Influence of allowable stress on structural design of ring-stiffened cylindrical shells
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摘要:
目的 旨在研究不同肋骨的许用应力对圆柱壳结构设计的影响。 方法 采用全因子试验设计和信息熵方法，建立基于综合裕度的环肋圆柱壳多目标优化模型，并利用宽容度排序法对建立的多目标优化模型进行优化求解，以及通过改变肋骨许用应力安全系数，分析肋骨许用应力对圆柱壳各属性均匀度的影响。 结果 结果表明，圆柱壳肋骨应力为主要设计约束，当肋骨许用应力安全系数为 0.675时, 圆柱壳各属性裕度较均匀，约15%, 此时结构重量也相对较小。 结论 因此，适当放宽肋骨许用应力可以解决肋骨应力为结构设计主要约束问题，使最优解的各属性裕度之间更加均匀。 Abstract:Objective This paper aims to study the influences of different allowable stresses of ribs in cylindrical shell design. Methods To this end, this paper uses full factorial experimental design and information entropy method to establish a multi-objective optimization model of ring-stiffened cylindrical shells based on the weighted-sum method, then uses the tolerance ranking method to optimize the solution of the model. Through changing the safety factor of allowable stress of ribs, the influences of them on the uniformity of the attributes of the cylindrical shell are analyzed. Results The results show that the rib stress is the main constraint in design. When the safety factor of the allowable stress of ribs is 0.675, the margins of each attribute value are more uniform at about 15%, and the structural weight is relatively small at this time. Conclusions Therefore, properly extending the allowable stress can solve the problem being the main constraint in structural design, and make the margins of each attribute value of the optimal solution more uniform. -
图 1 典型舱段的环肋圆柱壳结构示意图
Figure 1. Schematic diagram of ring-stiffened cylindrical shell structure for a typical compartment
图 2 可行解的各属性裕度统计盒式图
Figure 2. Box plot of margins of each attribute value for feasible solutions
表 1 宽容度排序法的计算过程
Table 1. Computing process of tolerance ranking method
序号 目标函数 约束条件 最优值 宽容度约束 1 $ {f_1}\left( X \right) $ $ g\left( x \right) \geqslant \;e(x) $ $ {f_1}^\prime $ ${j_1}:(1 - {\delta _1}){f_1}^\prime \leqslant {f_1} \leqslant {f_1}^\prime$ 2 $ {f_2}\left( X \right) $ $ g\left( x \right) \geqslant \;e(x) $,${j_1}$ $ {f_2}^\prime $ ${j_2}:(1 - {\delta _2}){f_2}^\prime \leqslant {f_2} \leqslant {f_2}^\prime$ … … … … … q-1 ${f_{ { {q} } - 1} }\left( X \right)$ $ g\left( x \right) \geqslant \;e(x) $,${j_1}$,${j_2},\cdots$,${j_{q - 2} }$ ${f'_{ { {q} } - 1} }$ ${j_{ {{q} } - 1} }:(1 - {\sigma _{ { {q} } - 1} }){f'_{ { {q} } - 1} } {\leqslant} {f_{ { {q} } - 1} } {\leqslant} {f'_{ { {q} } - 1} }$ q ${f_{ {q} } }\left( X \right)$ $ g\left( x \right) \geqslant \;e(x) $,${j_1}$,${j_2},\cdots$,${j_{q - 1} }$ ${f_{ {q} } }^\prime$ -- 注： $ g\left( x \right) \geqslant \;e(x) $为约束条件，其中$ g\left( x \right) $为约束函数，$ e(x) $为约束边界；δ为宽容度取值的变量。 
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表 2 典型舱段环肋圆柱壳结构设计变量取值范围
Table 2. Range of design variables of ring-stiffened cylindrical shell structure for a typical compartment
设计变量 下限值 上限值 水平 步长 R/m 4.2 5.8 5 0.4 L/m 9 14 6 1 h/m 0.03 0.05 21 0.001 l/m 0.5 0.7 5 0.05 cn 31 39 9 1
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表 3 各属性裕度约束范围及可行解的占比
Table 3. The constraint range of margins of each attribute value and proportion of feasible solutions
属性 $ \sigma _2^0 $ $ {\sigma '_1} $ ${\sigma _{ {\rm{l} }{\kern 1pt} {\kern 1pt} {\kern 1pt} } }$ ${P_{{\rm{cr}}} }$ ${P'_{{\rm{cr}}} }$ 设定的裕度约束上限值/% 15 30 15 20 20 裕度约束范围内可行解占比/% 40 42 84 46 55
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表 4 最优解
Table 4. The optimum solutions（g1-8%, g2-10%）
R/m h/m L/m l/m cn $ {w'_1} $ /% $ w_2^0 $/% ${w_{ \rm{l} } }$/% ${w_{{\rm{cr}}} }$/% ${w'_{{\rm{cr}}} }$/% g1 g2 M/t 4.6 0.036 9 0.65 35 29.69 13.51 2.94 15.90 17.58 0.063 0.162 96.77
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表 5 不同肋骨许用应力对应的最优解（g2-10%，g1-8%）
Table 5. The optimum solutions of different allowable stress of ribs（g2-10%，g1-8%）
xf R/m h/m L/m l/m cn $ {w'_1} $ % $ w_2^0 $/% ${w_{\rm{l} } }$/% ${w_{{\rm{cr}}} }$/% ${w'_{{\rm{cr}}} }$/% g1 g2 M/t 0.60 4.6 0.036 9 0.65 35 29.69 13.51 2.94 15.90 17.58 0.09 0.17 96.77 0.625 4.6 0.036 9 0.65 35 29.69 13.51 6.82 15.90 17.58 0.11 0.17 96.77 0.65 4.6 0.036 9 0.65 35 29.69 13.51 10.41 15.90 17.58 0.13 0.17 96.77 0.675 4.2 0.033 9 0.60 32 29.21 13.52 14.00 15.64 16.82 0.15 0.16 82.46 0.70 4.6 0.035 9 0.65 34 27.64 9.94 13.27 12.17 12.86 0.13 0.12 92.89 0.725 4.6 0.035 9 0.65 32 29.39 8.56 14.10 12.17 7.04 0.14 0.10 90.73 0.75 4.6 0.034 9 0.60 31 29.96 6.97 14.48 10.23 5.88 0.13 0.08 90.28 0.775 5.4 0.039 9 0.70 35 29.12 4.38 14.66 8.10 2.69 0.12 0.06 118.10 0.80 5.8 0.040 9 0.70 37 27.07 1.36 14.39 3.47 1.70 0.11 0.03 131.93
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表 6 不同肋骨许用应力对应的最优解（g2-30%，g1-15%）
Table 6. The optimum solutions of different allowable stress of ribs（g2-30%，g1-15%）
xf R/m h/m L/m l/m cn $ {w'_1} $ % $ w_2^0 $/% ${w_{\rm{l} } }$/% ${w_{{\rm{cr}}} }$/% ${w'_{{\rm{cr}}} }$/% g1 g2 M/t 0.60 4.2 0.033 9 0.65 32 26.33 11.08 2.09 13.21 13.30 0.07 0.13 79.19 0.625 4.2 0.032 9 0.60 32 25.14 10.96 5.30 11.73 15.04 0.09 0.13 80.60 0.65 4.2 0.033 9 0.65 32 26.33 11.08 9.62 13.21 13.30 0.12 0.13 79.19 0.675 4.2 0.033 9 0.65 31 28.13 9.92 10.86 13.21 10.34 0.12 0.12 77.65 0.70 4.2 0.031 9 0.55 31 25.87 9.61 12.85 9.76 13.39 0.13 0.11 78.43 0.725 4.2 0.030 9 0.55 31 21.34 6.84 14.09 5.96 11.33 0.12 0.08 76.57 0.75 4.6 0.034 9 0.65 31 27.33 4.73 13.39 8.41 2.84 0.12 0.06 86.99 0.775 5.0 0.036 9 0.65 32 28.65 3.61 13.99 7.51 0.34 0.12 0.05 100.75 0.80 5.8 0.040 9 0.70 37 27.07 1.36 14.39 3.47 1.70 0.11 0.03 131.93
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表 7 不同肋骨许用应力对应的最优解（g2-40%，g1-20%）
Table 7. The optimum solutions of different allowable stress of ribs（g2-40%，g1-20%）
xf R/m h/m L/m l/m cn $ {w'_1} $ % $ w_2^0 $/% ${w_{\rm{l} } }$/% ${w_{{\rm{cr}}} }$/% ${w'_{{\rm{cr}}} }$/% g1 g2 M/t 0.60 4.2 0.030 9 0.55 33 17.82 9.86 1.72 5.96 18.14 0.06 0.11 80.44 0.625 4.2 0.031 9 0.55 31 25.87 9.61 2.39 9.76 13.39 0.07 0.11 78.43 0.65 4.2 0.031 9 0.55 31 25.87 9.61 6.14 9.76 13.39 0.09 0.11 78.43 0.675 4.2 0.032 9 0.65 32 21.98 8.32 11.31 9.07 11.57 0.11 0.10 77.33 0.70 4.2 0.032 9 0.65 31 23.92 7.13 12.34 9.07 8.65 0.12 0.09 75.78 0.725 4.6 0.034 9 0.65 32 25.62 6.01 12.43 8.41 5.54 0.11 0.07 88.68 0.75 4.6 0.034 9 0.65 31 27.33 4.73 13.39 8.41 2.84 0.12 0.06 86.99 0.775 5.0 0.036 9 0.65 32 28.65 3.61 13.99 7.51 0.34 0.12 0.05 100.75 0.80 5.4 0.037 9 0.60 34 28.91 2.62 14.97 2.60 2.71 0.12 0.03 118.20
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