Ultimate strength prediction of I-core sandwich plate based on BP neural network

参数	数值
上下面板厚度t_p /mm	2，3，4
腹板厚度t_w /mm	2，4，6，8
腹板高度h_w /mm	40，60，80
腹板间距d_w /mm	80，120，160
横梁间距a/mm	2 500，3 000，3 500
屈曲半波数e	15
屈服强度σ_Y /MPa	235，315，390

Table 2. Boundary condition of longitudinal 3 spans model with actual strong members
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Table 2. Boundary condition of longitudinal 3 spans model with actual strong members
施加范围 U_x U_y U_z R_x R_y R_z
A1-B1，A1'-B1'，A2-B2，A2'-B2' 0 0 0
A1-A2，A1'-A2' 位移载荷 0 0 0 0
B1-B2，B1'-B2' 0 0 0 0 0
C1-D1，C2-D2，E1-F1，E2-F2，G1-H1，G2-H2，J1-K1，J2-K2 0

Table 3. Boundary condition of longitudinal 1/2+1+1/2 spans (boundary conditions instead of strong beams) model
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Table 3. Boundary condition of longitudinal 1/2+1+1/2 spans (boundary conditions instead of strong beams) model
施加范围 U_x U_y U_z R_x R_y R_z
A1-B1，A1'-B1'，A2-B2，A2'-B2' 0 0 0
A1-A2，A1'-A2' 位移载荷 0 0
B1-B2，B1'-B2' 0 0 0
K1-K2，L1-L2 0 0

Table 4. Boundary condition of longitudinal 1 span (boundary conditions instead of strong members) model
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Table 4. Boundary condition of longitudinal 1 span (boundary conditions instead of strong members) model
施加范围 U_x U_y U_z R_x R_y R_z
A1-B1，A1'-B1'，A2-B2，A2'-B2' 0 0 0
A1-A2，A1'-A2' 位移载荷 0 0 0 0
B1-B2，B1'-B2' 0 0 0 0 0

Table 5. Numerical results of I-core sandwich panels with different mesh densities
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Table 5. Numerical results of I-core sandwich panels with different mesh densities
网格大小/mm σ_u /MPa
1/8h_w 183.671 7
1/4h_w 184.319 9
1/2h_w 189.535 6
h_w 207.345 3

Table 6. Performance comparison of different training function

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Table 6. Performance comparison of different training function

函数	算法	迭代次数	迭代精度
Trainlm	Levenberg-Marquardt法	25	0.002 0
Traingd	梯度递减法	1 000	0.012 1
Traingdm	带动量因子的梯度递减法	1 000	0.034 7
Traingda	带自适应学习率的梯度递减法	1 000	0.005 9
Traingdx	带自适应学习率和动量因子的梯度递减法	1 000	0.010 1

Table 7. Performance comparison of different number of neurons

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Table 7. Performance comparison of different number of neurons

隐藏层1的神经元个数	隐藏层2的神经元个数	迭代次数	迭代精度
3	0	1 000	0.002 2
4	0	1 000	0.003 4
5	0	1 000	0.002 5
6	0	1 000	0.002 7
7	0	235	0.002 0
8	0	360	0.002 0
9	0	25	0.002 0
10	0	72	0.001 9
11	0	133	0.002 0
12	0	71	0.001 9
3	3	71	0.002 0
3	4	150	0.002 0
3	5	153	0.001 9
3	6	192	0.001 9
3	7	52	0.002 0
3	8	289	0.002 0
3	9	85	0.002 0

Table 8. The results of FE simulation

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Table 8. The results of FE simulation

序号	λ	β_p	β_w	σ_u /σ_Y	序号	λ	β_p	β_w	σ_u /σ_Y
1	6.370 6	1.351 0	0.675 5	0.880 7	33	3.185 3	0.675 5	1.351 0	0.954 9
2	6.715 4	1.351 0	0.337 8	0.892 1	34	3.357 7	0.675 5	0.675 5	0.992 9
3	7.003 7	1.351 0	0.225 2	0.850 4	35	3.501 9	0.675 5	0.450 3	0.996 8
4	7.249 1	1.351 0	0.168 9	0.795 4	36	3.624 5	0.675 5	0.337 8	0.996 7
5	6.099 1	0.900 7	0.675 5	0.944 7	37	6.240 0	2.026 5	0.675 5	0.581 4
6	6.352 8	0.900 7	0.337 8	0.982 0	38	6.492 9	2.026 5	0.337 8	0.604 5
7	6.576 6	0.900 7	0.225 2	0.981 9	39	6.715 4	2.026 5	0.225 2	0.585 9
8	6.775 9	0.900 7	0.168 9	0.976 4	40	6.913 0	2.026 5	0.168 9	0.565 0
9	5.894 5	0.675 5	0.675 5	0.953 1	41	6.006 7	1.351 0	0.675 5	0.710 8
10	6.094 4	0.675 5	0.337 8	0.996 0	42	6.187 3	1.351 0	0.337 8	0.788 9
11	6.276 1	0.675 5	0.225 2	0.997 4	43	6.352 8	1.351 0	0.225 2	0.776 7
12	6.442 2	0.675 5	0.168 9	0.996 9	44	6.505 0	1.351 0	0.168 9	0.760 1
13	4.431 3	1.351 0	1.013 3	0.861 6	45	5.823 3	1.013 3	0.675 5	0.751 6
14	4.731 1	1.351 0	0.506 6	0.872 9	46	5.963 4	1.013 3	0.337 8	0.882 1
15	4.965 2	1.351 0	0.337 8	0.856 0	47	6.094 4	1.013 3	0.225 2	0.891 3
16	5.153 8	1.351 0	0.253 3	0.830 8	48	6.217 4	1.013 3	0.168 9	0.883 9
17	4.247 1	0.900 7	1.013 3	0.928 1	49	4.311 5	2.026 5	1.013 3	0.669 0
18	4.476 9	0.900 7	0.506 6	0.974 1	50	4.540 3	2.026 5	0.506 6	0.714 0
19	4.669 2	0.900 7	0.337 8	0.974 6	51	4.731 1	2.026 5	0.337 8	0.703 6
20	4.832 7	0.900 7	0.253 3	0.970 2	52	4.893 0	2.026 5	0.253 3	0.685 6
21	4.119 3	0.675 5	1.013 3	0.942 9	53	4.160 0	1.351 0	1.013 3	0.801 5
22	4.304 9	0.675 5	0.506 6	0.992 0	54	4.328 6	1.351 0	0.506 6	0.852 6
23	4.466 4	0.675 5	0.337 8	0.995 1	55	4.476 9	1.351 0	0.337 8	0.851 7
24	4.608 4	0.675 5	0.253 3	0.992 0	56	4.608 6	1.351 0	0.253 3	0.837 3
25	3.429 3	1.351 0	1.351 0	0.900 3	57	4.051 0	1.013 3	1.013 3	0.847 2
26	3.692 6	1.351 0	0.675 5	0.918 6	58	4.184 2	1.013 3	0.506 6	0.907 1
27	3.886 9	1.351 0	0.450 3	0.902 4	59	4.304 9	1.013 3	0.337 8	0.913 6
28	4.036 6	1.351 0	0.337 8	0.883 4	60	4.414 9	1.013 3	0.253 3	0.909 0
29	3.282 4	0.900 7	1.351 0	0.943 7	61	3.319 0	2.026 5	1.351 0	0.714 7
30	3.491 5	0.900 7	0.675 5	0.980 0	62	3.527 0	2.026 5	0.675 5	0.775 6
31	3.658 4	0.900 7	0.450 3	0.979 4	63	3.692 6	2.026 5	0.450 3	0.783 6
32	3.795 1	0.900 7	0.337 8	0.969 3	64	3.828 0	2.026 5	0.337 8	0.777 2

Table 9. Parameter values of prediction equation for ultimate strength of I-core sandwich panels

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Table 9. Parameter values of prediction equation for ultimate strength of I-core sandwich panels

k	j	i	w_ij	b_j	w_jk	b_k
1	1	1	15.787 83	−8.060 5	−1.134 29	3.508 448
		2	−1.317 5
		3	1.242 68
	2	1	−3.184 67	14.235 29	0.202 705
		2	−12.944 9
		3	−1.725 95
	3	1	−5.953 61	1.084 991	−0.376 16
		2	11.236 42
		3	0.961 726
	4	1	29.143 18	−14.747 2	0.815 201
		2	−3.361 12
		3	4.365 897
	5	1	0.309 728	−3.401 43	−0.135 02
		2	15.531 94
		3	−12.604 4
	6	1	−1.301 16	−1.886 73	−2.492 59
		2	−6.731 54
		3	8.029 399
	7	1	6.911 944	−9.691 39	−0.172 38
		2	12.653 35
		3	6.526 226
	8	1	2.203 471	1.637 875	−2.538 26
		2	6.820 759
		3	−7.541 44
	9	1	−6.343 71	5.825 758	0.036 682
		2	−13.337 1
		3	−3.522 82

Table 10. Parameters of I-core sandwich panels

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Table 10. Parameters of I-core sandwich panels

序号	λ	β_p	β_w	σ_u /σ_Y
1	4.962 2	0.965 0	0.562 9	0.921 4
2	5.131 2	0.965 0	0.337 8	0.949 6
3	5.283 2	0.965 0	0.241 3	0.945 0
4	5.829 0	2.346 2	0.651 7	0.502 8
5	6.013 8	2.346 2	0.391 0	0.512 9
6	6.180 7	2.346 2	0.279 3	0.502 2
7	5.638 6	1.675 9	0.651 7	0.618 2
8	5.779 2	1.675 9	0.391 0	0.648 9
9	5.909 6	1.675 9	0.279 3	0.647 4
10	4.927 6	1.740 4	1.015 3	0.675 8
11	5.174 9	1.740 4	0.609 2	0.679 8
12	5.380 0	1.740 4	0.435 1	0.666 9
13	4.943 5	1.243 2	0.609 2	0.852 1
14	5.116 1	1.243 2	0.435 1	0.851 7
15	3.713 2	2.026 5	0.788 1	0.681 2
16	3.859 8	2.026 5	0.472 9	0.705 2
17	3.987 5	2.026 5	0.337 8	0.709 6
18	3.596 2	1.447 5	0.788 1	0.801 5
19	3.710 2	1.447 5	0.472 9	0.829 8
20	3.813 2	1.447 5	0.337 8	0.834 1

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Yuwen WEI, Qiang ZHONG, Deyu WANG. Ultimate strength prediction of I-core sandwich plate based on BP neural network[J]. Chinese Journal of Ship Research, 2022, 17(2): 125

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Paper Information

Category: Ship Structure and Fittings

Received: Mar. 30, 2021

Accepted: --

Published Online: Mar. 24, 2025

The Author Email:

DOI:10.19693/j.issn.1673-3185.02335

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Geometrical size and material parameters of I-core sandwich panels

Table 1. Geometrical size and material parameters of I-core sandwich panels

Table 2. Boundary condition of longitudinal 3 spans model with actual strong members

Table 2. Boundary condition of longitudinal 3 spans model with actual strong members

Table 3. Boundary condition of longitudinal 1/2+1+1/2 spans (boundary conditions instead of strong beams) model

Table 3. Boundary condition of longitudinal 1/2+1+1/2 spans (boundary conditions instead of strong beams) model

Table 4. Boundary condition of longitudinal 1 span (boundary conditions instead of strong members) model

Table 4. Boundary condition of longitudinal 1 span (boundary conditions instead of strong members) model

Table 5. Numerical results of I-core sandwich panels with different mesh densities

Table 5. Numerical results of I-core sandwich panels with different mesh densities

Table 6. Performance comparison of different training function

Table 6. Performance comparison of different training function

Table 7. Performance comparison of different number of neurons

Table 7. Performance comparison of different number of neurons

Table 8. The results of FE simulation

Table 8. The results of FE simulation

Table 9. Parameter values of prediction equation for ultimate strength of I-core sandwich panels

Table 9. Parameter values of prediction equation for ultimate strength of I-core sandwich panels

Table 10. Parameters of I-core sandwich panels

Table 10. Parameters of I-core sandwich panels