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Research Papers

Decomposition Templates and Joint Morphing Operators for Genetic Algorithm Optimization of Multicomponent Structural Topology

[+] Author and Article Information
Zebin Zhou

CAE Engineering,
Safety Engineering
and Virtual Technology Technical Center,
SAIC Motor Passenger Vehicle Co.,
Jiading, Shanghai 201804, China
e-mail: zhouzebin@saicmotor.com

Karim Hamza

Senior Research Fellow
e-mail: khamza@umich.edu

Kazuhiro Saitou

Professor
e-mail: kazu@umich.edu
Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109-2102

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received September 14, 2012; final manuscript received November 1, 2013; published online December 11, 2013. Assoc. Editor: Michael Kokkolaras.

J. Mech. Des 136(2), 021004 (Dec 11, 2013) (13 pages) Paper No: MD-12-1456; doi: 10.1115/1.4026030 History: Received September 14, 2012; Revised November 01, 2013

This paper presents a continuum-based approach for multi-objective topology optimization of multicomponent structures. Objectives include minimization of compliance, weight, and cost of assembly and manufacturing. Design variables are partitioned into two main groups: those pertaining to material allocation within a design domain (base topology problem), and those pertaining to decomposition of a monolithic structure into multiple components (joint allocation problem). Generally speaking, the two problems are coupled in the sense that the decomposition of an optimal monolithic structure is not always guaranteed to produce an optimal multicomponent structure. However, for spot-welded sheet-metal structures (such as those often found in automotive applications), certain assumptions can be made about the performance of a monolithic structure that favor the adoption of a two-stage approach that decouples the base topology and joint allocation problems. A multi-objective genetic algorithm (GA) is used throughout the studies in this paper. While the problem decoupling in two-stage approaches significantly reduces the size of the search space and allows better performance of the GA, the size of the search space can still be quite enormous in the second stage. To further improve the performance, a new mutation operator based on decomposition templates and localized joints morphing is proposed. A cantilever-loaded structure is used to study and compare various setups of single and two-stage GA approaches and establish the merit of the proposed GA operators. The approach is then applied to a simplified model of an automotive vehicle floor subject to global bending loading condition.

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Figures

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Fig. 3

Repairing disconnected structures: (a) detection of disconnected material islands, (b) some-to-some shortest path identification, (c) addition of material along the shortest path

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Fig. 4

Repairing joint elements: (a) detection of cut edges within one component, (b) connecting the cut edges

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Fig. 5

Illustration of convex hull and bounding box enclosing a component

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Fig. 6

Spider-web diagram illustration of a Pareto-optimal design and its equivalent monolithic structure

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Fig. 7

Illustration of geometric crossover

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Fig. 8

Localized joint morphing mutation operator: (a) complementary joints, (b) single-cell island removal, and (c) joint propagation

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Fig. 9

Twelve-cell example design domain and boundary conditions

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Fig. 10

Select Pareto-optimal designs for the twelve-cell example

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Fig. 11

Short cantilever example design domain, loading and boundary conditions

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Fig. 12

Monolithic designs in Φ for two-stage approaches in short cantilever example

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Fig. 13

Normalized Pareto-plots for GA1, GA2, GA3, and GA4

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Fig. 14

Normalized Pareto-plots for GA3, GA4, GA5, and GA6

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Fig. 15

Normalized Pareto-plots for GA3, GA4, GA7, and GA8

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Fig. 16

Normalized Pareto-plots for GA5, GA6, GA9, and GA10

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Fig. 17

Structural details of select designs in short cantilever example

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Fig. 18

Spider-web diagram illustration of objective values for select designs in short cantilever example

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Fig. 19

Design domain and boundary conditions for simplified vehicle floor model

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Fig. 20

Monolithic designs in Φ for vehicle floor study

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Fig. 21

Normalized Pareto-plots for vehicle floor study

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Fig. 22

Structural details of select designs in vehicle floor study

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Fig. 23

Spider-web diagram illustration of objective values for select designs in vehicle floor study

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