between the average stress and the average strain of the element by using the modified baroclinic field theory.2. The calculation method of three-dimensional displacement loading control is perfected.The nonlinear finite element analysis of reinforced concrete structures is similar to the structural tests in that there are two kinds of load control modes: force loading and displacement loading.The "rising section" curve of the relationship between force and deformation of reinforced concrete structures can be obtained by force loading mode.By displacement loading mode, the whole process curve of structural force and deformation relationship can be obtained.Therefore, displacement loading can be used to study the behavior of reinforced concrete structures.3. The starting point translation algorithm is proposed to solve the iterative numerical problem of Secant stiffness.The nonlinear finite element analysis in this paper is based on the iterative method of Secant stiffness. In view of the complexity of the constitutive model of reinforced concrete, it is inevitable to encounter numerical problems caused by abnormal Secant stiffness in 3D finite element analysis.Only by solving these numerical problems can reasonable analysis results be obtained.4. The problem of inheritance of historical variables in 3D hysteretic analysis is solved.In the three-dimensional hysteretic analysis of reinforced concrete, the hysteretic constitutive model of reinforced concrete should be adopted.A large number of historical variables need to be stored in the hysteretic model. For the three sets of historical variables in three directions, there exists the problem of inheritance of historical variables.In three dimensional hysteretic finite element analysis of reinforced concrete, this problem directly affects the stability and correctness of the analysis results.Through the research work of this paper, the main achievements are as follows:1. Based on the finite element analysis algorithm and element model presented in this paper, a nonlinear finite element program for reinforced concrete is developed.2 the monotone and hysteretic analysis of beam, shear plate and shear wall with flange are carried out by using the program in this paper, and good simulation results are obtained, and the validity of the program is verified.
【学位授予单位】：重庆大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TU375

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