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Research Papers: Design Automation

Cluster-Based Optimization of Cellular Materials and Structures for Crashworthiness

[+] Author and Article Information
Kai Liu

School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47907
e-mail: liu915@purdue.edu

Duane Detwiler

Honda R&D Americas, Inc.,
Raymond, OH 43067
e-mail: ddetwiler@oh.hra.com

Andres Tovar

Purdue School of Engineering and Technology,
Department of Mechanical and Energy
Engineering,
Indiana University-Purdue University
Indianapolis,
Indianapolis, IN 46202
e-mail: tovara@iupui.edu

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received March 15, 2018; final manuscript received July 9, 2018; published online September 10, 2018. Assoc. Editor: Nam H. Kim.

J. Mech. Des 140(11), 111412 (Sep 10, 2018) (10 pages) Paper No: MD-18-1219; doi: 10.1115/1.4040960 History: Received March 15, 2018; Revised July 09, 2018

The objective of this work is to establish a cluster-based optimization method for the optimal design of cellular materials and structures for crashworthiness, which involves the use of nonlinear, dynamic finite element models. The proposed method uses a cluster-based structural optimization approach consisting of four steps: conceptual design generation, clustering, metamodel-based global optimization, and cellular material design. The conceptual design is generated using structural optimization methods. K-means clustering is applied to the conceptual design to reduce the dimensional of the design space as well as define the internal architectures of the multimaterial structure. With reduced dimension space, global optimization aims to improve the crashworthiness of the structure can be performed efficiently. The cellular material design incorporates two homogenization methods, namely, energy-based homogenization for linear and nonlinear elastic material models and mean-field homogenization for (fully) nonlinear material models. The proposed methodology is demonstrated using three designs for crashworthiness that include linear, geometrically nonlinear, and nonlinear models.

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Figures

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Fig. 1

Design domain for the 2D bumper problem

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Fig. 2

Conceptual design for the 2D bumper problem, f=1.77×103

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Fig. 3

Clustered designs with K=1…10

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Fig. 4

K-means objective as a function of the number of clusters K for the 2D bumper-like problem

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Fig. 5

Optimal cellular structure with K = 4

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Fig. 6

Design domain for the bumper design problem

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Fig. 7

The final topology generated for the bumper problem with internal energy =1.90×106 J and mass fraction =0.50

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Fig. 8

Clustered design with K=1…10

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Fig. 9

K-means objective as a function of the number of clusters K for the 3D bumper-like problem

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Fig. 10

Design optimization results with K = 3

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Fig. 11

Material nonlinear responses with volume fraction from 0.1 to 1.0 with step 0.1

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Fig. 12

Comparison of the Pareto optimal cellular structures

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