Reliability and global sensitivity analysis for static strength of quartz/epoxy composite
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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。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.
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Key words:
- composite structure /
- global sensitivity analysis /
- Kriging model /
- MATLAB /
- reliability
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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. 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 $ 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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