﻿ 考虑几何缺陷的刚架结构力学性能研究
 舰船科学技术  2018, Vol. 40 Issue (7): 42-46 PDF

Research on physical properties of frame structure with geometrical imperfection
WANG Jian-ling, LV Zhi-min
The 713 Research Institute of CSIC, Zhengzhou 450015, China
Abstract: Analyzed the model of frame structure, in order to obtain a efficient and reliable mechanical performance assessment method for it. Balanced the accuracy and computational efficiency, established the mixed finite element model, considered the geometrical and material nonlinearity in finite element analysis. To account for geometrical imperfection of frame structure effect, carried out eigen buckling analysis, selected the most unfavorable geometrical imperfection instead of utilizing the minimum order buckling mode as geometrical imperfection, and then calculated the frame structural stability. The stochastic imperfection method result verified the correctness and reliability of the above method. Calculations showed the frame structure was sensitive to initial geometrical imperfection, the stability coefficient considering the initial geometrical imperfection was round 30%~40% of perfection structure. For the sake of the reasonable geometrical imperfection, analyzed and compared different geometrical imperfection distribution patterns were necessary.
Key words: geometrical imperfection     frame structure     double nonlinearity     consistent mode imperfection
0 引　言

1 刚架结构

2 仿真模型 2.1 有限元模型

 图 1 混合单元模型 Fig. 1 Mixed finite element model
2.2 双重非线性

 ${\Delta f} = \left( {{{{ K}_0}} + {{{ K}_\sigma }} +{{{ K}_L}} } \right) \cdot {\Delta u} {\text{。}}$ (1)

 ${\Delta f} = \left( { {{{ K}_0}} +{{{ K}_\sigma }} + {{{ K}_L}} - {{{ K}_R}}} \right) \cdot {\Delta u}\text{，}$ (2)

2.3 模型计算

 图 2 材料应力-应变曲线 Fig. 2 stress-strain curve of material

3 缺陷模态分析 3.1 结构几何缺陷

 图 3 非线性分析流程 Fig. 3 Nonlinear analysis flowchart

3.2 结构特征值屈曲

 图 4 第1~15阶屈曲模态 Fig. 4 1st–15th failure mode of frame structure

 图 5 各阶模态稳定系数 Fig. 5 Stability coefficient under different geometrical imperfection
3.3 结构可靠性分析

 $\left| {X' - X} \right| \leqslant R{\text{，}}$ (3)

 $f(x') = \frac{1}{{\sqrt {2\pi } \sigma }}{e^{ - \frac{{{{(x' - \mu )}^2}}}{{2{\sigma ^2}}}}} = \frac{1}{{\sqrt {2\pi } \sigma }}{e^{ - \frac{{{{(x' - x)}^2}}}{{2{\sigma ^2}}}}}{\text{。}}$ (4)

 图 6 架体节点缺陷分布 Fig. 6 Node imperfection distribution of frame structure

 图 7 结构稳定系数分布 Fig. 7 Stability coefficient distribution

4 总　结

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