平面钢框架弹塑性分析的QR法及程序设计

发布时间：2018-06-09 02:07

本文选题：平面钢框架 + QR法　；参考：《广西大学》2017年硕士论文

【摘要】：本文综合考虑材料非线性和几何非线性对平面钢框架结构的影响,基于层纤维模型和三段式线性分布刚度模型,利用VC6.0程序软件编写了平面钢框架弹塑性分析的QR法计算程序。该程序既能很好地描述平面钢框架结构塑性沿杆件截面高度的渐变过程,又能描述塑性沿杆件长度的渐变过程。另外,该程序摒弃了根据线性叠加原理确定结构最不利内力和采用计算长度系数近似考虑结构整体稳定和局部稳定的相关性的现行钢结构规范做法,免去了单个构件逐一计算的繁琐过程,大大提高了计算效率。本文主要研究方法如下:方法一:基于平截面假定和层纤维模型,考虑梁柱单元杆件截面瞬时抗拉刚度EA和截面瞬时抗弯刚度EI随截面塑性沿截面高度的渐变,编制C语言程序Solve_EA_EI.c用于求解梁柱单元在塑性状态下的杆件单元截面瞬时刚度值。方法二:介绍了 QR法的基本原理并利用QR方法对平面钢框架进行了相关分析。方法三:采用三段式线性分布刚度模型,推导了该分布塑性模型下的单元刚度矩阵,包括一阶弹塑性分析的单元刚度矩阵和二阶弹塑性分析的单元刚度矩阵。编制了平面钢框架非线性分析的QR法计算格式,对相关典型文献中的案例和有限元模拟结果进行分析对比,验证了本文方法的高效性、实用性和精确性。研究表明:与集中塑性铰模型相比,采用三段式线性分布塑性区模型对钢框架结构的侧移具有增大作用,本文所采用的模型不但可以判断塑性沿截面高度的渐变过程,还可以判断塑性变形沿杆长的渐变过程,克服了集中塑性模型将塑性限定在有限单元结点的缺陷,并且根据塑性区的渐变高度和渐变长度,可以综合评估塑性区的严重程度。利用文本编制的QR计算程序不但可以提高计算效率和计算精度,还能根据塑性的发展方向,初步估计结构的薄弱层,为结构的优化设计提供新思路。同时考虑二阶效应时,钢框架顶层的侧移量将进一步增大,延性提高,整体极限承载力降低;另外结构塑性扩展顺序与集中塑性交模型也略有不同,本文的结果准确性相对较高。
[Abstract]:In this paper, considering the influence of material nonlinearity and geometric nonlinearity on plane steel frame structure, based on layer fiber model and three-segment linear distributed stiffness model, a QR program for elastic-plastic analysis of plane steel frame is developed by using VC6.0 program software. The program can not only describe the gradual change process of the plasticity along the height of the member section, but also describe the gradual change process of the plasticity along the length of the bar. In addition, the program abandons the current steel structure code which determines the most unfavorable internal force of the structure according to the principle of linear superposition and considers the correlation between the global and local stability of the structure by using the calculated length coefficient approximately. The calculation efficiency is greatly improved by eliminating the tedious process of calculating single component one by one. The main research methods of this paper are as follows: method 1: based on the assumption of plane section and fiber model, the transient tensile stiffness EA and the bending stiffness ei of Liang Zhu element members are considered. A C language program, SolveEAS EI.c, is developed to solve the transient stiffness of the member section of Liang Zhu element in plastic state. Method two: the basic principle of QR method is introduced and the correlation analysis of plane steel frame is carried out by using QR method. Method three: the element stiffness matrix under the distributed plastic model is derived by using the three-segment linear distributed stiffness model, including the element stiffness matrix of the first order elastic-plastic analysis and the element stiffness matrix of the second-order elastic-plastic analysis. The QR method for nonlinear analysis of plane steel frames is developed and compared with the results of finite element simulation in some typical literatures. The effectiveness, practicability and accuracy of the proposed method are verified. The results show that compared with the concentrated plastic hinge model, the three-segment linear distribution plastic zone model can increase the lateral displacement of the steel frame structure, and the model used in this paper can not only judge the gradual change process of the plasticity along the section height. It is also possible to judge the gradual process of plastic deformation along the bar length, overcome the limitation of the concentrated plastic model to limit the plasticity to the finite element node, and evaluate the severity of the plastic zone synthetically according to the gradient height and the gradual length of the plastic zone. The QR program compiled by the text can not only improve the calculation efficiency and accuracy, but also estimate the weak layer of the structure according to the development direction of plasticity, and provide a new way of thinking for the optimization design of the structure. At the same time, considering the second order effect, the lateral displacement of the top layer of the steel frame will further increase, the ductility will increase, and the overall ultimate bearing capacity will be reduced. In addition, the plastic expansion sequence of the structure is slightly different from that of the concentrated plastic joint model. The accuracy of this paper is relatively high.
【学位授予单位】：广西大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TU391

【参考文献】