石英纤维/环氧树脂复合材料结构静强度的可靠度计算及全局灵敏度分析

周春苹; 刘付超; 周长聪; 李兴德

doi:10.13801/j.cnki.fhclxb.20190930.002

石英纤维/环氧树脂复合材料结构静强度的可靠度计算及全局灵敏度分析

doi: 10.13801/j.cnki.fhclxb.20190930.002

1.
航空工业特种所　高性能电磁窗航空科技重点实验室，济南 250023
2.
西北工业大学　力学与土木建筑学院，西安 710072

基金项目: 国家自然科学基金(51975476)

详细信息

通讯作者:
周春苹，硕士，高级工程师，研究方向为复合材料结构的强度计算、试验及可靠性分析 E-mail：zcp99241@126.com

中图分类号: TB330.1；TB114.3
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- 被引次数: 0
出版历程
- 收稿日期: 2019-07-12
- 录用日期: 2019-09-17
- 网络出版日期: 2019-09-30
- 刊出日期: 2020-07-15

Reliability and global sensitivity analysis for static strength of quartz/epoxy composite

1.
Key Lab for Airborne Hi-performance Electro-magnetic Window, RISAC, Ji’nan 250023, China
2.
School of Mechanics and Civil Engineering, Northwestern Polytechnical University, Xi’an 710072, China

摘要

摘要: 以石英纤维/环氧树脂复合材料结构为研究对象，考虑设计参数的随机性，采用全局灵敏度分析理论，研究了各输入随机因素对石英纤维/环氧树脂复合材料结构静强度响应的影响。首先利用MATLAB和NASTRAN的联合仿真得到各输入变量样本值对应的输出响应值，结合自适应Kriging模型构建极限状态函数的代理模型，在此基础上实现石英纤维/环氧树脂复合材料结构静强度可靠度及各输入变量的不确定性对输出响应及失效概率全局灵敏度的计算，得到输入变量的全局灵敏度排序结果，为工程实际中复合材料结构的优化设计提供一定指导。
- 复合材料结构 /
- 全局灵敏度分析 /
- Kriging模型 /
- MATLAB /
- 可靠性
Abstract: Taking the quartz/epoxy composite structure as the object, the global sensitivity theory was adopted to analyze the influences of the input parameters on the strength response of quartz/epoxy composite structure by considering the random characteristics of the input parameters. MATLAB and NASTRAN were combined to obtain the output response after considering all the input parameter randomness, then the adaptive Kriging model was introduced to construct the ultimate surrogate model. On basis of this surrogate model, the reliability of overall strength of the quartz/epoxy composite structure was computed, and the global sensitivity indices reflecting the influences of the input parameters on the output response were also obtained. The importance of the input parameters can be ranked according to the sensitivity results, which can provide guidance information for the design of composite structure.
- composite structure /
- global sensitivity analysis /
- Kriging model /
- MATLAB /
- reliability

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图 1 石英纤维/环氧树脂复合材料结构有限元模型

Figure 1. Finite element model of quartz/epoxy composite structure

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图 2 石英纤维/环氧树脂复合材料结构最小强度比

Figure 2. Minimum strength ratio of quartz/epoxy composite structure

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图 3 石英纤维/环氧树脂复合材料结构的变形

Figure 3. Deformation of quartz/epoxy composite structure

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图 4 Kriging模型训练流程

Figure 4. Diagram for training of Kriging model

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图 5 石英纤维/环氧树脂复合材料结构输入变量对输出响应最大z向位移方差的影响

Figure 5. Influence of input variable randomness of quartz/epoxy composite structure on square variance of maximum z deformation output response

S—Main indice; S_T—Total indice

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图 6 石英纤维/环氧树脂复合材料结构输入变量对输出响应强度裕度方差的影响

Figure 6. Influence of input variable randomness of quartz/epoxy composite structure on square variance for margin of safety output response

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图 7 石英纤维/环氧树脂复合材料结构的输入变量对输出响应最大z向位移失效概率的影响

Figure 7. Influence of input variable randomness of quartz/epoxy composite structure on failure probability of maximum z displacement output response

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图 8 石英纤维/环氧树脂复合材料结构的输入变量对输出响应强度裕度失效概率的影响

Figure 8. Influence of input variable randomness of quartz/epoxy composite structure on safety margin failure probability output response

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表 1 石英纤维/环氧树脂复合材料结构参数化建模输入随机因素设置

Table 1. Settings of input randomness for parametric modeling of quartz/epoxy composite structure

Mark	Mean	Standard deviation	Distribution type
${E_{11}}/{\rm{GPa}}$	37	3.7	Normal
${E_{22}}/{\rm{GPa}}$	10	1.0	Normal
${G_{12}}/{\rm{GPa}}$	4.1	0.41	Normal
${G_{13}}/{\rm{GPa}}$	3.3	0.33	Normal
${G_{23}}/{\rm{GPa}}$	3.3	0.33	Normal
A₀/(°)	0	4.5	Normal
A₉₀/(°)	90	4.5	Normal
A₄₅/(°)	45	4.5	Normal
A₋₄₅/(°)	−45	4.5	Normal
t/mm	0.13	0.013	Normal
$\rho$/(kg·m⁻³)	1 700	170	Normal
${T_{11}}/{\rm{MPa}}$	1 500	150	Normal
${C_{11}}/{\rm{MPa}}$	750	75.0	Normal
${T_{22}}/{\rm{MPa}}$	390	39.0	Normal
${C_{22}}/{\rm{MPa}}$	180	18.0	Normal
${S_{12}}/{\rm{MPa}}$	100	10.0	Normal
${S_{\rm{S}}}/{\rm{MPa}}$	85.0	8.5	Normal
Notes: ${E_{11}}$—Modulus in 11 direction; ${E_{22}}$—Modulus in 22 direction; ${G_{12}}$—Modulus in 12 direction; ${G_{13}}$—Modulus in 13 direction; ${G_{23}}$—Modulus in 23 direction; A₀—0° ply angle; A₉₀—90° ply angle; A₄₅—45° ply angle; A₋₄₅—–45° ply angle; $t$—Monolayer thickness; $\rho $—Material density; ${T_{11}}$—Tensile strength in 11 direction; ${C_{11}}$—Compression strength in 11 direction; ${T_{22}}$—Tensile strength in 22 direction; ${C_{22}}$—Compression strength in 22 direction; ${S_{12}}$—Shear strength in plane; ${S_{\rm{S}}}$—Shear strength in interlayer.

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表 2 计算石英纤维/环氧树脂复合材料结构强度裕度用变量

Table 2. Variables used in strength analysis of quartz/epoxy composite structure

Variable	Mark
${X_1}$	${E_{11}}$; ${E_{22}}$; ${G_{12}}$; ${G_{13}}$; ${G_{23}}$
${X_2}$	${T_{11}}$; ${C_{11}}$; ${T_{22}}$; $C{}_{22}$; ${S_{12}}$; ${S_{\rm{S}}}$
${X_3}$	${A_0}$
${X_4}$	${A_{90}}$
${X_5}$	${A_{45}}$
${X_6}$	${A_{{\rm{ - }}45}}$
${X_7}$	$t$
${X_8}$	$\rho $

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表 3 计算石英纤维/环氧树脂复合材料结构变形用变量

Table 3. Variables used in deformation analysis of quartz/epoxy composite structure

Variable	Mark
${X_1}$	${E_{11}}$; ${E_{22}}$; ${G_{12}}$; ${G_{13}}$; ${G_{23}}$
${X_2}$	${A_0}$
${X_3}$	${A_{90}}$
${X_4}$	${A_{45}}$
${X_5}$	${A_{{\rm{ - }}45}}$
${X_6}$	$t$
${X_7}$	$\rho $

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