0
Research Papers

Multicomponent Topology Optimization for Additive Manufacturing With Build Volume and Cavity Free Constraints

[+] Author and Article Information
Yuqing Zhou

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109
e-mail: yuqingz@umich.edu

Tsuyoshi Nomura

Toyota Research Institute of North America,
Ann Arbor, MI 48105;
Toyota Central R & D Labs., Inc.,
Yokomichi,
Nagakute 480-1192, Japan
e-mail: tsuyoshi.nomura@toyota.com

Kazuhiro Saitou

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109
e-mail: kazu@umich.edu

Contributed by the Computers and Information Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received July 31, 2018; final manuscript received January 21, 2019; published online March 6, 2019. Assoc. Editor: Yong Chen.

J. Comput. Inf. Sci. Eng 19(2), 021011 (Mar 06, 2019) (10 pages) Paper No: JCISE-18-1193; doi: 10.1115/1.4042640 History: Received July 31, 2018; Revised January 21, 2019

Topology optimization for additive manufacturing has been limited to the design of single-piece components that fit within the printer's build volume. This paper presents a gradient-based multicomponent topology optimization method for structures assembled from components built by powder bed additive manufacturing (MTO-A), which enables the design of multipiece assemblies larger than the printer's build volume. Constraints on component geometry for powder bed additive manufacturing are incorporated in a density-based topology optimization framework, with an additional design field governing the component partitioning. For each component, constraints on the maximum allowable build volume (i.e., length, width, and height) and the elimination of enclosed cavities are imposed during the simultaneous optimization of the overall topology and component partitioning. Numerical results of the minimum compliance designs revealed that manufacturing constraints, previously applied to single-piece topology optimization, can unlock richer design exploration space when applied to multicomponent designs.

FIGURES IN THIS ARTICLE
<>
Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.

References

Bendsøe, 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.
Dede, E. M. , Joshi, S. N. , and Zhou, F. , 2015, “ Topology Optimization, Additive Layer Manufacturing, and Experimental Testing of an Air-Cooled Heat Sink,” ASME J. Mech. Des., 137(11), p. 111403.
Zegard, T. , and Paulino, G. H. , 2016, “ Bridging Topology Optimization and Additive Manufacturing,” Struct. Multidiscip. Optim., 53(1), pp. 175–192.
Zhu, B. , Skouras, M. , Chen, D. , and Matusik, W. , 2017, “ Two-Scale Topology Optimization With Microstructures,” ACM Trans. Graph., 36(4). p. 164.
Vogiatzis, P. , Chen, S. , and Zhou, C. , 2017, “ An Open Source Framework for Integrated Additive Manufacturing and Level-Set-Based Topology Optimization,” ASME J. Comput. Inf. Sci. Eng., 17(4), p. 041012.
Steuben, J. C. , Iliopoulos, A. P. , and Michopoulos, J. G. , 2018, “ Multiscale Topology Optimization for Additively Manufactured Objects,” ASME J. Comput. Inf. Sci. Eng., 18(3), p. 031002.
Luo, L. , Baran, I. , Rusinkiewicz, S. , and Matusik, W. , 2012, “ Chopper: Partitioning Models Into 3D-Printable Parts,” ACM Trans. Graph., 31(6), pp. 129:1–129:9.
Attene, M. , 2015, “ Shapes in a Box: Disassembling 3D Objects for Efficient Packing and Fabrication,” Comput. Graph. Forum, 34(8), pp. 64–76.
Turner, B. N. , Strong, R. , and Gold, S. A. , 2014, “ A Review of Melt Extrusion Additive Manufacturing Processes—Part I: Process Design and Modeling,” Rapid Prototyping J., 20(3), pp. 192–204.
Liu, S. , Li, Q. , Chen, W. , Tong, L. , and Cheng, G. , 2015, “ An Identification Method for Enclosed Voids Restriction in Manufacturability Design for Additive Manufacturing Structures,” Front. Mech. Eng., 10(2), pp. 126–137.
Li, Q. , Chen, W. , Liu, S. , and Tong, L. , 2016, “ Structural Topology Optimization Considering Connectivity Constraint,” Struct. Multidiscip. Optim., 54(4), pp. 971–984.
Ambrosio, L. , and Buttazzo, G. , 1993, “ An Optimal Design Problem With Perimeter Penalization,” Calculus Var. Partial Differ. Equations, 1(1), pp. 55–69.
Haber, R. B. , Jog, C. S. , and Bendsøe, M. P. , 1996, “ A New Approach to Variable-Topology Shape Design Using a Constraint on Perimeter,” Struct. Multidiscip. Optim., 11(1–2), pp. 1–12.
Petersson, J. , and Sigmund, O. , 1998, “ Slope Constrained Topology Optimization,” Int. J. Numer. Methods Eng., 41(8), pp. 1417–1434.
Sigmund, O. , 1997, “ On the Design of Compliant Mechanisms Using Topology Optimization,” J. Struct. Mech., 25(4), pp. 493–524.
Bruns, T. E. , and Tortorelli, D. A. , 2001, “ Topology Optimization of Non-Linear Elastic Structures and Compliant Mechanisms,” Comput. Methods Appl. Mech. Eng., 190(26–27), pp. 3443–3459.
Guest, J. K. , Prévost, J. H. , and Belytschko, T. , 2004, “ Achieving Minimum Length Scale in Topology Optimization Using Nodal Design Variables and Projection Functions,” Int. J. Numer. Methods Eng., 61(2), pp. 238–254.
Lazarov, B. S. , and Sigmund, O. , 2011, “ Filters in Topology Optimization Based on Helmholtz-Type Differential Equations,” Int. J. Numer. Methods Eng., 86(6), pp. 765–781.
Thomsen, J. , 1992, “ Topology Optimization of Structures Composed of One or Two Materials,” Struct. Optim., 5(1–2), pp. 108–115.
Sigmund, O. , 2001, “ Design of Multiphysics Actuators Using Topology Optimization—Part II: Two-Material Structures,” Comput. Methods Appl. Mech. Eng., 190(49–50), pp. 6605–6627.
Stegmann, J. , and Lund, E. , 2005, “ Discrete Material Optimization of General Composite Shell Structures,” Int. J. Numer. Methods Eng., 62(14), pp. 2009–2027.
Zuo, W. , and Saitou, K. , 2017, “ Multi-Material Topology Optimization Using Ordered SIMP Interpolation,” Struct. Multidiscip. Optim., 55(2), pp. 477–491.
Lyu, N. , and Saitou, K. , 2005, “ Topology Optimization of Multicomponent Beam Structure Via Decomposition-Based Assembly Synthesis,” ASME J. Mech. Des., 127(2), pp. 170–183.
Yildiz, A. R. , and Saitou, K. , 2011, “ Topology Synthesis of Multicomponent Structural Assemblies in Continuum Domains,” ASME J. Mech. Des., 133(1), p. 011008.
Guirguis, D. , Hamza, K. , Aly, M. , Hegazi, H. , and Saitou, K. , 2015, “ Multi-Objective Topology Optimization of Multi-Component Continuum Structures Via a Kriging-Interpolated Level Set Approach,” Struct. Multidiscip. Optim., 51(3), pp. 733–748.
Rozvany, G. I. , 2009, “ A Critical Review of Established Methods of Structural Topology Optimization,” Struct. Multidiscip. Optim., 37(3), pp. 217–237.
Sigmund, O. , 2011, “ On the Usefulness of Non-Gradient Approaches in Topology Optimization,” Struct. Multidiscip. Optim., 43(5), pp. 589–596.
Zhou, Y. , and Saitou, K. , 2018, “ Gradient-Based Multi-Component Topology Optimization for Stamped Sheet Metal Assemblies (MTO-S),” Struct. Multidiscip. Optim., 58(1), pp. 83–94.
Zhou, Y. , Nomura, T. , and Saitou, K. , 2018, “ Multi-Component Topology and Material Orientation Design of Composite Structures (MTO-C),” Comput. Methods Appl. Mech. Eng., 342, pp. 438–457.
Formlab, 2016, “ How to Create Models Larger Than a 3D Printer's Build Volume,” Formlab, accessed Dec. 15, 2018, https://goo.gl/9mz1Zb
Zhou, Y. , and Saitou, K. , 2017, “ Gradient-Based Multi-Component Topology Optimization for Additive Manufacturing (MTO-A),” ASME Paper No. DETC2017-68207.
Kawamoto, A. , Matsumori, T. , Yamasaki, S. , Nomura, T. , Kondoh, T. , and Nishiwaki, S. , 2011, “ Heaviside Projection Based Topology Optimization by a PDE-Filtered Scalar Function,” Struct. Multidiscip. Optim., 44(1), pp. 19–24.
Bendsøe, M. P. , and Sigmund, O. , 2004, Topology Optimization Theory, Methods, and Applications, Springer, Berlin.
O'Rourke, J. , 1985, “ Finding Minimal Enclosing Boxes,” Int. J. Comput. Inf. Sci., 14(3), pp. 183–199.
Barequet, G. , and Har-Peled, S. , 2001, “ Efficiently Approximating the Minimum-Volume Bounding Box of a Point Set in Three Dimensions,” J. Algorithms, 38(1), pp. 91–109.
Chan, C. , and Tan, S. , 2001, “ Determination of the Minimum Bounding Box of an Arbitrary Solid: An Iterative Approach,” Comput. Struct., 79(15), pp. 1433–1449.
Dimitrov, D. , Knauer, C. , Kriegel, K. , and Rote, G. , 2009, “ Bounds on the Quality of the PCA Bounding Boxes,” Comput. Geom., 42(8), pp. 772–789.
Moon, S. J. , and Yoon, G. H. , 2013, “ A Newly Developed qp-Relaxation Method for Element Connectivity Parameterization to Achieve Stress-Based Topology Optimization for Geometrically Nonlinear Structures,” Comput. Methods Appl. Mech. Eng., 265, pp. 226–241.
Svanberg, K. , 1987, “ The Method of Moving Asymptotes—A New Method for Structural Optimization,” Int. J. Numer. Methods Eng., 24(2), pp. 359–373.
Olesen, L. H. , Okkels, F. , and Bruus, H. , 2006, “ A High-Level Programming-Language Implementation of Topology Optimization Applied to Steady-State Navier-Stokes Flow,” Int. J. Numer. Methods Eng., 65(7), pp. 975–1001.
Aage, N. , Andreassen, E. , and Lazarov, B. S. , 2015, “ Topology Optimization Using PETSc: An Easy-to-Use, fully Parallel, Open Source Topology Optimization Framework,” Struct. Multidiscip. Optim., 51(3), pp. 565–572.
Zhou, Y. , Nomura, T. , and Saitou, K. , 2018, “ Multi-Component Topology Optimization for Powder Bed Additive Manufacturing (MTO-A),” ASME Paper No. DETC2018-86284.
Brackett, D. , Ashcroft, I. , and Hague, R. , 2011, “ Topology Optimization for Additive Manufacturing,” Solid Freeform Fabrication Symposium, Austin, TX, Aug. 8–10, pp. 348–362.
Gaynor, A. T. , and Guest, J. K. , 2016, “ Topology Optimization Considering Overhang Constraints: Eliminating Sacrificial Support Material in Additive Manufacturing Through Design,” Struct. Multidiscip. Optim., 54(5), pp. 1157–1172.
Mirzendehdel, A. M. , and Suresh, K. , 2016, “ Support Structure Constrained Topology Optimization for Additive Manufacturing,” Comput.-Aided Des., 81, pp. 1–13.
Qian, X. , 2017, “ Undercut and Overhang Angle Control in Topology Optimization: A Density Gradient Based Integral Approach,” Int. J. Numer. Methods Eng., 111(3), pp. 247–272.
Langelaar, M. , 2017, “ An Additive Manufacturing Filter for Topology Optimization of Print-Ready Designs,” Struct. Multidiscip. Optim., 55(3), pp. 871–883.
Guo, X. , Zhou, J. , Zhang, W. , Du, Z. , Liu, C. , and Liu, Y. , 2017, “ Self-Supporting Structure Design in Additive Manufacturing Through Explicit Topology Optimization,” Comput. Methods Appl. Mech. Eng., 323, pp. 27–63.
Liu, P. , Luo, Y. , and Kang, Z. , 2016, “ Multi-Material Topology Optimization Considering Interface Behavior Via XFEM and Level Set Method,” Comput. Methods Appl. Mech. Eng., 308, pp. 113–133.

Figures

Grahic Jump Location
Fig. 1

Two-layer design field for a three-component example case (K  = 3)

Grahic Jump Location
Fig. 2

Design domain and boundary condition settings for the MBB beam example

Grahic Jump Location
Fig. 3

Iterative details for the MBB example: (a) iteration 1, (b) iteration 35, (c) iteration 80, and (d) iteration 311

Grahic Jump Location
Fig. 4

Implicit component interface due to regularization. The gray zone between component boundaries is less stiff than the base material.

Grahic Jump Location
Fig. 5

Iterative details of manufacturing constraints for the MBB example: (a) iteration 1, (b) iteration 35, (c) iteration 80, and (d) iteration 311

Grahic Jump Location
Fig. 6

Optimized multicomponent topology for the MBB example. The prescribed maximum build volume is plotted over each component.

Grahic Jump Location
Fig. 7

Design domain and boundary condition settings for the cantilever example

Grahic Jump Location
Fig. 8

Optimized multicomponent topologies for the cantilever example with different prescribed maximum allowable build volumes: (a) 2.0 by 1.0, (b) 1.5 by 0.6, (c) 1.0 by 0.4, (d) 2.5 by 0.3, and (e) radius 0.4 (spherical approximation); (f) prescribed maximum build volumes for (ae)

Grahic Jump Location
Fig. 9

Design domain and boundary condition settings for the 3D cantilever example

Grahic Jump Location
Fig. 10

Optimized topology for the 3D cantilever example: (a) single-piece design and (b) three-component design

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In