PAPERS: Multimaterial Design Methods for AM

A Generalized Optimality Criteria Method for Optimization of Additively Manufactured Multimaterial Lattice Structures

[+] Author and Article Information
Tino Stanković

Engineering Design and Computing Laboratory,
Department of Mechanical and Process Engineering,
ETH Zürich,
Tannenstr. 3, 8092 Zürich, Switzerland
e-mail: tinos@ethz.ch

Jochen Mueller

Engineering Design and Computing Laboratory,
Department of Mechanical and Process Engineering,
ETH Zürich,
Tannenstr. 3, 8092 Zürich, Switzerland
e-mail: jm@ethz.ch

Paul Egan

Engineering Design and Computing Laboratory,
Department of Mechanical and Process Engineering,
ETH Zürich,
Tannenstr. 3, 8092 Zürich, Switzerland
e-mail: pegan@ethz.ch

Kristina Shea

Engineering Design and Computing Laboratory,
Department of Mechanical and Process Engineering,
ETH Zürich,
Tannenstr. 3, 8092 Zürich, Switzerland
e-mail: kshea@ethz.ch

1Corresponding author.

Early iterations of this work were accepted to the 2015 ASME Computers and Information in Engineering Conference (Stanković et al. 2015).Contributed by the Design for Manufacturing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 15, 2015; final manuscript received June 15, 2015; published online October 12, 2015. Assoc. Editor: Timothy W. Simpson.

J. Mech. Des 137(11), 111405 (Oct 12, 2015) (12 pages) Paper No: MD-15-1126; doi: 10.1115/1.4030995 History: Received February 15, 2015; Revised June 15, 2015

Recent progress in additive manufacturing (AM) allows for printing customized products with multiple materials and complex geometries that could form the basis of multimaterial designs with high performance and novel functions. Effectively designing such complex products for optimal performance within the confines of AM constraints is challenging due to the need to consider fabrication constraints while searching for optimal designs with a large number of variables, which stem from new AM capabilities. In this study, fabrication constraints are addressed through empirically characterizing multiple printed materials' Young's modulus and density using a multimaterial inkjet-based 3D-printer. Data curves are modeled for the empirical data describing two base printing materials and 12 mixtures of them as inputs for a computational optimization process. An optimality criteria (OC) method is developed to search for solutions of multimaterial lattices with fixed topology and truss cross section sizes. Two representative optimization studies are presented and demonstrate higher performance with multimaterial approaches in comparison to using a single material. These include the optimization of a cubic lattice structure that must adhere to a fixed displacement constraint and a compliant beam lattice structure that must meet multiple fixed displacement constraints. Results demonstrate the feasibility of the approach as a general synthesis and optimization method for multimaterial, lightweight lattice structures that are large-scale and manufacturable on a commercial AM printer directly from the design optimization results.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Huang, S. H., Liu, P., Mokasdar, A., and Hou, L., 2013, “Additive Manufacturing and Its Societal Impact: A Literature Review,” Int. J. Adv. Manuf. Technol., 67(5–8), pp. 1191–1203. [CrossRef]
Vaezi, M., Chianrabutra, S., Mellor, B., and Yang, S., 2013, “Multiple Material Additive Manufacturing—Part 1: A Review: This Review Paper Covers a Decade of Research on Multiple Material Additive Manufacturing Technologies Which Can Produce Complex Geometry Parts With Different Materials,” Virtual Phys. Prototyping, 8(1), pp. 19–50. [CrossRef]
Beyer, C., 2014, “Strategic Implications of Current Trends in Additive Manufacturing,” ASME J. Manuf. Sci. Eng., 136(6), p. 064701. [CrossRef]
Hiller, J., and Lipson, H., 2009, “Design and Analysis of Digital Materials for Physical 3D Voxel Printing,” Rapid Prototyping J., 15(2), pp. 137–149. [CrossRef]
Gaynor, A. T., Meisel, N. A., Williams, C. B., and Guest, J. K., 2014, “Multiple-Material Topology Optimization of Compliant Mechanisms Created Via PolyJet Three-Dimensional Printing,” ASME J. Manuf. Sci. Eng., 136(6), p. 061015. [CrossRef]
Hammetter, C., Rinaldi, R., and Zok, F., 2013, “Pyramidal Lattice Structures for High Strength and Energy Absorption,” ASME J. Appl. Mech., 80(4), p. 041015. [CrossRef]
Bendsoe, M. P., and Sigmund, O., 2003, Topology Optimization: Theory, Methods and Applications, Springer-Verlag, Berlin, Germany.
Khot, N., 1981, “Algorithms Based on Optimality Criteria to Design Minimum Weight Structures,” Eng. Optim., 5(2), pp. 73–90. [CrossRef]
Jamiolahmadi, S., and Barari, A., 2014, “Surface Topography of Additive Manufacturing Parts Using a Finite Difference Approach,” ASME J. Manuf. Sci. Eng., 136(6), p. 061009. [CrossRef]
Ma, R. R., Belter, J. T., and Dollar, A. M., 2015, “Hybrid Deposition Manufacturing: Design Strategies for Multi-Material Mechanisms Via 3D-Printing and Material Deposition,” ASME J. Mech. Rob., 7(2), p. 021002. [CrossRef]
Nelaturi, S., Kim, W., Rangarajan, A., and Kurtoglu, T., 2014, “Manufacturability Feedback and Model Correction for Additive Manufacturing,” ASME Paper No. DETC2014-34222.
Hu, Y., Fadel, G. M., Blouin, V. Y., and White, D. R., 2006, “Optimal Design for Additive Manufacturing of Heterogeneous Objects Using Ultrasonic Consolidation,” Virtual Phys. Prototyping, 1(1), pp. 53–62. [CrossRef]
Begley, M. R., and Zok, F. W., 2014, “Optimal Material Properties for Mitigating Brain Injury During Head Impact,” ASME J. Appl. Mech., 81(3), p. 031014. [CrossRef]
KrzeminskI, D. E., Goetz, J. T., Janisse, A. P., Lippa, N. M., Gould, T. E., Rawlins, J. W., and Piland, S. G., 2011, “Investigation of Linear Impact Energy Management and Product Claims of a Novel American Football Helmet Liner Component,” Sports Technol., 4(1–2), pp. 65–76.
Hammetter, C., and Zok, F., 2014, “Compressive Response of Pyramidal Lattices Embedded in Foams,” ASME J. Appl. Mech., 81(1), p. 011006. [CrossRef]
Stanković, T., Mueller, J., Egan, P., and Shea, K., 2015, “Optimization of Additively Manufactured Multi-Material Lattice Structures Using Generalized Optimality Criteria,” Computers and Information in Engineering Conference, Boston, ASME Paper No. DETC2015-47403.
Hansen, K., Dau, N., Feist, F., Deck, C., Willinger, R., Madey, S. M., and Bottlang, M., 2013, “Angular Impact Mitigation System for Bicycle Helmets to Reduce Head Acceleration and Risk of Traumatic Brain Injury,” Accid. Anal. Prev., 59, pp. 109–117. [CrossRef] [PubMed]
Benson., B. W., Hamilton, G. M., Meeuwisse, W. H., McCrory, P., and Dvorak, J., 2009, “Is Protective Equipment Useful in Preventing Concussion? A Systematic Review of the Literature,” Br. J. Sports Med., 43(1), pp. i56–i67. [CrossRef] [PubMed]
Venkayya, V. B., 1978, “Structural Optimization: A Review and Some Recommendations,” Int. J. Numer. Methods Eng., 13(2), pp. 203–228. [CrossRef]
Venkayya, V. B., 1989, “Optimality Criteria: A Basis for Multidisciplinary Design Optimization,” Comput. Mech., 5(1), pp. 1–21. [CrossRef]
Venkayya, V. B., Tischler, V. A., Kolonay, R. M., and Canfield, R. A., 1990, “A Generalized Optimality Criteria Method for Mathematical Optimization,” SIAM Conference on Geometric on Industrial Design Theory, Wright-Patterson Air Force Base, OH, pp. 124–153.
Chang, P. S., and Rosen, D. W., 2013, “The Size Matching and Scaling Method: A Synthesis Method for the Design of Mesoscale Cellular Structures,” Int. J. Comput. Integr. Manuf., 26(10), pp. 907–927. [CrossRef]
Chu, J., Engelbrecht, S., Graf, G., and Rosen, D. W., 2010, “A Comparison of Synthesis Methods for Cellular Structures With Application to Additive Manufacturing,” Rapid Prototyping J., 16(4), pp. 275–283. [CrossRef]
Ning, X., and Pellegrino, S., 2012, “Design of Lightweight Structural Components for Direct Digital Manufacturing,” 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Honolulu, p. 1807.
Shea, K., and Smith, I. F., 2006, “Improving Full-Scale Transmission Tower Design Through Topology and Shape Optimization,” J. Struct. Eng., 132(5), pp. 781–790. [CrossRef]
Doubrovski, Z., Verlinden, J. C., and Geraedts, J. M., 2011, “Optimal Design for Additive Manufacturing: Opportunities and Challenges,” ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering, Washington, DC, August 28–31, ASME Paper No. DETC2011-48131.
Eiamsa-ard, K., Ruan, J., Ren, L., and Liou, F. W., 2005, “Building Sequence of Boundary Model in Layered Manufacturing,” ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering (DETC2005-85163), Long Beach, CA, September 24–28, ASME Paper No. (DETC2005-85163).
Routhu, S., Kanakanala, D., Ruan, J., Liu, X. F., and Liou, F., 2010, “2-D Path Planning for Direct Laser Deposition Process,” ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Montreal, QC, Canada, January 01, 2010 ASME Paper No. CP002010044090000415000001.
Skouras, M., Thomaszewski, B., Coros, S., Bickel, B., and Gross, M., 2013, “Computational Design of Actuated Deformable Characters,” ACM Trans. Graphics (TOG), 32(4), pp. 1–9. [CrossRef]
Hiller, J., and Lipson, H., 2012, “Automatic Design and Manufacture of Soft Robots,” IEEE Trans. Rob., 28(2), pp. 457–466. [CrossRef]
Hu, Y., Blouin, V. Y., and Fadel, G. M., 2008, “Design for Manufacturing of 3D Heterogeneous Objects With Processing Time Consideration,” ASME J. Mech. Des., 130(3), p. 031701. [CrossRef]
Prager, W., 1968, “Optimality Criteria in Structural Design,” Proc. Natl. Acad. Sci. U. S. A., 61(3), pp. 794–796. [CrossRef] [PubMed]
Zhou, M., and Rozvany, G., 1992, “DCOC: An Optimality Criteria Method for Large Systems. Part I: Theory,” Struct. Optim., 5(1–2), pp. 12–25. [CrossRef]
Khot, N., Venkayya, V. B., and Berke, N., 1976, “Optimum Structural Design With Stability Constraints,” Int. J. Numer. Methods Eng., 10(5), pp. 1097–1114. [CrossRef]
Venkayya, V. B., and Khot, N., 1975, “Design of Optimum Structures to Impulse Type Loading,” AIAA J., 13(8), pp. 989–994. [CrossRef]
Flager, F., Soremekun, G., Adya, A., Shea, K., Haymaker, J., and Fischer, M., 2014, “Fully Constrained Design: A General and Scalable Method for Discrete Member Sizing Optimization of Steel Truss Structures,” Comput. Struct., 140, pp. 55–65. [CrossRef]
Grierson, D., and Chan, C.-M., 1993, “An Optimality Criteria Design Method for Tall Steel Buildings,” Adv. Eng. Software, 16(2), pp. 119–125. [CrossRef]
Venkayya, V., Khot, N., and Reddy, V., 1969, “Energy Distribution in an Optimum Structural Design,” Air Force Flight Dynamics Lab, Wright-Patterson, OH, Report No. AFFDL-TR-68-156.
Mueller, J., Kim, S., Shea, K., and Daraio, C., 2015, “Tensile Properties of PolyJet 3D-Printed Parts: Critical Process Parameters and How to Efficiently Analyze Them,” ASME 2015 International Computers and Information in Engineering, Boston, MA, ASME Paper No. DETC2015-48024.
Venkayya, V. B., and Tischler, V. A., 1989, A Compound Scaling Algorithm for Mathematical Optimization, Air Force Flight Dynamics Lab, Wright-Patterson, OH.
Ashby, M. F., 1999, Materials Selection and Process in Mechanical Design, Butterworth Heinemann, Oxford, UK.


Grahic Jump Location
Fig. 1

DfAM product design methodology

Grahic Jump Location
Fig. 2

Results of benchmarking algorithms for a steel lattice test-case

Grahic Jump Location
Fig. 3

Empirical AM data for Young's modulus as a function of density. Shown are the experimentally obtained values (rectangle), the values taken from the materials' datasheets (circle), and the fitted curve.

Grahic Jump Location
Fig. 4

Cubic cell definition

Grahic Jump Location
Fig. 5

Cube lattice topology and boundary conditions

Grahic Jump Location
Fig. 6

Displacement constraint definition for cubic lattice

Grahic Jump Location
Fig. 10

Cantilever beam boundary conditions and constraints

Grahic Jump Location
Fig. 14

Cantilever beam in plane displacement results for the x1 i = 3000 MPa starting point. The allowed displacement range is shown with two parallel lines per each constrained node pair.




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