Influence of allowable stress on structural design of ring-stiffened cylindrical shells

序号	目标函数	约束条件	最优值	宽容度约束
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。
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} }$	${f_{ {q} } }^\prime$	--

Table 2. Range of design variables of ring-stiffened cylindrical shell structure for a typical compartment
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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
c_n 31 39 9 1

Table 3. The constraint range of margins of each attribute value and proportion of feasible solutions

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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

Table 4. The optimum solutions（g₁-8%, g₂-10%）
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Table 4. The optimum solutions（g₁-8%, g₂-10%）
R/m h/m L/m l/m c_n $ {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

Table 5. The optimum solutions of different allowable stress of ribs（g₂-10%，g₁-8%）

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Table 5. The optimum solutions of different allowable stress of ribs（g₂-10%，g₁-8%）

x_f	R/m	h/m	L/m	l/m	c_n	$ {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

Table 6. The optimum solutions of different allowable stress of ribs（g₂-30%，g₁-15%）

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Table 6. The optimum solutions of different allowable stress of ribs（g₂-30%，g₁-15%）

x_f	R/m	h/m	L/m	l/m	c_n	$ {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

Table 7. The optimum solutions of different allowable stress of ribs（g₂-40%，g₁-20%）

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Table 7. The optimum solutions of different allowable stress of ribs（g₂-40%，g₁-20%）

x_f	R/m	h/m	L/m	l/m	c_n	$ {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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Sheng LI, Zhiqiang WANG, Hong YIN. Influence of allowable stress on structural design of ring-stiffened cylindrical shells[J]. Chinese Journal of Ship Research, 2022, 17(1): 126

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Paper Information

Category: Ship Structure and Fittings

Received: Dec. 24, 2020

Accepted: Dec. 29, 2021

Published Online: Mar. 24, 2025

The Author Email:

DOI:10.19693/j.issn.1673-3185.02239

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Computing process of tolerance ranking method

Table 1. Computing process of tolerance ranking method

Table 2. Range of design variables of ring-stiffened cylindrical shell structure for a typical compartment

Table 2. Range of design variables of ring-stiffened cylindrical shell structure for a typical compartment

Table 3. The constraint range of margins of each attribute value and proportion of feasible solutions

Table 3. The constraint range of margins of each attribute value and proportion of feasible solutions

Table 4. The optimum solutions（g1-8%, g2-10%）

Table 4. The optimum solutions（g1-8%, g2-10%）

Table 5. The optimum solutions of different allowable stress of ribs（g2-10%，g1-8%）

Table 5. The optimum solutions of different allowable stress of ribs（g2-10%，g1-8%）

Table 6. The optimum solutions of different allowable stress of ribs（g2-30%，g1-15%）

Table 6. The optimum solutions of different allowable stress of ribs（g2-30%，g1-15%）

Table 7. The optimum solutions of different allowable stress of ribs（g2-40%，g1-20%）

Table 7. The optimum solutions of different allowable stress of ribs（g2-40%，g1-20%）

Table 4. The optimum solutions（g₁-8%, g₂-10%）

Table 4. The optimum solutions（g₁-8%, g₂-10%）

Table 5. The optimum solutions of different allowable stress of ribs（g₂-10%，g₁-8%）

Table 5. The optimum solutions of different allowable stress of ribs（g₂-10%，g₁-8%）

Table 6. The optimum solutions of different allowable stress of ribs（g₂-30%，g₁-15%）

Table 6. The optimum solutions of different allowable stress of ribs（g₂-30%，g₁-15%）

Table 7. The optimum solutions of different allowable stress of ribs（g₂-40%，g₁-20%）

Table 7. The optimum solutions of different allowable stress of ribs（g₂-40%，g₁-20%）