钛合金耐压夹层圆柱壳芯层结构拓扑优化

张浩宇; 贺章勋; 程远胜

doi:10.19693/j.issn.1673-3185.02385

钛合金耐压夹层圆柱壳芯层结构拓扑优化

doi: 10.19693/j.issn.1673-3185.02385

1.
华中科技大学船舶与海洋工程学院，湖北武汉 430074
2.
武汉第二船舶设计研究所，湖北武汉 430205

详细信息

作者简介:
张浩宇，男，1996 年生，硕士。研究方向：船舶结构优化设计。E-mail：m201971703@hust.edu.cn

贺章勋，男，1981 年生，硕士，高级工程师

程远胜，男，1962 年生，博士，教授，博士生导师。研究方向：船舶海洋结构优化设计。E-mail：yscheng@hust.edu.cn

通信作者:
程远胜

中图分类号: U661.43
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出版历程
- 收稿日期: 2021-05-21
- 修回日期: 2021-11-04
- 网络出版日期: 2023-04-24
- 刊出日期: 2023-04-28

Topology optimization of core structure of titanium alloy sandwich cylindrical shell

1.
School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
2.
Wuhan Second Ship Design and Research Institute, Wuhan 430205, China

钛合金耐压夹层圆柱壳芯层结构拓扑优化由张浩宇，等创作，采用知识共享署名4.0国际许可协议进行许可。

摘要

摘要: 目的因对于钛合金耐压夹层圆柱壳这种新型耐压结构研究得较少，其芯层拓扑形式有待优化确认，需开展芯层拓扑优化。方法首先，选择一个壁厚较大的无加筋圆柱壳作为分析对象，采用ANSYS轴对称单元计算结构的应力；然后，沿圆柱壳厚度方向划分为上、中、下3个区域，将中部区域的结构设为设计变量，并建立其芯层结构形式的两阶段拓扑优化数学模型；最后，基于Matlab建立遗传算法主控程序，针对无加筋圆柱壳芯层的布置，分别仅沿轴向、轴向与径向布置形式两个阶段进行拓扑优化，以验证上述耐压夹层圆柱壳加筋形式的合理性。结果优化方案芯层拓扑形式为等间距设置，垂直连接内壳和外壳的肋板。结论静水压力载荷下的耐压夹层圆柱壳结构是一种合理的耐压结构形式。
- 双层耐压圆柱壳 /
- 强度 /
- 拓扑优化
Abstract: Objectives As a new type of pressure-resistant structure, the titanium alloy sandwich cylindrical shell has not yet been studied comprehensively. The topology of the core layer needs to be confirmed using the optimization method. This paper carries out the core topology optimization of titanium alloy pressure- resistant sandwich cylindrical shells. methods An unreinforced cylindrical shell with high thickness is selected as the analysis object, and the axisymmetric element is used to calculate the structural stresses via ANSYS. The cylindrical shell is divided into the upper, middle and lower regions along the thickness direction. The structures of the middle region are set as the design variables, and a two-stage topology optimization mathematical model of its core structure is proposed. Based on Matlab, the main control program of the genetic algorithm is established to carry out the core layout optimization of the unreinforced cylindrical shell along the axial direction only and both the axial direction and radial direction respectively. results The optimal core topological form consists of equidistant ribs connecting the inner shell and outer shell vertically. Conclusions A sandwich cylindrical shell under hydrostatic pressure is a reasonable pressure-resistant structure.
- pressure-resistant sandwich cylindrical shells /
- strength /
- topology optimization

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图 1 无加筋圆柱壳设计空间

Figure 1. Design space of solid unreinforced cylindrical shell

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图 2 无加筋圆柱壳拓扑优化设计变量定义示意图

Figure 2. Schematics of variable definition for topology optimization design of solid unreinforced cylindrical shell

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图 3 第1阶段设计变量示意图

Figure 3. Design variables in the first stage of topology optimization

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图 4 第1阶段优化方案的几何模型

Figure 4. Geometric model obtained in the first stage of optimization scheme

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图 5 第2阶段优化方案的设计变量定义示意图

Figure 5. Schematic diagram of design variable definition in the second stage of optimization scheme

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图 6 约束条件示意图

Figure 6. Schematic diagram of constraint conditions

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图 7 第2阶段优化方案的几何模型

Figure 7. Geometric model in the second stage of optimization scheme

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图 8 第2阶段优化方案的特征应力云图

Figure 8. Contour plots of characteristic stress obtained in the second stage of optimization scheme

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图 9 工程化处理后的方案几何模型

Figure 9. Geometric model of the scheme after engineering treatment

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图 10 工程化处理后的设计方案应力云图

Figure 10. Contour plots of characterisitic stress in design scheme after engineering treatment

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图 11 耐压夹层圆柱壳几何模型

Figure 11. Geometric model of pressure resisting sandwich cylindric-al shell

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表 1 特征应力约束限界值

Table 1. Limit values of characteristic stress

特征应力	限界值
内壳中面周向应力/MPa	520
外壳中面周向应力/MPa	472
内壳内表面纵向应力/MPa	572
外壳内表面纵向应力/MPa	674
肋骨应力/MPa	400

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表 2 第1阶段优化方案的设计变量取值

Table 2. Selection of design variables in the first stage of optimization scheme

编号	取值	编号	取值	编号	取值
1	0	11	0	21	0
2	1	12	0	22	1
3	0	13	0	23	0
4	0	14	0	24	0
5	0	15	1	25	0
6	0	16	0	26	0
7	0	17	0	27	0
8	0	18	0	28	0
9	1	19	0	29	1
10	0	20	0	30	0

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表 3 第1阶段优化方案的特征应力取值及其限界值

Table 3. Selection of characteristic stresses and their limit values in the first stage of optimization scheme

特征应力	取值	限界值	约束裕度/%
内壳中面周向应力/MPa	519.6	520	0.07
外壳中面周向力/MPa	469.2	472	0.59
内壳内表面纵向应力/MPa	363.1	572	36.50
外壳内表面纵向应力/MPa	202.0	674	70.00
肋骨应力/MPa	349.8	400	12.60

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表 4 第2阶段优化方案的特征应力阻值及其限界值

Table 4. Selection of characteristic stresses and their limit values in the second stage of optimization scheme

特征应力	取值	限界值	约束裕度/%
内壳中面周向应力/MPa	686.1	728.0	5.76
外壳中面周向应力/MPa	595.5	660.8	9.88
肋板中部的Mises应力/MPa	582.3	583.3	0.17
肋板与内壳相连处的Mises应力/MPa	1 287.2	1 520.0	15.30
肋板与外壳相连处的Mises应力/MPa	1 354.6	1 520.0	10.90

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参考文献(11)

[1]	夏贤坤, 谢祚水. 夹层圆柱壳结构的应力与总稳定性分析[J]. 华东船舶工业学院学报(自然科学版), 2004, 18(1): 10–12. XIA X K, XIE Z S. Stress and stability analysis of double shell structure[J]. Journal of East China Shipbuilding Institute (Natural Science Edition), 2004, 18(1): 10–12 (in Chinese).
[2]	高上地, 陈静, 卢骏锋, 等. 内压下矩形耐压舱角隅结构形状和拓扑优化设计[J]. 中国造船, 2017, 58(1): 94–100. doi: 10.3969/j.issn.1000-4882.2017.01.011 GAO S D, CHEN J, LU J F, et al. Shape and topology optimization design of rectangular tank's corner structure under internal pressure[J]. Shipbuilding of China, 2017, 58(1): 94–100 (in Chinese). doi: 10.3969/j.issn.1000-4882.2017.01.011
[3]	钦伦洋. 基于拓扑优化的船舶结构轻量化研究[D]. 大连: 大连海事大学, 2016. QIN L Y. The lightweight research on ship structure based on topological optimization[D]. Dalian: Dalian Mari-time University, 2016 (in Chinese).
[4]	王存福, 赵敏, 葛彤. 水下耐压结构拓扑优化设计方法探究[J]. 工程力学, 2015, 32(1): 247–256. WANG C F, ZHAO M, GE T. Study on the topology optimi-zation design of underwater pressure structure[J]. Engineer-ing Mechanics, 2015, 32(1): 247–256 (in Chinese).
[5]	LI Z M, YU J X, YU Y, et al. Topology optimization of pressure structures based on regional contour tracking technology[J]. Structural and Multidisciplinary Optimization, 2018, 58(2): 687–700. doi: 10.1007/s00158-018-1923-5
[6]	戴睿婕, 刘勇, 程远胜, 等. 外置式耐压液舱实肋板拓扑和开孔尺寸优化[J]. 中国舰船研究, 2019, 14(6): 139–146 . doi: 10.19693/j.issn.1673-3185.01460 DAI R J, LIU Y, CHENG Y S, et al. Topology and opening size optimization design of solid floors in an outer tank of the pressure hull[J]. Chinese Journal of Ship Research, 2019, 14(6): 139–146 (in Chinese). doi: 10.19693/j.issn.1673-3185.01460
[7]	宋晓飞, 肖伟, 何其健, 等. 加筋圆柱壳开孔围栏肘板拓扑优化设计[J]. 中国舰船研究, 2018, 13(1): 46–52. doi: 10.3969/j.issn.1673-3185.2018.01.007 SONG X F, XIAO W, HE Q J, et al. Topological optimization of opening fence brackets on ring-stiffened cylindrical shell[J]. Chinese Journal of Ship Research, 2018, 13(1): 46–52 (in Chinese). doi: 10.3969/j.issn.1673-3185.2018.01.007
[8]	JIANG C T, CHENG Y S, XIAO W, et al. Shape opti-mization design of brackets connecting girders of an internal bulkhead and pressure hull under external pressure[C]//Proceedings of the ASME 36th International Conference on Ocean, Offshore and Arctic Engineering. Trondheim, Norway: ASME, 2017.
[9]	高原, 黄进浩, 王永军, 等. 基于拓扑优化和尺寸优化的水下耐压球壳轻量化设计[J]. 舰船科学技术, 2019, 41(11): 54–58. doi: 10.3404/j.issn.1672-7649.2019.11.011 GAO Y, HUANG J H, WANG Y J, et al. Lightweight study of spherical shell based on topology and size optimi-zation[J]. Ship Science and Technology, 2019, 41(11): 54–58 (in Chinese). doi: 10.3404/j.issn.1672-7649.2019.11.011
[10]	程远胜, 刘甜甜, 刘均. 船舶肘板拓扑优化设计[J]. 中国舰船研究, 2015, 10(5): 53–58,70. doi: 10.3969/j.issn.1673-3185.2015.05.009 CHENG Y S, LIU T T, LIU J. Topology optimization of ship bracket structures[J]. Chinese Journal of Ship Research, 2015, 10(5): 53–58,70 (in Chinese). doi: 10.3969/j.issn.1673-3185.2015.05.009
[11]	王月, 沈志华, 肖伟, 等. 水下结构物长基座拓扑与尺寸优化设计[J]. 中国舰船研究, 2019, 14(6): 147–154. doi: 10.19693/j.issn.1673-3185.01461 WANG Y, SHEN Z H, XIAO W, et al. Topology and size optimization design of a long underwater foundation[J]. Chinese Journal of Ship Research, 2019, 14(6): 147–154 (in Chinese). doi: 10.19693/j.issn.1673-3185.01461