Please wait a minute...
Chin. Phys. B, 2017, Vol. 26(8): 080203    DOI: 10.1088/1674-1056/26/8/080203
GENERAL Prev   Next  

Topology optimization using the improved element-free Galerkin method for elasticity

Yi Wu(吴意)1, Yong-Qi Ma(马永其)1,2, Wei Feng(冯伟)1, Yu-Min Cheng(程玉民)1
1 Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
2 Department of Mechanics, Shanghai University, Shanghai 200444, China
Abstract  

The improved element-free Galerkin (IEFG) method of elasticity is used to solve the topology optimization problems. In this method, the improved moving least-squares approximation is used to form the shape function. In a topology optimization process, the entire structure volume is considered as the constraint. From the solid isotropic microstructures with penalization, we select relative node density as a design variable. Then we choose the minimization of compliance to be an objective function, and compute its sensitivity with the adjoint method. The IEFG method in this paper can overcome the disadvantages of the singular matrices that sometimes appear in conventional element-free Galerkin (EFG) method. The central processing unit (CPU) time of each example is given to show that the IEFG method is more efficient than the EFG method under the same precision, and the advantage that the IEFG method does not form singular matrices is also shown.

Keywords:  meshless method      improved moving least-squares approximation      improved element-free Galerkin method      topology optimization  
Received:  19 December 2016      Revised:  05 April 2017      Published:  05 August 2017
PACS:  02.60.Cb (Numerical simulation; solution of equations)  
  02.60.-x (Numerical approximation and analysis)  
  45.10.Db (Variational and optimization methods)  
  46.15.-x (Computational methods in continuum mechanics)  
Fund: 

Project supported by the National Natural Science Foundation of China (Grant Nos. 11571223 and U1433104).

Corresponding Authors:  Yu-Min Cheng     E-mail:  ymcheng@shu.edu.cn
About author:  0.1088/1674-1056/26/8/

Cite this article: 

Yi Wu(吴意), Yong-Qi Ma(马永其), Wei Feng(冯伟), Yu-Min Cheng(程玉民) Topology optimization using the improved element-free Galerkin method for elasticity 2017 Chin. Phys. B 26 080203

[1] Bendsøe M P 1995 Optimization of structural topology, shape, and material (Publication city: Springer)
[2] Bendsøe M P 1989 Structural Optimization 1 193
[3] Rietz A 2001 Structural and Multidisciplinary Optimization 21 159
[4] Rozvany G, Bendsøe M P and Kirsch U 1995 Appl. Mech. Rev. 48 41
[5] Sigmund O 2001 Structural and Multidisciplinary Optimization 21 120
[6] Tcherniak D and Sigmund O 2001 Structural and Multidisciplinary Optimization 22 179
[7] Xie Y M and Steven G P 1993 Computers & Structures 49 885
[8] De Ruiter M and Van Keulen F 2004 Structural and Multidisciplinary Optimization 26 406
[9] Sethian J A and Wiegmann A 2000 J. Comput. Phys. 163 489
[10] Sigmund O and Petersson J 1998 Structural Optimization 16 68
[11] Noratoa J A, Bellb B K and Tortorellic D A 2015 Comput. Methods Appl. Mech. Eng. 293 306
[12] Hong W, Liu Z S and Suo Z G 2009 International Journal of Solids and Structures 46 3282
[13] Li D M, Liew K M and Cheng Y M 2014 Comput. Mech. 53 1149
[14] Belytschko T, Krysl P and Krongauz Y 1997 Int. J. Numer. Methods Fluids 24 1253
[15] Lu Y, Belytschko T and Gu L 1994 Comput. Methods Appl. Mech. Eng. 113 397
[16] Belytschko T, Krongauz Y, Organ D, Fleming M and Krysl P 1996 Comput. Methods Appl. Mech. Eng. 139 3
[17] Yagawa G and Furukawa T 2000 Int. J. Numer. Methods Eng. 47 1419
[18] Zheng J, Long S Y and Li G Y 2010 Engineering Analysis with Boundary Elements 34 666
[19] Du Y X, Luo Z, Tian Q H and Chen L P 2009 Engineering Optimization 41 753
[20] Deng Y J, Liu C, Peng M J and Cheng Y M 2015 Int. J. Appl. Mech. 7 1550017
[21] Cheng Y M and Chen M J 2003 Acta Mech. Sin. 35 181 (in Chinese)
[22] Zhang Z, Liew K M, Cheng Y M and Lee Y Y 2008 Engineering Analysis with Boundary Elements 32 241
[23] Zhang Z, Hao S Y, Liew K M and Cheng Y M 2013 Engineering Analysis with Boundary Elements 37 1576
[24] Zhang Z, Wang J F, Cheng Y M and Liew K M 2013 Sci. China-Phys. Mech. Astron. 56 1568
[25] Peng M J, Li R X and Cheng Y M 2014 Engineering Analysis with Boundary Elements 40 104
[26] Zhang Z, Li D M, Cheng Y M and Liew K M 2012 Acta Mech. Sin. 28 808
[27] Cheng Y M, Bai F N, Liu C and Peng M J 2016 Int. J. Comput. Mater. Sci. Eng. 5 1650023
[28] Peng M J, Liu P and Cheng Y M 2009 Int. J. Appl. Mech. 1 367
[29] Sun F X, Wang J F and Cheng Y M 2016 Int. J. Appl. Mech. 8 1650096
[30] Zheng J, Yang X J and Long S Y 2015 Int. J. Mech. Mater. Design 11 231
[1] Design of small-scale gradient coils in magnetic resonance imaging by using the topology optimization method
Hui Pan(潘辉), Feng Jia(贾峰), Zhen-Yu Liu(刘震宇), Maxim Zaitsev, Juergen Hennig, Jan G Korvink. Chin. Phys. B, 2018, 27(5): 050201.
[2] Improved reproducing kernel particle method for piezoelectric materials
Ji-Chao Ma(马吉超), Gao-Feng Wei(魏高峰), Dan-Dan Liu(刘丹丹). Chin. Phys. B, 2018, 27(1): 010201.
[3] Meshless analysis of an improved element-free Galerkin method for linear and nonlinear elliptic problems
Yao-Zong Tang(唐耀宗), Xiao-Lin Li(李小林). Chin. Phys. B, 2017, 26(3): 030203.
[4] Two-dimensional fracture analysis of piezoelectric material based on the scaled boundary node method
Shen-Shen Chen(陈莘莘), Juan Wang(王娟), Qing-Hua Li(李庆华). Chin. Phys. B, 2016, 25(4): 040203.
[5] Solving unsteady Schrödinger equation using the improved element-free Galerkin method
Rong-Jun Cheng(程荣军) and Yu-Min Cheng(程玉民). Chin. Phys. B, 2016, 25(2): 020203.
[6] Hybrid natural element method for large deformation elastoplasticity problems
Ma Yong-Qi, Zhou Yan-Kai. Chin. Phys. B, 2015, 24(3): 030204.
[7] Analysis of elastoplasticity problems using an improved complex variable element-free Galerkin method
Cheng Yu-Min, Liu Chao, Bai Fu-Nong, Peng Miao-Juan. Chin. Phys. B, 2015, 24(10): 100202.
[8] Hybrid natural element method for viscoelasticity problems
Zhou Yan-Kai, Ma Yong-Qi, Dong Yi, Feng Wei. Chin. Phys. B, 2015, 24(1): 010204.
[9] A meshless algorithm with moving least square approximations for elliptic Signorini problems
Wang Yan-Chong, Li Xiao-Lin. Chin. Phys. B, 2014, 23(9): 090202.
[10] A meshless method based on moving Kriging interpolation for a two-dimensional time-fractional diffusion equation
Ge Hong-Xia, Cheng Rong-Jun. Chin. Phys. B, 2014, 23(4): 040203.
[11] Analysis of variable coefficient advection–diffusion problems via complex variable reproducing kernel particle method
Weng Yun-Jie, Cheng Yu-Min. Chin. Phys. B, 2013, 22(9): 090204.
[12] A complex variable meshless local Petrov-Galerkin method for transient heat conduction problems
Wang Qi-Fang, Dai Bao-Dong, Li Zhen-Feng. Chin. Phys. B, 2013, 22(8): 080203.
[13] A meshless Galerkin method with moving least square approximations for infinite elastic solids
Li Xiao-Lin, Li Shu-Ling. Chin. Phys. B, 2013, 22(8): 080204.
[14] Analysis of the generalized Camassa and Holm equation with the improved element-free Galerkin method
Cheng Rong-Jun, Wei Qi. Chin. Phys. B, 2013, 22(6): 060209.
[15] An element-free Galerkin (EFG) method for generalized Fisher equations (GFE)
Shi Ting-Yu, Cheng Rong-Jun, Ge Hong-Xia. Chin. Phys. B, 2013, 22(6): 060210.
No Suggested Reading articles found!