Mode Tracking Scheme Among Remeshed Models for Structural Optimization

doi:10.1007/s12204-019-2133-z

Journal of Shanghai Jiao Tong University (Science) ›› 2019, Vol. 24 ›› Issue (6): 706-715.doi: 10.1007/s12204-019-2133-z

Mode Tracking Scheme Among Remeshed Models for Structural Optimization

LIU Jun (刘俊), DING Ziqi (丁子祈), LU Qi (陆麒), HAN Xianhong (韩先洪)

(1. National Engineering Research Center of Die & Mold CAD, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200030, China; 2. Robotics and Discrete Automation Business Research China, ABB Engineering (Shanghai) Ltd., Shanghai 201319, China)

出版日期:2019-12-15 发布日期:2019-12-07
通讯作者: HAN Xianhong (韩先洪) E-mail:hanxh@sjtu.edu.cn

Mode Tracking Scheme Among Remeshed Models for Structural Optimization

LIU Jun (刘俊), DING Ziqi (丁子祈), LU Qi (陆麒), HAN Xianhong (韩先洪)

(1. National Engineering Research Center of Die & Mold CAD, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200030, China; 2. Robotics and Discrete Automation Business Research China, ABB Engineering (Shanghai) Ltd., Shanghai 201319, China)

Online:2019-12-15 Published:2019-12-07
Contact: HAN Xianhong (韩先洪) E-mail:hanxh@sjtu.edu.cn

摘要/Abstract

摘要： Mode tracking is required in the structural optimization when the frequencies of certain specified modes must be maintained within a suitable range. A simple tracking method employing the mode number is invalid or misleading when local modes appear or disappear during mesh updating. In this work, a mode tracking scheme combining the nearest neighbor method (NNM) with the modal assurance criterion (MAC) is proposed. Several NNM algorithms are compared, and the k-dimensional tree (kd-tree) NNM is used to transform eigenvectors (mode shapes) from different scales to identical one. A threshold determination method is implemented for the MAC to assess the similarities in all the calculated modes. On the basis of the mode tracking scheme, specified modes can be tracked between different finite element method (FEM) models which have different meshes and optimized shapes. The effectiveness is verified through an example of shape optimization using an electric motor structure.

关键词: mode tracking scheme, remeshed models, optimization process, nearest neighbor method (NNM), modal assurance criterion (MAC)

Abstract: Mode tracking is required in the structural optimization when the frequencies of certain specified modes must be maintained within a suitable range. A simple tracking method employing the mode number is invalid or misleading when local modes appear or disappear during mesh updating. In this work, a mode tracking scheme combining the nearest neighbor method (NNM) with the modal assurance criterion (MAC) is proposed. Several NNM algorithms are compared, and the k-dimensional tree (kd-tree) NNM is used to transform eigenvectors (mode shapes) from different scales to identical one. A threshold determination method is implemented for the MAC to assess the similarities in all the calculated modes. On the basis of the mode tracking scheme, specified modes can be tracked between different finite element method (FEM) models which have different meshes and optimized shapes. The effectiveness is verified through an example of shape optimization using an electric motor structure.

Key words: mode tracking scheme, remeshed models, optimization process, nearest neighbor method (NNM), modal assurance criterion (MAC)

中图分类号:

TB 123

LIU Jun (刘俊), DING Ziqi (丁子祈), LU Qi (陆麒), HAN Xianhong (韩先洪) . Mode Tracking Scheme Among Remeshed Models for Structural Optimization[J]. Journal of Shanghai Jiao Tong University (Science), 2019, 24(6): 706-715.

参考文献 15

[9]	GARCIA V, DEBREUVE E, BARLAUD M. Fast k nearest neighbor search using GPU [C]//2008 IEEEComputer Society Conference on Computer Vision andPattern Recognition Workshops. Anchorage, Alaska,USA: IEEE, 2008: 1-6.
[1]	MOORE J, CUTRIGHT S, VIKEN J K. Structural design exploration of an electric powered multi-propulsor wing configuration [C]//58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference.Grapevine, Texas, USA: AIAA, 2017: 1-16.
[2]	ARA′UJO D C, CASTRO L C E, SHZU M A M, etal. Modal identification of a wind turbine [J]. ProcediaEngineering, 2017, 199: 2250-2255.
[10]	BENTLEY J L. Multidimensional binary search trees used for associative searching [J]. Communications ofthe ACM, 1975, 18(9): 509-517.
[11]	RAJANI N, MCARDLE R, DHILLON I S. Parallel k nearest neighbor graph construction using tree-baseddata structures [C]//High Performance Graph Mining.Sydney, Australia: 1st HPGM Workshop, 2015: 1-8.
[3]	PASTOR M, BINDA M, HARˇCARIK T, et al. Modalassurance criterion [J]. Procedia Engineering, 2012, 48:543-548.
[12]	MULCHRONE K F. Application of Delaunay triangulationto the nearest neighbour method of strain analysis[J]. Journal of Structural Geology, 2003, 25(5):689-702.
[4]	ALLEMANG R J. The modal assurance criterion:Twenty years of use and abuse [J]. Sound and Vibration,2003, 37(8): 14-23.
[13]	BROWN R A. Building a balanced k-d tree in O(kn log n) time [J]. Journal of Computer Graphics Techniques,2015, 4(1): 50-68.
[5]	KIM T S, KIM Y Y. MAC-based mode-tracking instructural topology optimization [J]. Computers andStructures, 2000, 74(3): 375-383.
[14]	LEE D T, SCHACHTER B J. Two algorithms for constructinga Delaunay triangulation [J]. InternationalJournal of Computer and Information Sciences, 1980,9(3): 219-242.
[6]	BREHM M, ZABEL V, BUCHER C. An automaticmode pairing strategy using an enhanced modal assurancecriterion based on modal strain energies [J].Journal of Sound and Vibration, 2010, 329(25): 5375-5392.
[15]	LUDICK D J, JAKOBUS U, VOGEL M. A tracking algorithm for the eigenvectors calculated with characteristicmode analysis [C]//8th European Conferenceon Antennas and Propagation (EuCAP 2014 ). TheHague, the Netherlands: IEEE, 2014: 569-572.
[7]	LUDICK D J, TONDER J V, JAKOBUS U. A hybrid tracking algorithm for characteristic mode analysis[C]//2014 International Conference on Electromagneticsin Advanced Applications (ICEAA). Palm Beach, Netherlands, Antilles: IEEE, 2014: 455-458.
[8]	ESCHENAUER H A, OLHOFF N. Topology optimizationof continuum structures: A review [J]. AppliedMechanics Reviews, 2001, 54(4): 331-390.
[9]	GARCIA V, DEBREUVE E, BARLAUD M. Fast k nearest neighbor search using GPU [C]//2008 IEEEComputer Society Conference on Computer Vision andPattern Recognition Workshops. Anchorage, Alaska,USA: IEEE, 2008: 1-6.
[10]	BENTLEY J L. Multidimensional binary search trees used for associative searching [J]. Communications ofthe ACM, 1975, 18(9): 509-517.
[11]	RAJANI N, MCARDLE R, DHILLON I S. Parallel k nearest neighbor graph construction using tree-baseddata structures [C]//High Performance Graph Mining.Sydney, Australia: 1st HPGM Workshop, 2015: 1-8.
[12]	MULCHRONE K F. Application of Delaunay triangulationto the nearest neighbour method of strain analysis[J]. Journal of Structural Geology, 2003, 25(5):689-702.
[13]	BROWN R A. Building a balanced k-d tree in O(kn log n) time [J]. Journal of Computer Graphics Techniques,2015, 4(1): 50-68.
[14]	LEE D T, SCHACHTER B J. Two algorithms for constructinga Delaunay triangulation [J]. InternationalJournal of Computer and Information Sciences, 1980,9(3): 219-242.
[15]	LUDICK D J, JAKOBUS U, VOGEL M. A tracking algorithm for the eigenvectors calculated with characteristicmode analysis [C]//8th European Conferenceon Antennas and Propagation (EuCAP 2014 ). TheHague, the Netherlands: IEEE, 2014: 569-572.

Mode Tracking Scheme Among Remeshed Models for Structural Optimization

Mode Tracking Scheme Among Remeshed Models for Structural Optimization

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献 15

相关文章 0

编辑推荐

Metrics

本文评价