In the present work, we intend to demonstrate how to do topology optimization in an explicit and geometrical way. To this end, a new computational framework for structural topology optimization based on the concept of moving morphable components is proposed. Compared with the traditional pixel or node point-based solution framework, the proposed solution paradigm can incorporate more geometry and mechanical information into topology optimization directly and therefore render the solution process more flexibility. It also has the great potential to reduce the computational burden associated with topology optimization substantially. Some representative examples are presented to illustrate the effectiveness of the proposed approach.
Issue Section:
Research Papers
References
1.
Bendsoe
, M. P.
, and Kikuchi
, N.
, 1988
, “Generating Optimal Topologies in Structural Design Using a Homogenization Method
,” Comput. Methods Appl. Mech. Eng.
, 71
(2
), pp. 197
–224
.10.1016/0045-7825(88)90086-22.
Altair HyperWorks,
2012
, OptiStruct-12.0 User's Guide, Altair Engineering, Troy, MI.3.
DS Simulia, 2011, “Topology and Shape
Optimization With Abaqus,” Dassault Systèmes, Waltham, MA.4.
Eschenauer
, H. A.
, and Olhoff
, N.
, 2001
, “Topology Optimization of Continuum Structures: A Review
,” ASME Appl. Mech. Rev.
, 54
(4
), pp. 331
–390
.10.1115/1.13880755.
Bendsoe
, M. P.
, Lund
, E.
, Olhoff
, N.
, and Sigmund
, O.
, 2005
, “Topology Optimization-Broadening the Areas of Application
,” Control Cybern.
, 34
(1
), pp. 7
–35
.6.
Guo
, X.
, and Cheng
, G. D.
, 2010
, “Recent Development in Structural Design and Optimization
,” Acta Mech. Sin.
, 26
(6
), pp. 807
–823
.10.1007/s10409-010-0395-77.
Sigmund
, O.
, and Maute
, K.
, 2013
, “Topology Optimization Approaches
,” Struct. Multidiscip. Optim.
, 48
(6
), pp. 1031
–1055
.10.1007/s00158-013-0978-68.
Bendsoe
, M. P.
, 1989
, “Optimal Shape Design as a Material Distribution Problem
,” Struct. Optim.
, 1
(4
), pp. 193
–202
.10.1007/BF016509499.
Zhou
, M.
, and Rozvany
, G. I. N.
, 1991
, “The COC Algorithm, Part II: Topological, Geometry, and Generalized Shape Optimization
,” Comput. Methods Appl. Mech. Eng.
, 89
(1–3)
, pp. 309
–336
.10.1016/0045-7825(91)90046-910.
Mlejnek
, H. P.
, 1992
, “Some Aspects of the Genesis of Structures
,” Struct. Optim.
, 5
(1–2
), pp. 64
–69
.10.1007/BF0174469711.
Bendsoe
, M. P.
, Guedes
, J. M.
, Haber
, R. B.
, Pedersen
, P.
, and Taylor
, J. E.
, 1994
, “An Analytical Model to Predict Optimal Material Properties in the Context of Optimal Structural Design
,” ASME J. Appl. Mech.
, 61
(4
), pp. 930
–937
.10.1115/1.290158112.
Wang
, M. Y.
, Wang
, X. M.
, and Guo
, D. M.
, 2003
, “A Level Set Method for Structural Topology Optimization
,” Comput. Methods Appl. Mech. Eng.
, 192
(1–2
), pp. 227
–246
.10.1016/S0045-7825(02)00559-513.
Allaire
, G.
, Jouve
, F.
, and Toader
, A. M.
, 2004
, “Structural Optimization Using Sensitivity Analysis and a Level Set Method
,” J. Comput. Phys.
, 194
(1
), pp. 363
–393
.10.1016/j.jcp.2003.09.03214.
Cheng
, G. D.
, and Jiang
, Z.
, 1992
, “Study on Topology Optimization With Stress Constraints
,” Eng. Optim.
, 20
(2
), pp. 129
–148
.10.1080/0305215920894127615.
Cheng
, G. D.
, and Guo
, X.
, 1997
, “Epsilon-Relaxed Approach in Structural Topology Optimization
,” Struct. Optim.
, 13
(4
), pp. 258
–266
.16.
Eftekharian
, A. A.
, and Ilies
, H. T.
, 2009
, “Distance Functions and Skeletal Representations of Rigid and Non-Rigid Planar Shapes
,” Comput. Aided Des.
, 41
(12
), pp. 856
–876
.10.1016/j.cad.2009.05.00617.
Guo
, X.
, Zhang
, W. S.
, and Zhong
, W. L.
, 2014
, “Explicit Feature Control in Structural Topology Optimization Via Level Set Method
,” Comput. Methods Appl. Mech. Eng.
, 272
, pp. 354
–378
.10.1016/j.cma.2014.01.01018.
Wei
, P.
, Wang
, M. Y.
, and Xing
, X. H.
, 2010
, “A Study on X-FEM in Continuum Structural Optimization Using a Level Set Model
,” Comput. Aided Des.
, 42
(8
), pp. 708
–719
.10.1016/j.cad.2009.12.00119.
Sigmund
, O.
, 2009
, “Manufacturing Tolerant Topology Optimization
,” Acta Mech. Sina.
, 25
(2
), pp. 227
–239
.10.1007/s10409-009-0240-z20.
Chen
, S. K.
, Chen
, W.
, and Lee
, S. H.
, 2010
, “Level Set Based Robust Shape and Topology Optimization Under Random Field Uncertainties
,” Struct. Multidiscip. Optim.
, 41
(4), pp. 507
–524
.10.1007/s00158-009-0449-221.
Guo
, X.
, Zhang
, W. S.
, and Zhang
, L.
, 2013
, “Robust Topology Optimization Considering Boundary Uncertainties
,” Comput. Methods Appl. Mech. Eng.
, 253
, pp. 356
–368
.10.1016/j.cma.2012.09.00522.
Svanberg
, K.
, 1987
, “The Method of Moving Asymptotes—A New Method for Structural Optimization
,” Int. J. Numer. Methods Eng.
, 24
(2
), pp. 359
–373
.10.1002/nme.162024020723.
Fleury
, C.
, 2007
, “Structural Optimization Methods for Large Scale Problems: Status and Limitations
,” ASME
Paper No. DETC2007-34326.10.1115/DETC2007-34326Copyright © 2014 by ASME
You do not currently have access to this content.