Journal of Jilin University(Engineering and Technology Edition) ›› 2024, Vol. 54 ›› Issue (10): 2781-2791.doi: 10.13229/j.cnki.jdxbgxb.20221612

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Reliability-based topology optimization and engineering design of stiffened plates

Jian-xing YU1,2(),Ming-xiu WEI1,2,Yang YU1,2,Yu-peng CUI1,2,Yu PAN1,2   

  1. 1.State Key Laboratory of Hydraulic Engineering Simulation and Safety，Tianjin University，Tianjin 300072，China
    2.Tianjin Key Laboratory of Port and Ocean Engineering，Tianjin University，Tianjin 300072，China
  • Received:2022-12-19 Online:2024-10-01 Published:2024-11-22

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Abstract:

For the three-dimensional stiffened plate， a non-nested reliability based topology optimization is proposed in order to achieve lightweight and engineering design while ensuring its safety and reliability. And the reliability concept-detailed combination optimization design is carried out for three-dimensional engineering stiffened plates. By virtue of the decoupling characteristics of the sequential optimization and reliability assessment method external optimization software with variable density method as the core was applied to carry out deterministic topology optimization to improve optimization efficiency. And considering the randomness of loads and materials， the hybrid mean value method was used to search the most probable point in the reliability evaluation stage. Furthermore， the layout of reliability conceptual design was interpreted and the size optimization was carried out to realize the engineering application. The result shows that compared with the deterministic topology optimization， the reliability topology optimization proposed in this paper can meet the requirements of structural reliability and lightweight. The combination optimization strategy of conceptual design and detailed design has realized that the engineering stiffened plate can reduce the material cost by 21.40% while simplifying the layout and ensuring the performance.

Key words: mechanical design, stiffened plate, reliability-based topology optimization, sequential optimization and reliability assessment method, hybrid mean value method, variable density method, size optimization

CLC Number: 

  • P751

Fig.1

Failure probability variation diagram of structure"

Fig.2

Flow chart of HMV method"

Fig.3

Flow chart of SORA reliability-based topology optimization"

Fig.4

Reference model of stiffened plate"

Table 1

Information of each working condition"

工况编号工况描述载荷约束
1面均布载荷均布载荷0.015 MPa四周简支
2线均布载荷两端线均布载荷250 N/mm两端约束Z向位移
3集中力载荷中点和1/4中点处各2×104N四周简支

Fig.5

Schematic diagram of each working condition"

Fig.6

Geometric domain of stiffened plate"

Table 2

Information of independent normal distribution random variable"

μσ
弹性模量E2.1×105 MPa2.1×104
工况1面均布载荷p0.015 MPa0.01
工况2线均布载荷q250 N/mm25
工况3集中力载荷F2.0×104 N2×103

Fig.7

Reliability-based topology optimization history of stiffened plate"

Table 3

Monte Carlo test results of RBTO structure"

项目工况1工况2工况3
可靠度指标β3.00454.26493.8082
可靠概率99.867%99.999%99.993%

Fig.8

Comparison of DTO and RBTO structures"

Fig.9

Displacements of RBTO structure at MPP"

Fig.10

Max displacements of different structures at MPP"

Fig.11

Interpretation of RBTO layout of stiffened plate"

Fig.12

Size optimization results for the topology interpretation layout"

Table 4

Size optimization results of each rectangla?? beam"

梁编号高度/mm宽度/mm梁编号高度/mm宽度/mm
11.5841.5691750.0001.500
21.7251.6131850.0001.506
350.0005.9611950.00043.830
44.3493.442202.4432.686
54.2464.314216.0025.086
63.7103.620224.6352.844
74.3223.879233.4523.341
83.5633.3132450.0001.503
97.3894.3032550.0002.868
103.5344.3572611.1132.010
112.1551.7092750.0001.523
124.1592.7882850.0002.710
134.4034.4172950.0002.330
143.7653.9593047.2603.153
1550.00035.39311.8581.678
163.5951.3533250.00034.750

Table 5

Analysis results of size optimized structure"

名称

工况1

最大位移/mm

工况2

最大位移/mm

工况3

最大位移/mm

结构

体积/mm3

原参考模型6.9785.9875.9982.29×107
尺寸优化 结构6.9995.9975.9991.80×107

Fig.13

Engineering design process of stiffened plates"

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