Topology optimization using a reaction-diffusion equation

被引:81
作者
Choi, Jae Seok [1 ]
Yamada, Takayuki [2 ]
Izui, Kazuhiro [1 ]
Nishiwaki, Shinji [1 ]
Yoo, Jeonghoon [3 ]
机构
[1] Kyoto Univ, Dept Mech Engn & Sci, Sakyo Ku, Kyoto 6068501, Japan
[2] Nagoya Univ, Dept Mech Sci & Engn, Chikusa Ku, Nagoya, Aichi 4648603, Japan
[3] Yonsei Univ, Sch Mech Engn, Seoul 120749, South Korea
关键词
Topology optimization; Reaction-diffusion equation; Phase field model; Allen-Cahn equation; Sensitivity analysis; PHASE-FIELD MODELS; LEVEL SET METHOD; STRUCTURAL OPTIMIZATION; DESIGN; SHAPE; SENSITIVITY; RELUCTIVITY;
D O I
10.1016/j.cma.2011.04.013
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
This paper presents a structural topology optimization method based on a reaction-diffusion equation. In our approach, the design sensitivity for the topology optimization is directly employed as the reaction term of the reaction-diffusion equation. The distribution of material properties in the design domain is interpolated as the density field which is the solution of the reaction-diffusion equation, so free generation of new holes is allowed without the use of the topological gradient method. Our proposed method is intuitive and its implementation is simple compared with optimization methods using the level set method or phase field model. The evolution of the density field is based on the implicit finite element method. As numerical examples, compliance minimization problems of cantilever beams and force maximization problems of magnetic actuators are presented to demonstrate the method's effectiveness and utility. (C) 2011 Elsevier B.V. All rights reserved.
引用
收藏
页码:2407 / 2420
页数:14
相关论文
共 50 条
[1]   The generation of plankton patchiness by turbulent stirring [J].
Abraham, ER .
NATURE, 1998, 391 (6667) :577-580
[2]  
Allaire G, 2005, CONTROL CYBERN, V34, P59
[3]  
Allaire G., 2007, Numerical analysis and optimization
[4]   MICROSCOPIC THEORY FOR ANTIPHASE BOUNDARY MOTION AND ITS APPLICATION TO ANTIPHASE DOMAIN COARSENING [J].
ALLEN, SM ;
CAHN, JW .
ACTA METALLURGICA, 1979, 27 (06) :1085-1095
[5]  
[Anonymous], 2013, Topology optimization: theory, methods, and applications
[6]  
Bastos J., 2003, Electromagnetic Modeling by Finite Element Methods
[7]  
Belegundu A., 1999, Optimization Concepts and Applications in Engineering
[8]  
Bendsoe M. P., 1989, Struct. Optim., V1, P193, DOI [10.1007/BF01650949, DOI 10.1007/BF01650949]
[9]   GENERATING OPTIMAL TOPOLOGIES IN STRUCTURAL DESIGN USING A HOMOGENIZATION METHOD [J].
BENDSOE, MP ;
KIKUCHI, N .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1988, 71 (02) :197-224
[10]   Topology optimization using regularized intermediate density control [J].
Borrvall, T ;
Petersson, J .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2001, 190 (37-38) :4911-4928