钢筋混凝土矩形板薄膜效应的有限元分析（可复制毕业论文）.pdf

华中科技大学
硕士学位论文
钢筋混凝土矩形板薄膜效应的有限元分析
姓名:李永春
申请学位级别:硕士
专业:结构工程
指导教师:张先进
20061106
摘要
已有的试验结果表明,在支承边界受到水平约束条件下,钢筋混凝土板的极限承
载力明显高于未受水平约束板的极限承载力,这种现象称为“薄膜效应”。如何准确
考虑薄膜效应对板承载力的影响,建立一种技术先进、经济合理的设计理论,已成为
工程界需要解决的一大问题。
本文首先介绍了薄板的弹性理论及相应的薄板弯曲内力方程和薄板平衡微分方
程,同时介绍了板的极限分析方法塑性铰线理论,该理论是本文研究的基础。
其次,详细介绍了有限单元法模型,混凝土本构关系,破坏准则以及非线性方程
的求解方法。运用有限元软件 ANSYS 对四边固支试验板进行了仿真计算,并将计算
值与最大薄膜应力法计算值和试验值进行对比分析,结果表明有限元法能较真实地反
映水平受约束板的实际受力特性。在此基础上运用建立的有限元模型改变板厚、平面
尺寸、板的配筋率、混凝土强度,分析各种参数对板薄膜效应的影响规律。
最后,基于塑性铰线理论给出了四边固支钢筋混凝土矩形薄板的破坏模型,由虚
功原理,推导出考虑薄膜效应情况下钢筋混凝土矩形板的极限承载力公式,其中平均
受压区高度为待定参数,通过用 MATLAB 对非线性有限元程序计算的结果进行了非
线性回归分析确定。对比分析表明,该公式与试验值吻合程度良好,可供工程设计以
及该问题的进一步研究提供参考。



关键词:薄膜效应塑性铰线理论最大薄膜应力有限元分析极限承载力
Abstract
Experiment results existed show that when horizontal boundaries of reinforced
concrete slab are restrained its ultimate bearing capacity is significantly higher than that
has not, which is called membrane effect. How to calculate membrane effect accurately so
as to create a more advanced and reasonable design theory has e a serious problem
that need to be solved in engineering.
At first, in the thesis, elastic theory of thin slab and Differential equation of thin slab
equilibrium and internal force equation of thin slab bending are introduced. In the
meanwhile, limit analysis method plastic hinged lines theory is introduced. My research is
based on this theory.
Secondly, finite element model、concrete constitutive relationship、damage criterion
and the solution of nonlinear equations are introduced. Simulation analysis of tested
rectangular slabs using finite element software ANSYS are carried out, the whole
boundaries of which are restrained. The calculation values pared with maximum
membrane force method ones and experimental ones. The result shows that the finite
element method can actually reflect mechanical characteristics of horizontal restrained slab.
Using this finite element model and changing slab thickness、slab dimension