Full-Text Search:
Home|Journal Papers|About CNKI|User Service|FAQ|Contact Us|中文
《Advances In Mechanics》 2004-04
Add to Favorite Get Latest Update

TOPOLOGICAL OPTIMIZATION DESIGN FOR CONTINUUM STRUCTURES

LUO Zhen CHEN Liping HUANG Yuying ZHANG YunqingNational Engineering Research Center for CAD, Huazhong University of Science and Technology, Wuhan, 430074, China Academy of Civil Engineering and Mechanics, Huazhong University of Science and Technology, Wuhan, 430074, China  
Structural topology optimization techniques are briefly discussed based on finite element approach. The mathematical model, with the objective to minimize compliance, as well as the explicit updating scheme for design variables are both worked out based on density-stiffness interpolation schemes and Optimality Criteria method. The computational model to maximize the fundamental eigenvalue, and the implicit retrieving pattern of design variables for vibrating structures, are also worked out using density method and a convex approach the method of moving asymptotes. Compliant mechanism designs employing topology optimization method, Multi-objective topology optimization problems considering static and vibrating structures, and multi-physics topology optimization problems are all discussed. Numerical instabilities, such as checkerboards and mesh dependencies, are introduced and investigated. The flowchart for topology optimization design is given. The efficiency and validity of methodologies in this paper are demonstrated by several typical examples. The future perspectives of topology optimization designs are outlined.
【Fund】: 国家"863"高技术研究发展计划(2003AA001031);; 国家"973"基础研究发展计划(2003CB716207)资助项目~~
【CateGory Index】: O302
Download(CAJ format) Download(PDF format)
CAJViewer7.0 supports all the CNKI file formats; AdobeReader only supports the PDF format.
【References】
Chinese Journal Full-text Database 10 Hits
1 FAN Wenfeng HE Jingwu (School of Aeronautical Science and Technology, Beihang University, Beijing 100083);The Research for Structural Topology Optimization Based on the Level Set Method[J];Journal of Anyang Institute of Technology;2007-01
2 LONG Kai,ZUO Zheng-xing(School of Mechanical and Vehicular Engineering,Beijing Institute of Technology,Beijing 100081,China);Independent Continuous Mapping Method for Topology Optimization of Continuum Structure Based on RAMP Interpolation Scheme[J];Transactions of Beijing Institute of Technology;2007-04
3 LONG Kai,ZUO Zheng-xing(School of Mechanical and Vehicular Engineering,Beijing Institute of Technology,Beijing 100081,China);Perimeter Control with Variational Upper-Bound Based on Nodal Independent Continuous Mapping Method[J];Transactions of Beijing Institute of Technology;2009-04
4 Kemin Zhou(College of Civil Engineering,Huaqiao University,Fujian 362021);Discussion on Structural Optimum Design——Review of Competition of Structural Design for College[J];Fujian Architecture & Construction;2006-04
5 SUI Yun-kang , YE Hong-ling , DU Jia-zheng (Numerical Simulation Center for Engineering, Beijing University of Technology, Beijing 100022, China);DEVELOPMENT OF STRUCTURAL TOPOLOGICAL OPTIMIZATION AND IMMINENCY OF ITS MODEL TRANSFORMATION INTO INDEPENDENT LEVEL[J];Engineering Mechanics;2005-S1
6 Kai Long Zhengxing Zuo(School of Mechanical and Vehicular Engineering,Beijing Institute of Technology,Beijing,100081);DYNAMIC TOPOLOGICAL OPTIMIZATION METHOD OF CONTINUUM STRUCTURES BASED ON NODAL INDEPENDENT DESIGN VARIABLES[J];Chinese Journal of Solid Mechanics;2008-01
7 JIANG Su-qing1,DU Juan2(1.Department of Mechanical Engineering,Southeast University,Nanjing 223001,China;2.Guannan Xinan Primary School,LianYungang 222500,China);Topological Optimization Design of Vertical Machining Center Based on HyperMesh[J];Industrial Measurement;2008-01
8 ;HyperWorks Based Free Dimension Optimization of Telescopic Boom for a Telehandler[J];Construction Machinery and Equipment;2009-12
9 ZHANG Ji,QIU Fu-sheng (College of Aviation and Space Engineering,Shenyang Institute of Aeronautical Engineering,Shenyang 110136,China);Vertical Tail Design Based on Topology Optimization[J];Aircraft Design;2010-03
10 Juan Zheng1 Shuyao Long1 Yuanbo Xiong2 Guangyao Li1 (1 State Key Laboratory of Advanced Design and Manufacture for Vehicle Body,Hunan University,Changsha,410082) (2 School of Mechanics Engineering and Automation,Fuzhou University,Fuzhou,350108);AN APPLICATION OF THE MESHLESS RADIAL POINT INTERPOLATION METHOD TO THE STRUCTURAL TOPOLOGY OPTIMIZATION DESIGN[J];Chinese Journal of Solid Mechanics;2010-04
China Proceedings of conference Full-text Database 5 Hits
1 SUI Yun-kang , YE Hong-ling, DU Jia-zheng (Numerical Simulation Center for Engineering, Beijing University of Technology, Beijing 100022, China);DEVELOPMENT OF STRUCTURAL TOPOLOGICAL OPTIMIZATION AND IMMINENCY OF ITS MODEL TRANSFORMATION INTOINDEPENDENT LEVEL[A];[C];2005
2 LONG Kai, XIAO Tao, ZUO Zheng-xing (Beijing Institute of Technology, Beijing 100081, China);Topology Optimization of Continuous Structures With the objective of Minimizing Dynamic Compliance[A];[C];2007
3 Du Yi-xian,Tian Qi-hua,Wu Zheng-jia (China Three Gorges University,Yichang 443002,China);Topology Optimization Designing and Performance Testing of Inverter Mechanisms Using Meshless Method[A];[C];2009
4 QIN Dongchen Zhu Qiang YANG Menglin (School of Mechanical Engineering,Zhengzhou University,Zhengzhou 450001,China);A STUDY FOR STRUCTURAL TOPOLOGY OPTIMIZATION OF BOX GIRDER BASED ON METHOD OF MOVING ASYMPTOTES(MMA)[A];[C];2009
5 Niu Dongzhen~1,Zhao Yaxin~2,Yan Mingsheng~1,Zhu Shengli~1 (1.The First Aircraft Institute,Aviation Industry Corporation of China,Xi'an 710089,China) (2.The Flight Test Establishment,Aviation Industry Corporation of China,Xi'an 710089,China);Optimization Design in Aircraft Structure of Supporting Floor Panel[A];[C];2010
【Citations】
Chinese Journal Full-text Database 10 Hits
1 CHENG Geng dong ( State Key Lab. of Struct. Anal. for Ind. Equip., Dalian Univ. of Technol., Dalian 116024, China );On singular optima of structural topology optimization of trusses[J];JOURNAL OF DALIAN UNIVERSITY OF TECHNOLOGY;2000-04
2 Cheng Gengdong;Zhang Dongxu(Research Institute of Engineering Mechanics,DUT);Topological optimization of plane elastic continuum with stress constraints[J];JOURNAL OF DALIAN UNIVERSITY OF TECHNOLOGY;1995-01
3 Sui Yunkang 1 Yu Xin 2 Ye Baorui 1 ( 1 College of Mech Electr.Eng., Beijing Polytechnic University, Beijing, 100022) ( 2 Dept. of Mech.Eng., Anshan Institute of Iron and Steel Technology, Anshan, 114002);THE UNIFORM MODEL BASED ON THE EXIST-NULL COMBINATION FOR THE TRUSS AND MEMBRANE TOPOLOGICAL OPTIMIZATION WITH STRESS CONSTRAINT[J];Acta Mechanica Solida Sinica;2001-01
4 Yuan Zhen (Department of Modern Mechanics, University of Science & Technology of China, Hefei, 230026) Wu Changchun (School of Civil Engineering & Mechanics, Shanghai Jiaotong University, Shanghai, 200240);TOPOLOGY OPTIMIZATION FOR PERIODIC LINEAR ELASTIC MICROSTRUCTURES OF COMPOSITE MATERIALS[J];Acta Mechanica Solida Sinica;2003-01
5 SUI Yun\|kang 1, YANG De\|qing 1 SUN Huan\|chun 2 SUI Yun\|kang 1, YANG De\|qing 1 SUN Huan\|chun 2 (1.Dept. of Mechanics, Beijing Polytechnic University, Beijing 100022, China; 2.Dept. of Mechanics, Dalian Univ. of Tech., Dalian 116023, China);Uniform ICM theory and method on optimization of structural topology for skeletonal and continuum structures[J];Chinese Journal of Computational Mechanics;2000-01
6 Sui Yunkang1,Ren Xuchun2,\ Long Lianchun1,Ye Baorui1(1. Beijing Polytechnic University, Beijing 100022, China;2. Tsinghua University, Beijing 100084, China);Topological optimization of frame based on ICM method[J];Chinese Journal of Computational Mechanics;2003-03
7 Sui Yunkang ,Yu Xin (Beijing Polytechnic University, Beijing 100022, China) (Anshan institute of Iron and Steel Technology, Anshan 114002, China);THE EXIST-NULL COMBINATION METHOD FOR THE TOPOLOGICAL OPTIMIZATION OF PLANE MEMBRANE STRUCTURE[J];Acta Mechanica Sinica;2001-03
8 Yuan Zhen Wu Changchun(School of Civil Engineering and Mechanics, Shanghai Jiaotong University, Shanghai 200240, China);TOPOLOGY OPTIMIZATION OF CONTINUUM STRUCTURES USING INCOMPATIBLE FINITE ELEMENTS[J];Acta Mechanica Sinica;2003-02
9 Liu Shutian Cheng Gengdong ( Dalian University of Technology, Dalian 116023,China );HOMOGENIZATION METHOD OF STRESS ANALYSIS OF COMPOSITE STRUCTURES[J];ACTA MECHANICA SINICA;1997-03
10 YUAN Zhen, WU Chang-chun, ZHUANG Shou-bing (Department of Modern Mechanics, USTC, Hefei 230026, China);Topology Optimization of Continuum Structure Using Hybrid Elements and Artificial Material Model[J];Journal of University of Science and Technology of China;2001-06
【Co-citations】
Chinese Journal Full-text Database 10 Hits
1 Li Jing (College of Mechanical Engineering, Guangxi University, Nanning 530004, China);VARIABLE DENSITY TOPOLOGICAL OPTIMIZATION METHOD AND ITS APPLICATION RESEARCH IN THE REAR PLATEN'S STRUCTURE DESIGN[J];Engineering Plastics Application;2008-08
2 REN Shan LI Shu(School of Aeronautic Science and Engineering,Beijing University of Aeronautics and Astronautics,Beijing 100083 ,China);Topology Optimization Design for Microstructures of Cellular Materials[J];Journal of Anyang Institute of Technology;2008-02
3 YE Hong-ling, SUI Yun-kang (Numerical Simulation Center for Engineering, Beijing University of Technology, Beijing 100022, China);Topological Optimization of Continuum Structure With Stress Constraints Based on ICM Method[J];Journal of Beijing Polytechnic University;2005-S1
4 ZHANG Xue-sheng, SUI Yun-kang, LONG Lian-chun, YE Hong-ling (College of Mechanical Engineering and Applied Electronic Technology, Beijing University of Technology, Beijing 100022, China);The Stiffness Filter Function Based on Independent, Continuous, Mapping Method[J];Journal of Beijing University of Technology;2006-01
5 YE Hong-ling, SUI Yun-kang (Numerical Simulation Center for Engineering, Beijing University of Technology, Beijing 100022, China);Tbpological Optimization of Continuum Structure Under Stress Constraints[J];Journal of Beijing University of Technology;2006-04
6 BIAN Bing-chuan, SUI Yun-kang,YE Hong-ling (The Centre of Numerical Simulation for Engineering, College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing 100022, China);ICM Method With Topological Optimization of the Continuum Structure Subjected to the Buckling Constraints[J];Journal of Beijing University of Technology;2006-S1
7 YE Hong-ling, SUI Yun-kang, DU Jia-zheng, BIAN Bing-chuan (College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing 100022, China);Optimal Topology Design of Truck Frame Structure With Stress Constraints[J];Journal of Beijing University of Technology;2006-S1
8 YE Hong-ling SUI Yun-kang LIU Zhao-miao (College of Mechanical Engineering and Applied Electronics Technology,Beijing University of Technology,Beijing 100022,China);Topological Optimization Analysis of Two-dimensional Continuum Thin Plate Structure[J];Journal of Beijing University of Technology;2007-08
9 YE Hong-ling SUI Yun-kang DU Jia-zheng (College of Mechanical Engineering and Applied Electronics Technology Beijing University of Technology,Beijing 100022,China);Topological Optimization Analysis of Continuum Structure With Displacement Constraints[J];Journal of Beijing University of Technology;2007-09
10 LONG Kai,ZUO Zheng-xing(School of Mechanical and Vehicular Engineering,Beijing Institute of Technology,Beijing 100081,China);Topology Extraction in the Topological Optimization of Continuum Structure Based on Nodal Density[J];Transactions of Beijing Institute of Technology;2008-08
China Proceedings of conference Full-text Database 6 Hits
1 WANG Dong (Dept.of Aeronautical Structural Engineering,Northwestern Polytechnical University,Xi'an 710072,China);Shape Optimization of Planar Frames with Displacement Constraints[A];[C];2004
2 SUI Yun-kang , YE Hong-ling, DU Jia-zheng (Numerical Simulation Center for Engineering, Beijing University of Technology, Beijing 100022, China);DEVELOPMENT OF STRUCTURAL TOPOLOGICAL OPTIMIZATION AND IMMINENCY OF ITS MODEL TRANSFORMATION INTOINDEPENDENT LEVEL[A];[C];2005
3 Lan Qian Yongfeng Du Hui Li (School of Civil Engineering, Lanzhou University of Technology, Lanzhou, Gansu, 730050);The Simulation of Transmitting Force Way of the Raft Foundation Using Topology Optimization[A];[C];2006
4 Wang Xin~1 Huang Lin~1 Gao Yuan~1 Wang Yi Hua~2 1.School of Mechanical Engineering,Da Lian University of Technology,Da Lian,116023,P.R.China 2.71811 Arming Department of Army,Zhu Madian,463000,P.R.China;The Topological Optimization of Mobile Crane Telescopic Boom-Section[A];[C];2007
5 Guobin Shen Rong Wang(School of Mechantronic Engineering,Guilin University of Electronic Technology,Guilin,541004,P.R.China);The optimization design of truss structure based on ANSYS analysis[A];[C];2010
6 Liu Yuandong Yin Yihui Hu Wenjun(Institute of Systems Engineering,CAEP,Mianyang,Sichuan 621900);Multi-Objective Topology Optimization for Microstructure of Periodic Composite Material[A];[C];2010
【Co-references】
Chinese Journal Full-text Database 10 Hits
1 Xu Zhengcang (China's Light Industry Machine Corporation, Beijing 100032, China);SURVEY AND FORECAST OF CHINA'S PLASTICS MACHINERY MANUFACTURE INDUSTRY[J];Engineering Plastics Application;2002-07
2 REN Shan LI Shu(School of Aeronautic Science and Engineering,Beijing University of Aeronautics and Astronautics,Beijing 100083 ,China);Topology Optimization Design for Microstructures of Cellular Materials[J];Journal of Anyang Institute of Technology;2008-02
3 CHU Jin kui,HAO Xiu chun,WANG Li ding (Micro system Center,School of Mechanical Engineering,Dalian University of Technology,Dalian 116024,China);Developments of topology optimization method and its application in micro-mechanism design[J];Micronanoelectronic Technology;2003-Z1
4 YANG Gui-yu,SUN Bao-yuan,LI Zhen(School of Mechanical Engineering,Dalian University of Technology,Dalian 116024,China);Using filter to eliminate checkerboard in topology optimization[J];Micronanoelectronic Technology;2004-08
5 CHU Jin-kui,HAO Xiu-chun,WANG Li-ding(Research Center of Micro System Technology,School of Mechanical Engineering,Dalian University of Technology,Dalian 116023,China);Comparison of the Solutions in Topology Optimization for Compliant Mechanisms[J];Micronanoelectronic Technology;2005-10
6 Xu Yanqiu\ Ji Wenyu\ Xu Kebin (College of Civil Engineering and Architecture, Northern Jiaotong University, Beijing 100044);A Theoretical Calculating Method for Ultimate Torsional Strength of Prestressed Concrete Box Beams[J];JOURNAL OF NORTHERN JIAOTONG UNIVERSITY;1998-01
7 Xu Yanqiu\ Xu Kebin (College of Civil Engineering and Architecture, Northern Jiaotong University, Beijing 100044);The Calculation for Ultimate Pure Torsional Strength of Reinforced Concrete Beams[J];JOURNAL OF NORTHERN JIAOTONG UNIVERSITY;1999-01
8 Xu Xiangyang;Xu Jinxia;Xu Zhiying;shao Weiling;Liu Ying(Harbin Institute of Technology,Harbin,150001)(Harbin First Machine Manufacturer);FEM ANALYSIS FOR THE STIFFNESS AND STRENGTH OF THE BODY OF A TRACKED VEHICLE[J];Acta Armamentarii;1996-01
9 ZHANG Xue-sheng, SUI Yun-kang, LONG Lian-chun, YE Hong-ling (College of Mechanical Engineering and Applied Electronic Technology, Beijing University of Technology, Beijing 100022, China);The Stiffness Filter Function Based on Independent, Continuous, Mapping Method[J];Journal of Beijing University of Technology;2006-01
10 YE Hong-ling, SUI Yun-kang (Numerical Simulation Center for Engineering, Beijing University of Technology, Beijing 100022, China);Tbpological Optimization of Continuum Structure Under Stress Constraints[J];Journal of Beijing University of Technology;2006-04
【Secondary References】
Chinese Journal Full-text Database 10 Hits
1 FAN Wenfeng HE Jingwu (School of Aeronautical Science and Technology, Beihang University, Beijing 100083);The Research for Structural Topology Optimization Based on the Level Set Method[J];Journal of Anyang Institute of Technology;2007-01
2 YE Hong-ling SUI Yun-kang DU Jia-zheng (College of Mechanical Engineering and Applied Electronics Technology Beijing University of Technology,Beijing 100022,China);Topological Optimization Analysis of Continuum Structure With Displacement Constraints[J];Journal of Beijing University of Technology;2007-09
3 LONG Kai,ZUO Zheng-xing(School of Mechanical and Vehicular Engineering,Beijing Institute of Technology,Beijing 100081,China);Independent Continuous Mapping Method for Topology Optimization of Continuum Structure Based on RAMP Interpolation Scheme[J];Transactions of Beijing Institute of Technology;2007-04
4 LONG Kai,ZUO Zheng-xing(School of Mechanical and Vehicular Engineering,Beijing Institute of Technology,Beijing 100081,China);Topology Extraction in the Topological Optimization of Continuum Structure Based on Nodal Density[J];Transactions of Beijing Institute of Technology;2008-08
5 SUN Yong-gang,LEI Gang(Chongqing Institute of Technology,Chongqing 400050,China);Modern CAE Technology Based on Structural Optimization Theory[J];Journal of Chongqing Institute of Technology(Natural Science Edition);2007-09
6 LI Gui-hua,XIONG Fei,LONG Jiang-qi(School of Mechanical & Automotive Engineering,South China University of Technology,Guangzhou 510640,China);Applications of Lightweight of Car Body Material and New Technology[J];Development and Application of Materials;2009-02
7 WANG Xin*1,HUANG Lin1,2,GAO Yuan1,GAO Shun-de1,WANG Yi-hua3(1.School of Mechanical Engineering,Dalian University of Technology,Dalian 116024,China;2.DHI·DCW Group Co.,Ltd.,Dalian 116013,China;3.Armament Department of PLA 71811 Command,Zhumadian 463000,China);Topological optimization for crane telescopic boom-section[J];Journal of Dalian University of Technology;2009-03
8 SUI Yun-kang1 , BIAN Bing-chuan2 (1. The Centre of Numerical Simulation for Engineering, College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing 100124, China; 2. Department of Applied Science and Technology, Taishan University, Taian, Shandong 271021, China);TOPOLOGY OPTIMIZATION OF CONTINUUM STRUCTURES UNDER BUCKLING AND STRESS CONSTRAINTS[J];Engineering Mechanics;2008-08
9 SUI Yun-kang , YE Hong-ling , LIU Jian-xin , CHEN Shi , YU Hui-ping (Numerical Simulation Center for Engineering, Beijing University of Technology, Beijing 100124, China);A STRUCTURAL TOPOLOGICAL OPTIMIZATION METHOD BASED ON EXPLORING CONCEPTUAL ROOT[J];Engineering Mechanics;2008-S2
10 Peng Xirong1 Sui Yunkang2 (1Graduate School at Shenzhen Tsinghua Univerty,Shenzhen,518055) (2Numerical Simulation Center for Engineering,The College of Mechanical Engineering and Applied Elctronics Technology,Beijing University of Technology,Beijing,100022);TOPOLOGICAL OPTIMIZATION OF THE CONTINUUM STRUCTURE WITH NON-FREQUENCY-BAND CONSTRAINTS[J];Acta Mechanica Solida Sinica;2007-02
China Proceedings of conference Full-text Database 5 Hits
1 Huang Yi-song,Chen Ji-qing,Li Yu-tong*, Qiu Zhi-min* ( School of Mechanical Automotive Engineering, South China Univ. of Tech, Guangzhou, China) (* Guangdong Fudi Automotive Works. Ltd., Guangzhou, Foshan, China);Applications of Lightweight Car Body Materials and Researches on Forming Properties[A];[C];2009
2 LONG Kai, XIAO Tao, ZUO Zheng-xing (Beijing Institute of Technology, Beijing 100081, China);Topology Optimization of Continuous Structures With the objective of Minimizing Dynamic Compliance[A];[C];2007
3 LONG Kai, LI Tao, ZUO Zheng-xing, SUN Yu-juan (Beijing Institute of Technology, Beijing 100081, China);Dynamic Topological Optimization Method of Continuum Structure Based on Independent Node-based Design Variables[A];[C];2007
4 Huang Yi-song,Chen Ji-qing,Li Yu-tong~*,Qiu Zhi-min~* (School of Mechanical Automotive Engineering,South China Univ.of Tech,Guangzhou,China) (* Guangdong Fudi Automotive Works.Ltd.,Guangzhou,Foshan,China);Applications of Lightweight Car Body Materials and Researches on Forming Properties[A];[C];2009
5 QU Xiang,LIAO Linqing,XU Kefeng (Chongqing Automobile College,Chongqing University of Technology,Chongqing 400050);Analysis and Optimization of Static and Dynamic Characteristics of Structure of Body-in-White[A];[C];2009
【Secondary Citations】
Chinese Journal Full-text Database 4 Hits
1 Sui Yunkang 1 Yu Xin 2 Ye Baorui 1 ( 1 College of Mech Electr.Eng., Beijing Polytechnic University, Beijing, 100022) ( 2 Dept. of Mech.Eng., Anshan Institute of Iron and Steel Technology, Anshan, 114002);THE UNIFORM MODEL BASED ON THE EXIST-NULL COMBINATION FOR THE TRUSS AND MEMBRANE TOPOLOGICAL OPTIMIZATION WITH STRESS CONSTRAINT[J];Acta Mechanica Solida Sinica;2001-01
2 SUI Yun\|kang 1, YANG De\|qing 1 SUN Huan\|chun 2 SUI Yun\|kang 1, YANG De\|qing 1 SUN Huan\|chun 2 (1.Dept. of Mechanics, Beijing Polytechnic University, Beijing 100022, China; 2.Dept. of Mechanics, Dalian Univ. of Tech., Dalian 116023, China);Uniform ICM theory and method on optimization of structural topology for skeletonal and continuum structures[J];Chinese Journal of Computational Mechanics;2000-01
3 Sui Yunkang (Department of Engineering Mechanics, College of Mechanical Engineering and Applied Electronic Technique, Beijing Polytechnic University, Beijing 100022, China) Yang Deqing;Wang Bei (Department of Engineerics Mechanics, Dalian University of T;TOPOLOGICAL OPTIMIZATION OF CONTINUUM STRUCTURE WITH STRESS AND DISPLACEMENT CONSTRAINTS UNDER MULTIPLE LOADING CASES[J];ACTA MECHANICA SINICA;2000-02
4 Sui Yunkang(Research Institute of Fngineering Mechanics, Dalian Institute of Technology);Optimum Method of Discrete Variables for the Structure Composed of Multi-Elements and Program System DDDU4[J];;1987-04
©2006 Tsinghua Tongfang Knowledge Network Technology Co., Ltd.(Beijing)(TTKN) All rights reserved