频率约束的三维连续体结构动力拓扑优化设计

叶红玲; 沈静娴; 隋允康

doi:10.6052/0459-1879-12-069

频率约束的三维连续体结构动力拓扑优化设计

doi: 10.6052/0459-1879-12-069

北京工业大学机械工程与应用电子技术学院,北京 100124

基金项目: 国家自然科学基金资助项目(11072009, 11172013).

详细信息

通讯作者:
叶红玲

中图分类号: O343.1
计量
- 文章访问数: 1782
- HTML全文浏览量: 77
- PDF下载量: 1374
- 被引次数: 0
出版历程
- 收稿日期: 2012-03-16
- 修回日期: 2012-06-14
- 刊出日期: 2012-11-18

DYNAMIC TOLOGICAL OPTIMAL DESIGN OF THREE-DIMENSIONAL CONTINUUM STRUCTURES WITH FREQUENCIES CONSTRAINTS

College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology,Beijing 100124, China

Funds: The project was supported by the National Natural Science Foundation of China (11072009, 11172013).

摘要

摘要: 针对频率约束和结构重量最小的动力拓扑优化问题, 基于(independent continuous mapping, ICM)独立、连续、映射方法,建立了频率约束下的三维连续体拓扑优化模型. 利用瑞利商和一阶泰勒展式对频率约束进行了显式化处理,并采用幂函数与复合指数函数作为过滤函数,将优化模型进行了标准化转换, 利用对偶理论及数学规划法进行了求解. 另外,利用质量矩阵和刚度矩阵过滤函数比值与动态约束处理了局部模态和模态交换等数值问题. 最后,通过应用两类不同过滤函数的数值算例表明了文中模型及方法在处理动力拓扑优化问题上的合理性与有效性.
- 拓扑优化 /
- 独立连续映射方法 /
- 频率约束 /
- 三维连续体
Abstract: The purpose of present work is to study structural optimal design of dynamics for three-dimensional (3D) continuum structures, and to aim at constructing topological optimal formulation by using ICM method, which is considering weight as object function and fundamental eigenfrequency as constraints. An explicit expression of frequency-constraint(s) with respect to topological variables is obtained based on Rayleigh's quotient and first-order Taylor expansion. And two types of models with filter functions including power function and exponential function are standardized. As a result, the topology optimization problem is solved by the dual quadratic programming. Localized mode and mode switching often occurred in structural optimization with natural frequency constraints are handled by using filter functions and moving constraints in the optimal process. Finally, several numerical examples applying different filter functions in the optimal model are analyzed and discussed to demonstrate the feasibility and efficiency of the proposed method.
- topology optimization /
- ICM method /
- frequencies constraint /
- three-dimensional continuum structure

HTML全文

参考文献(28)

Bendsoe MP, Kikuchi N. Generating optimal topologies in structural design using a homogenization method. Comp Meth Appl Mech Engrg, 1988, 71(1): 197-224

Mlejnek HP, Schirrmacher R. An engineer's approach to optimal distribution and shape finding. Computer Methods in Applied Mechanics and Engineering, 1993, 106(1/2): 1-26

Xie YM, Steven GP. Evolutionary structural optimization. Berlin: Springer-Verlag, 1997

Sethian JA, Wiegmann A. Structural boundary design via level set and immersed interface methods. J Comput Hpys, 2000, 163: 489-528

Diaz A, Kikuchi N. Solution to shape and topology eigenvalue optimization problems using a homogenization method. International Journal for Numerical Methods in Engineering, 1992, 35: 1487-1502

Ma ZD, Cheng HC, Kikuchi N. Structural design for obtaining desired eigenfrequencies by using the topology and shape optimization method. Computer Systems in Engineering, 1994, 5(1): 77-89

Ma ZD, Kikuchi N, Cheng HC. Topological design for vibrating structures. Comput Methods Appl Mech Eng, 1995, 121: 259-280

Gea HC, Fu Y. Optimal 3D Stiffener design with frequency considerations. Advances in Engineering Software, 1997, 28: 525-531

Pedersen NL. Maximization of eigenvalues using topology optimization. Structural and Multidisciplinary Optimization, 2000, 20: 2-11

Tcherniak D. Topology optimization of resonating structures using SIMP method. International Journal for Numerical Methods in Engineering, 2002, 54: 1605-1622

罗震,陈立平,黄玉盈等. 连续体结构的拓扑优化设计. 力学进展,2004,34(4):463-476 (Luo Zhen, Chen Liping, Huang Yuying, et al. Topological optimization of design for continuum structures. Advances in Mechanics, 2004,34(4):462-476 (in Chinese))

朱继宏,张卫红,邱克鹏. 结构动力学拓扑优化局部模态现象分析. 航空学报,2005, 26(4):619-623 (Zhu Jihong, Zhang Weihong, Qiu Kepeng. Investigation of localized modes in topology optimization of dynamic structures. Acta Aeronautica et Astronautica Sinica, 2005, 26(4): 619-623 (in Chinese))

Du JB, Olhoff N. Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps. Struct Multidisc Optim, 2007, 34: 91-110

Niu B, Yan J, Cheng G. Optimum structure with homogeneous optimum cellular material for maximum fundamental frequency. Struct Multidisc Optim, 2009, 39: 115-132

Lee DK, Park SS, Shin SM. Maximum eigenfrequency based dynamic optimization design for topologically reinforcing concrete deep beams. Journal of Solid Mechanics and Materials Engineering, 2009, 3(11): 1137-1147

Huang X, Zuo ZH. Xie YM. Evolutionary topological optimization of vibrating continuum structures for natural frequencies. Computers & Structures, 2010, 88: 357-364

Jensen JS, Pedersen NL. On maximal eigenfrequency separation in two-material structures: the 1D and 2D scalar cases. J Sound Vib, 2006, 289: 967-986

Xia Q, Shi TL, Wang MY. A level set based shape and topology optimization method for maximizing simple or repeated first eigenvalue of structure vibration. Struct Multidisc Optim, 2011, 43: 473-485

Xia Q, Shi TL, Wang MY, et al. A level method for the optimization of cast part. Struct Multidisc Optim, 2010, 41: 735-747

杨振兴,荣见华,傅建林. 三维结构的频率拓扑优化设计. 振动与冲击,2006, 25(3):44-47 (Yang Zhengxing, Rong Jianhua, Fu Jianlin. Frequency topology optimal design of three-dimensional structures. Journal of Vibration and Shock, 2006, 25(3): 44-47 (in Chinese))

Achtziger W, Kocvara M. On the maximization of the fundamental eigenvalue in topology optimization. Struct Multidisc Optim, 2007, 34: 181-195

Krog LA, Olhoff N. Optimum topology and reinforcement design of disk and plate structures with multiple stiffness and eigenfrequency objectives. Computers and Structures, 1999, 72: 535-563

Lei S, Wang MY, Fang ZD, et al. Level set based structural topology optimization for minimizing frequency response. Journal of Sound and Vibration, 2011, 330: 5820-5834

彭细荣,隋允康. 有频率禁区的连续体结构拓扑优化. 固体力学学报,2007,28(2):145-150 (Peng Xirong, Sui Yunkang. Topological optimizaiton of the continuum structure with non-frequency-band constraints. Acta Mechanica Solida Sinica, 2007, 28(2): 145-150 (in Chinese))

彭细荣,隋允康. 强迫谐振动下连续体结构拓扑优化. 固体力学学报,2008,29(2):157-162 (Peng Xirong, Sui Yunkang. Topology optimization of continuum structure with response constraints. Acta Mechanica Solida Sinica,2008,29(2):157-162 (in Chinese))

隋允康. 建模· 变换· 优化---结构综合方法新进展. 大连:大连理工大学出版社,1996 (Sui Yunkang. Modeling, Transformation and Optimization: New Developments of Structural Synthesis Method. Dalian:Dalian University of Technology Press,1996 (in Chinese))

叶红玲,隋允康. 基于ICM方法三维连续体结构拓扑优化. 固体力学学报,2006, 27(4): 387-393 (Ye Hongling, Sui Yunkang. ICM-based topological optimization of three-dimensional continuum structure. Acta Mechanica Solida Sinica,2006, 27(4): 387-393 (in Chinese))

Fox RL, Kapoor MP. Rates of change of eigenvalues and eigenvectors. AIAA Journal,1969,6:2426-1968

施引文献

资源附件(0)

访问统计