基于拓扑优化的S弯管加筋布局设计方法

宋龙龙; 方平矗; 胡惠玉; 郭文杰; 高彤; 张少平; 张卫红

doi:10.13224/j.cnki.jasp.20250354

基于拓扑优化的S弯管加筋布局设计方法

doi: 10.13224/j.cnki.jasp.20250354

宋龙龙^{1, 2,},
方平矗¹,
胡惠玉¹,
郭文杰³,
高彤^1,*, ,,
张少平⁴,
张卫红¹

1.
西北工业大学机电学院航宇材料结构一体化设计与增材制造装备技术国际联合研究中心，西安 710072
2.
香港科技大学智能建造研发中心，香港 999077
3.
中国飞机强度研究所强度与结构完整性全国重点实验室，西安 710065
4.
中国航发四川燃气涡轮研究院，成都 610500

基金项目: 基础科研计划（JCKY2022205B020）；国家自然科学基金（U2441208）

详细信息

作者简介:
宋龙龙（1994-），男，博士，主要从事考虑工艺约束的结构拓扑优化设计研究。E-mail：songdlong@ust.hk

通讯作者:
高彤（1980-），男，教授，博士，主要从事结构拓扑优化设计理论与方法研究。E-mail：gaotong@nwpu.edu.cn

中图分类号: V214.19
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出版历程
- 收稿日期: 2025-07-25
- 网络出版日期: 2025-11-27

Stiffener layout design method for serpentine nozzles using topology optimization

1.
State International Joint Research Center of Aerospace Design and Additive Manufacturing，School of Mechanical Engineering，Northwestern Polytechnical University，Xi’an 710072，China
2.
Hong Kong Center for Construction Robotics，Hong Kong University of Science and Technology，Hong Kong 999077，China
3.
National Key Laboratory of Strength and Structural Integrity，Aircraft Strength Research Institute of China，Xi’an 710065，China
4.
Sichuan Gas Turbine Establishment，Aero Engine Corporation of China，Chengdu 610500，China

摘要

摘要:
基于热弹性耦合多材料拓扑优化方法建立了S弯管加筋布局优化设计方法，核心思路是引入虚拟材料概念并利用多材料尺寸控制技术，实现任意曲面上自由筋与定向环筋布局的协同优化设计。在热弹性耦合多材料拓扑优化三场法框架内，利用局部搜索建立单一材料环向变量链接模型，实现规整的定向环筋形态；进而构建了自由筋与定向环筋最大实体尺寸整体控制方法与定向环筋间距控制方法；采用了非设计域蒙皮柔顺度最小作为优化目标，满足内表面控形要求。采用所提方法完成了S弯管结构自由筋与定向环筋布局协同优化设计，通过定向环筋间距控制获得了多种S弯管设计方案。重构结果表明：在相同重量下，相比于常规的规则加筋方案，拓扑优化构型的重构设计方案的最大变形降低高达17.1%。
- S弯管 /
- 拓扑优化 /
- 热弹性耦合 /
- 多材料 /
- 尺寸控制
Abstract:
A stiffener layout design method for serpentine nozzles based on thermo-elastic coupling multi-material topology optimization was presented. The virtual material concept was introduced, and multi-material length scale control was utilized to achieve the collaborative optimization design of free and directional ring stiffeners on arbitrary curved surfaces. Within the framework of the thermo-elastic coupling multi-material topology optimization three-field method, a circumferential variable linking model for a single material was established using local search to achieve a regular directional ring stiffener morphology. Furthermore, a global control method for the maximum solid length scale of both free and directional ring stiffeners, and a control method for the spacing of the directional ring stiffeners were constructed. The minimization of non-design domain skin compliance was employed as the optimization objective to meet the inner surface shape control requirements. The proposed method was used to complete the collaborative optimization design of free and directional ring stiffener layouts in serpentine nozzles. Various serpentine nozzle designs were obtained by controlling the ring stiffener spacing. The reconstructed designs from the optimized configurations achieved a maximum deformation reduction of up to 17.1% compared with conventional, regularly stiffened designs under the same structural mass.
- serpentine nozzles /
- topology optimization /
- thermo-elastic coupling /
- multiple materials /
- length scale control

HTML

图 1 S弯管常规加筋布局设计方案

Figure 1. Conventional stiffener layout design for serpentine nozzle

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图 2 约束边界与载荷

Figure 2. Boundary conditions and loads

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图 3 整体思路

Figure 3. Methodology of the paper

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图 4 密度过滤局部搜索与距离权重

Figure 4. Local search for the density filter and the distance weight

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图 5 光滑Heaviside函数

Figure 5. Smooth Heaviside function

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图 6 弹性模量插值模型（E^（1）=70 GPa; E^（2）=210 GPa; p = 3）

Figure 6. Young’s modulus interpolation model （E^（1）=70 GPa; E^（2）=210 GPa; p = 3）

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图 7 多种情况下单元i的孔隙率与材料率

Figure 7. Porosities and material rates under different conditions

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图 8 不同尺寸控制方法的局部搜索形状

Figure 8. Local search shapes for different length scale control methods

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图 9 S弯管有限元信息

Figure 9. Finite element model of the serpentine nozzle

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图 10 在x方向不同搜索长度上限$ \overline {d_{ik}^x} $下的优化构型

Figure 10. Optimized configurations under different values of $ \overline {d_{ik}^x} $

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图 11 不同优化构型下的重构设计方案

Figure 11. Rebuilt models for optimized configurations

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