Abstract
This work presents a method for the topology optimization of welded frame structures to minimize the manufacturing cost. The structures considered here consist of assemblies of geometric primitives such as bars and plates that are common in welded frame construction. A geometry projection technique is used to map the primitives onto a continuous density field that is subsequently used to interpolate material properties. As in density-based topology optimization techniques, the ensuing ersatz material is used to perform the structural analysis on a fixed mesh, thereby circumventing the need for re-meshing upon design changes. The distinct advantage of the representation by geometric primitives is the ease of computation of the manufacturing cost in terms of the design parameters, while the geometry projection facilitates the analysis within a continuous design region. The proposed method is demonstrated via the manufacturing-cost-minimization subject to a displacement constraint of 2D bar, 3D bar, and plate structures.
Issue Section:
Design Automation
References
1.
Asadpoure
, A.
, Guest
, J. K.
, and Valdevit
, L.
, 2015
, “Incorporating Fabrication Cost Into Topology Optimization of Discrete Structures and Lattices
,” Struct. Multidiscipl. Optim.
, 51
(2
), pp. 385
–396
. 2.
Liu
, J.
, Chen
, Q.
, Liang
, X.
, and To
, A. C.
, 2019
, “Manufacturing Cost Constrained Topology Optimization for Additive Manufacturing
,” Front. Mech. Eng.
, 14
(2
), pp. 213
–221
. 3.
Ryan
, L.
, and Kim
, I. Y.
, 2019
, “A Multiobjective Topology Optimization Approach for Cost and Time Minimization in Additive Manufacturing
,” Int. J. Numer. Methods Eng.
, 118
(7
), pp. 371
–394
. 4.
Sabiston
, G.
, and Kim
, I. Y.
, 2020
, “3D Topology Optimization for Cost and Time Minimization in Additive Manufacturing
,” Struct. Multidiscipl. Optim.
, 61
(2
), pp. 731
–748
. 5.
Ulu
, E.
, Huang
, R.
, Kara
, L. B.
, and Whitefoot
, K. S.
, 2019
, “Concurrent Structure and Process Optimization for Minimum Cost Metal Additive Manufacturing
,” ASME J. Mech. Des.
, 141
(6
), p. 061701
. 6.
Zhou
, Z.
, Hamza
, K.
, and Saitou
, K.
, 2014
, “Decomposition Templates and Joint Morphing Operators for Genetic Algorithm Optimization of Multicomponent Structural Topology
,” ASME J. Mech. Des.
, 136
(2
), p. 021004
. 7.
Zhou
, Y.
, and Saitou
, K.
, 2018
, “Gradient-Based Multi-component Topology Optimization for Stamped Sheet Metal Assemblies (MTO-S)
,” Struct. Multidiscipl. Optim.
, 58
(1
), pp. 83
–94
. 8.
Li
, G.
, Xu
, F.
, Huang
, X.
, and Sun
, G.
, 2015
, “Topology Optimization of an Automotive Tailor-Welded Blank Door
,” ASME J. Mech. Des.
, 137
(5
), p. 055001
. 9.
Torii
, A. J.
, Lopez
, R. H.
, and Miguel
, L. F. F.
, 2016
, “Design Complexity Control in Truss Optimization
,” Struct. Multidiscipl. Optim.
, 54
(2
), pp. 289
–299
. 10.
Zhang
, W.
, Zhou
, J.
, Zhu
, Y.
, and Guo
, X.
, 2017
, “Structural Complexity Control in Topology Optimization Via Moving Morphable Component (MMC) Approach
,” Struct. Multidiscipl. Optim.
, 56
(3
), pp. 535
–552
. 11.
Zhang
, W.
, Liu
, Y.
, Wei
, P.
, Zhu
, Y.
, and Guo
, X.
, 2017
, “Explicit Control of Structural Complexity in Topology Optimization
,” Comput. Methods Appl. Mech. Eng.
, 324
, pp. 149
–169
. 12.
Norato
, J.
, Bell
, B.
, and Tortorelli
, D. A.
, 2015
, “A Geometry Projection Method for Continuum-Based Topology Optimization With Discrete Elements
,” Comput. Methods Appl. Mech. Eng.
, 293
, pp. 306
–327
. 13.
Zhang
, S.
, Norato
, J. A.
, Gain
, A. L.
, and Lyu
, N.
, 2016
, “A Geometry Projection Method for the Topology Optimization of Plate Structures
,” Struct. Multidiscipl. Optim.
, 54
(5
), pp. 1173
–1190
. 14.
Smith
, H.
, and Norato
, J.
, 2022
, “Topology Optimization of Structures Made of Fiber-Reinforced Plates
,” Struct. Multidiscipl. Optim.
, 65
(2
), pp. 1
–18
. 15.
Smith
, H.
, and Norato
, J. A.
, 2020
, “A MATLAB Code for Topology Optimization Using the Geometry Projection Method
,” Struct. Multidiscipl. Optim.
, 62
(3
), pp. 1579
–1594
. 16.
Smith
, H.
, and Norato
, J. A.
, 2021
, “Topology Optimization With Discrete Geometric Components Made of Composite Materials
,” Comput. Methods Appl. Mech. Eng.
, 376
, p. 113582
. 17.
Bendsøe
, M. P.
, and Sigmund
, O.
, 1999
, “Material Interpolation Schemes in Topology Optimization
,” Arch. Appl. Mech.
, 69
(9
), pp. 635
–654
.18.
Shapiro
, V.
, 2002
, “Solid Modeling,” Handbook of Computer Aided Geometric Design
, G.
Farin
, J.
Hoschek
, and M. S.
Kim
, eds., Elsevier
, Amsterdam
, pp. 473
–518
.19.
Jármai
, K.
, and Farkas
, J.
, 1999
, “Cost Calculation and Optimisation of Welded Steel Structures
,” J. Construct. Steel Res.
, 50
(2
), pp. 115
–135
. 20.
Svanberg
, K.
, 2007
, MMA and GCMMA – Two Methods for Nonlinear Optimization
.21.
Stolpe
, M.
, 2010
, “On Some Fundamental Properties of Structural Topology Optimization Problems
,” Struct. Multidiscipl. Optim.
, 41
(5
), pp. 661
–670
. 22.
Rozvany
, G. I.
, 2011
, “On Symmetry and Non-uniqueness in Exact Topology Optimization
,” Struct. Multidiscipl. Optim.
, 43
(3
), pp. 297
–317
. 23.
Wein
, F.
, Dunning
, P. D.
, and Norato
, J. A.
, 2020
, “A Review on Feature-Mapping Methods for Structural Optimization
,” Struct. Multidiscipl. Optim.
, 62
(4
), pp. 1597
–1638
. 24.
Ahrens
, James
, Geveci
, Berk
, and Law
, Charles
, 2005
, “ParaView: An End-User Tool for Large Data Visualization,” The Visualization Handbook
, Vol. 717
, C.
Hansen
, C.
Johnson
, eds., Elsevier
, Burlington-Oxford
, pp. 717
–732
.25.
Ayachit
, U.
, 2015
, The Paraview Guide: A Parallel Visualization Application
, Kitware, Inc.
, Clifton Park, NY
.Copyright © 2023 by ASME
You do not currently have access to this content.
