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Research Papers: Design for Manufacture and the Life Cycle

A Pareto-Optimal Approach to Multimaterial Topology Optimization

[+] Author and Article Information
Amir M. Mirzendehdel

Department of Mechanical Engineering,
UW-Madison,
Madison, WI 53706
e-mail: mirzendehdel@wisc.edu

Krishnan Suresh

Department of Mechanical Engineering,
UW-Madison,
Madison, WI 53706
e-mail: ksuresh@wisc.edu

Contributed by the Design for Manufacturing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 10, 2015; final manuscript received July 10, 2015; published online August 6, 2015. Assoc. Editor: Carolyn Seepersad.

J. Mech. Des 137(10), 101701 (Aug 06, 2015) (12 pages) Paper No: MD-15-1081; doi: 10.1115/1.4031088 History: Received February 10, 2015

As additive manufacturing (AM) expands into multimaterial, there is a demand for efficient multimaterial topology optimization (MMTO), where one must simultaneously optimize the topology and the distribution of various materials within the topology. The classic approach to multimaterial optimization is to minimize compliance or stress while imposing two sets of constraints: (1) a total volume constraint and (2) individual volume-fraction constraint on each of the material constituents. The latter can artificially restrict the design space. Instead, the total mass and compliance are treated as conflicting objectives, and the corresponding Pareto curve is traced; no additional constraint is imposed on the material composition. To trace the Pareto curve, first-order element sensitivity fields are computed, and a two-step algorithm is proposed. The effectiveness of the algorithm is demonstrated through illustrative examples in 3D.

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Figures

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Fig. 1

From problem specification to optimal part

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Fig. 2

Design space for a TO problem

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Fig. 3

The Pareto-optimal curve and topologies for a single material (A)

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Fig. 4

Topological and element sensitivity fields for the single-material 2D L-bracket problem: (a) plot of 2D topological sensitivity field and (b) plot of 2D element sensitivity field

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Fig. 5

Tracing the Pareto curve and the two substeps

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Fig. 6

Feasible regions with respect to change in inefficiency and cost

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Fig. 8

Subalgorithm 1, reducing C

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Fig. 9

Subalgorithm 2, increasing performance while keeping C constant

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Fig. 10

Three-dimensional structuring element for morphological filtering

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Fig. 11

The Pareto curves and topologies for single material (A) and two materials (A and B)

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Fig. 12

CG iterations for the L-bracket with (a) single material A and (b) two materials A and B

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Fig. 14

Pareto curves for 10,000 and 40,000 elements

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Fig. 15

MBB structure with 10,000 and 40,000 elements at weight fraction of 0.2

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Fig. 16

Cantilevered beam

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Fig. 17

Effect of number of materials on Pareto curve

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Fig. 18

C-bracket problem considered in Ref. [51]

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Fig. 19

Convergence plot of C-bracket

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Fig. 20

Table design geometry and boundary conditions

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Fig. 21

Table design using a single material

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Fig. 22

Table design using three materials

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