考虑嵌入移动孔洞的多相材料布局优化

王选; 胡平; 龙凯

doi:10.6052/0459-1879-18-327

考虑嵌入移动孔洞的多相材料布局优化

王选^*,
胡平^*2), ,,
龙凯^**

* 大连理工大学工业装备结构分析国家重点实验室,大连 116023
† 合肥工业大学土木与水利工程学院,合肥 230009
** 华北电力大学新能源电力系统国家重点实验室, 北京 102206

基金项目: 1) 国家自然科学基金( 11872017)和北京市自然科学基金(2182067)资助项目.

详细信息

通讯作者:
胡平

中图分类号: O342;
计量
- 文章访问数: 1624
- HTML全文浏览量: 251
- PDF下载量: 143
出版历程
- 收稿日期: 2018-10-07
- 刊出日期: 2019-05-17

MULTIPHASE MATERIAL LAYOUT OPTIMIZATION CONSIDERING EMBEDDING MOVABLE HOLES

Xuan Wang^*,
Ping Hu^*2), ,,
Kai Long^**

* State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116023, China
† College of Civil Engineering, Hefei University of Technology, Hefei 230009, China
** State Key Laboratory for Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University,Beijing 102206, China

摘要

摘要: 工程结构设计问题中经常需要预先嵌入一个或多个固定形状的孔洞以满足某些功能性或者制造性设计要求.为了有效求解这种带有嵌入可移动孔洞的多相材料连续体结构布局优化问题,通常需要同时优化这些嵌入孔洞的位置和方向及多相材料结构的拓扑构型,以改善结构的整体性能.为此,本文采用参数化的水平集函数描述嵌入孔洞的几何形状,并将定义多相材料结构拓扑的材料密度以及描述嵌入孔洞的位置和方向的几何参数视为所考虑优化问题的设计变量.为了避免由于孔洞移动造成的重新划分网格的繁琐及改善计算效率,使用平滑化的Heaviside函数将所有嵌入孔洞映射为固定网格上的密度场.同时,提出了一种在有限元水平上调用的类SIMP材料插值格式,用于优化问题的材料参数化,进而实现多相材料结构拓扑构型和嵌入孔洞位置和方向的同步优化.这种材料插值格式便于几何变量的解析灵敏度分析,使得当前的优化问题可以用基于梯度的优化算法求解.优化算例证明所提方法可以有效地处理带有多个嵌入孔洞的多相材料结构布局优化问题.
- 布局优化 /
- 移动孔洞 /
- 多相材料 /
- SIMP方法 /
- 拓扑优化
Abstract: In structural engineering design, it is often necessary to embed one or more fixed-shaped holes to meet certain functional or manufacturing design requirements. To effectively solve the multi-phase material layout optimization problem of continuum structure with embedded movable holes, it is usually necessary to simultaneously optimize the position and orientation of these embedded holes and the topology configuration of the multi-phase material structure to improve the overall performance of the structure. To this end, parameterized level set functions are used to describe the geometry of the embedded holes. The material densities defining the structural topology of multiphase materials, and the geometric parameters used to describe the position and orientation of the embedded holes, are considered as design variables of the optimization problem considered here. To avoid the cumbersome of re-meshing the grids caused by the movement of holes and improve the efficiency of computation, the embedded holes are mapped into a density field on a fixed grid using a smoothed Heaviside function. Meanwhile, a SIMP-like material interpolation invoked at the finite element level is introduced for material parameterization of the optimization problem, and then the simultaneous optimization of the topology configuration of the multi-phase material structure and the position and orientation of the embedded hole can be realized. The material interpolation scheme supports full analytical sensitivity analysis, which allows the current optimization problem to be solved using gradient-based optimization algorithms. Numerical examples illustrate that the proposed method can effectively deal with the layout optimization problem of multiphase material embedded with multiple embedded holes.
- layout optimization /
- movable holes /
- multi-material /
- SIMP method /
- undefined

HTML全文

参考文献(1)

[1]	Zhang W, Xia L, Zhu J, et al.Some recent advances in the integrated layout design of multicomponent systems. Journal of Mechanical Design, 2011, 133(10): 104503
[2]	Wang Y, Luo Z, Zhang X, et al.Topological design of compliant smart structures with embedded movable actuators. Smart Materials and Structures, 2014, 23(4): 045024
[3]	吴曼乔, 朱继宏, 杨开科等. 面向压电智能结构精确变形的协同优化设计方法. 力学学报, 2017, 49(2): 380-389
[3]	(Wu Manqiao, Zhu Jihong, Yang Kaike, et al.Integrated layout and topology optimization design of piezoelectric smart structure in accurate shape control. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(2): 380-389 (in Chinese))
[4]	Li Y, Wei P, Ma H.Integrated optimization of heat-transfer systems consisting of discrete thermal conductors and solid material. International Journal of Heat and Mass Transfer, 2017, 113: 1059-1069
[5]	Qian Z, Ananthasuresh GK.Optimal embedding of rigid objects in the topology design of structures. Mechanics Based Design of Structures and Machines, 2004, 32(2): 165-193
[6]	Zhu J, Zhang W, Beckers P, et al.Simultaneous design of components layout and supporting structures using coupled shape and topology optimization technique. Structural and Multidisciplinary Optimization, 2008, 36(1): 29-41
[7]	Xia L, Zhu J, Zhang W, et al.An implicit model for the integrated optimization of component layout and structure topology. Computer Methods in Applied Mechanics and Engineering, 2013, 257: 87-102
[8]	Kang Z, Wang Y, Wang Y.Structural topology optimization with minimum distance control of multiphase embedded components by level set method. Computer Methods in Applied Mechanics and Engineering, 2016, 306: 299-318
[9]	Zhang W, Zhong W, Guo X.Explicit layout control in optimal design of structural systems with multiple embedding components. Computer Methods in Applied Mechanics and Engineering, 2015, 290: 290-313
[10]	Wang X, Long K, Hoang VN, et al.An explicit optimization model for integrated layout design of planar multi-component systems using moving morphable bars. Computer Methods in Applied Mechanics and Engineering, 2018, 342: 46-70
[11]	Zhu J, Guo W, Zhang W, et al.Integrated layout and topology optimization design of multi-frame and multi-component fuselage structure systems. Structural and Multidisciplinary Optimization, 2017, 56(1): 21-45
[12]	Xia L, Zhu J, Zhang W.A superelement formulation for the efficient layout design of complex multi-component system. Structural and Multidisciplinary Optimization, 2012, 45(5): 643-655
[13]	Liu P, Kang Z.Integrated topology optimization of multi-component structures considering connecting interface behavior. Computer Methods in Applied Mechanics and Engineering, 2018, 341: 851-887
[14]	张卫红, 郭文杰, 朱继宏. 部件级多组件结构系统的整体式拓扑布局优化. 航空学报, 2015, 36(8): 2662-2669
[14]	(Zhang Weihong, Guo Wenjie, Zhu Jihong.Integrated layout and topology optimization design of multi-component systems with assembly units. Acta Aeronauticaet Astronautica Sinica, 2015, 36(8): 2662-2669 (in Chinese))
[15]	Zhu J, Zhang W, Beckers P.Integrated layout design of multi-component system. International Journal for Numerical Methods in Engineering, 2009, 78(6): 631-651
[16]	朱继宏, 赵华, 刘涛等. 简谐力激励下多组件结构系统的整体优化设计. 航空学报, 2018, 39(1): 231-242
[16]	(Zhu Jihong, Zhao Hua, Liu Tao, et al.Integrated layout and topology optimization design of multi-component structure system under harmonic force excitation. Acta Aeronauticaet Astronautica Sinica, 2018, 39(1): 231-242 (in Chinese))
[17]	Kang Z, Wang Y.Integrated topology optimization with embedded movable holes based on combined description by material density and level sets. Computer Methods in Applied Mechanics and Engineering, 2013, 255: 1-13
[18]	Clausen A, Aage N, Sigmund O.Topology optimization with flexible void area. Structural and Multidisciplinary Optimization, 2014, 50(6): 927-943
[19]	龙凯, 王选, 韩丹. 基于多相材料的稳态热传导结构轻量化设计. 力学学报, 2017, 49(2): 359-366
[19]	(Long Kai, Wang Xuan, Han Dan.Structural light design for steady heat conduction using multi-material. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(2): 359-366 (in Chinese))
[20]	Chen J, Shapiro V, Suresh K, et al.Shape optimization with topological changes and parametric control. International Journal for Numerical Methods in Engineering, 2007, 71(3): 313-346
[21]	Hoang VN, Jang GW.Topology optimization using moving morphable bars for versatile thickness control. Computer Methods in Applied Mechanics and Engineering, 2017, 317: 153-173
[22]	牛飞, 王博, 程耿东. 基于拓扑优化技术的集中力扩散结构设计.力学学报, 2012, 44(3): 528-536
[22]	(Niu Fei, Wang Bo, Cheng Gengdong.Optimum topology design of structural part for concentration force transmission. Chinese Journal of Theoretical and Applied Mechanics, 2012, 44(3): 528-536 (in Chinese))
[23]	郭旭, 赵康. 基于拓扑描述函数的连续体结构拓扑优化方法.力学学报, 2004, 36(5): 520-526
[23]	(Guo Xu, Zhao Kang.A new topology description function based approach for structural topology optimizationa. Chinese Journal of Theoretical and Applied Mechanics, 2004, 36(5): 520-526 (in Chinese))
[24]	王选, 刘宏亮, 龙凯等. 基于改进的双向渐进结构优化法的应力约束拓扑优化. 力学学报, 2018, 50(2): 385-394
[24]	(Wang Xuan, Liu Hongliang, Long Kai, et al.Stress-constrained topology optimization based on improved bi-directional evolutionary optimization method. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(2): 385-394 (in Chinese))
[25]	王选, 胡平, 祝雪峰等. 考虑结构自重的基于NURBS插值的3D拓扑描述函数法.力学学报, 2016, 48(6): 1437-1445
[25]	(Wang Xuan, Hu Ping, Zhu Xuefeng, et al.topology description function approach using NURBS interpolation for 3D structures with self-weight loads. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(6): 1437-1445 (in Chinese))
[26]	Rong JH, Tang ZL, Xie YM, et al.Topological optimization design of structures under random excitations using SQP method. Engineering Structures, 2013, 56: 2098-2106
[27]	Xia Q, Wang MY, Shi T.Topology optimization with pressure load through a level set method. Computer Methods in Applied Mechanics and Engineering, 2015, 283: 177-195
[28]	Wei P, Li Z, Li X, et al.An 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions. Structural and Multidisciplinary Optimization, 2018, 58(2): 831-849
[29]	Gao T, Zhang W.A mass constraint formulation for structural topology optimization with multiphase materials. International Journal for Numerical Methods in Engineering, 2011, 88(8): 774-796
[30]	Sigmund O.A 99 line topology optimization code written in Matlab. Structural and Multidisciplinary Optimization, 2001, 21(2): 120-127
[31]	Rojas-Labanda S, Stolpe M.An efficient second-order SQP method for structural topology optimization. Structural and Multidisciplinary Optimization, 2016, 53(6): 1315-1333
[32]	Svanberg K.The method of moving asymptotes---a new method for structural optimization. International Journal for Numerical Methods in Engineering, 1987, 24(2): 359-373
[33]	Sigmund O, Aage N, Andreassen E.On the (non-) optimality of Michell structures. Structural and Multidisciplinary Optimization, 2016, 54(2): 361-373
[34]	Long K, Wang X, Gu X.Multi-material topology optimization for the transient heat conduction problem using a sequential quadratic programming algorithm. Engineering Optimization, 2018, 50(12): 2091-2107

施引文献(11)

期刊类型引用(7)

1.	刘敏，卢飞扬，占金青，吴剑，朱本亮. 考虑最小尺寸约束的内嵌可移动压电驱动柔顺机构拓扑优化设计. 中国机械工程. 2025(02): 255-264 . 百度学术
2.	江旭东，马佳琪，熊志，滕晓艳，王亚萍. 基于多分辨率-多边形单元建模策略的多材料结构动刚度拓扑优化方法. 工程力学. 2024(02): 222-235 . 百度学术
3.	周焕林，郭鑫，王选，方立雪，龙凯. 考虑几何非线性的多相多孔结构拓扑优化设计. 吉林大学学报(工学版). 2024(10): 2754-2763 . 百度学术
4.	孙岩，邓学霖，何良莉，姚海艳. 界面离散网格点数据重规整化方法. 计算机辅助设计与图形学学报. 2022(05): 804-810 . 百度学术
5.	马晶，赵明宣，王浩淼，刘湃，亢战. 考虑界面力学性能的组件及结构的协同优化. 力学学报. 2021(06): 1758-1768 . 本站查看
6.	李宏宇，孙鹏文，张兰挺，牛磊，龙凯. 基于ICM的风力机叶片多相材料拓扑优化设计. 太阳能学报. 2021(12): 261-266 . 百度学术
7.	程长征，卞光耀，王选，龙凯，李景传，吴乔国. 连续纤维增强复合材料结构基频最大化设计. 力学学报. 2020(05): 1422-1430 . 本站查看