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TECHNICAL PAPERS

Decomposition-Based Assembly Synthesis for Structural Modularity

[+] Author and Article Information
O. L. Cetin, K. Saitou

Dept. of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109

J. Mech. Des 126(2), 234-243 (May 05, 2004) (10 pages) doi:10.1115/1.1666890 History: Received July 01, 2002; Revised July 01, 2003; Online May 05, 2004
Copyright © 2004 by ASME
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References

Figures

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Product topology graphs of (a) the structure on the left, and (b) the structure on the right in Fig. 1(b)
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Four types of joints that connects two beams A and B. (a) butt joint of A onto B (type 1), (b) butt joint of B onto A (type 2), (c) lap joint of A onto B from top (type 3), and (d) lap joint of B onto A from bottom (type 4).
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A detailed illustration of type 1 joint in Fig. 3(a) 18. Beams A and B are also made of sheet metals joined by spot welds.
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Example components that are (a) non-flat (not manufacturable), and (b) flat (manufacturable) via stamping processes
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Local, right-handed coordinate system ξ-ψ-ζ located at joint i, where the origin is at the intersection of the neutral axes of beams A and B, and x axis is inline with vector va of beam A. Note ζ axis is pointing out of the paper.
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Basic manufacturing points Mp vs. die complexity index Xp21
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Example decomposition of the 2D structures in Figure 1(b). The identified modules are annotated with “s.”
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Decomposed product topology graphs of (a) the structure on the left, and (b) the structure on the right in Fig. 8. Dashed lines indicate the edges with welds annotated with the joint types in Fig. 3. Subgraphs with thicker lines with “s” represent the identified modules. The direction of the arrow on the dashed line shows which beam is welded onto another, i.e., which beam corresponds to beam A or B, according to the definition in Fig. 3.
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Design variables x1,x2,y1 and y2 encoded as a “double strand” linear chromosome
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Simplified beam-based body structures of (a) sedan and (b) wagon. Both structures are approximately 4.6 [m] in length (x direction), 1.5 [m] in width (y direction), and 1.3 [m] in height (z direction).
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Product topology graphs of a half-body with respect to x-z plane of (a) the sedan structure and (b) the wagon structure in Fig. 11.
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Optimization history of a typical GA run. The values are the average of the elite population for each generation, normalized between 0 and 1.
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Global bending condition on (a) sedan model and (b) wagon model. A downward force of 8.0 [kN] is applied at the location indicated by an arrow.
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Objective function values of the ten Pareto optimal solutions for global bending. (a) number of modules and force on welds, and (b) number of welds and manufacturing cost.
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Graphical representation of (a) a lap weld and (b) a butt weld in the decomposition results.
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Decomposition results for solution 2 in the global bending condition.
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Decomposition results for solution 10 in the global bending condition. Identified modules are annotated with “s.”
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Global torsion condition on (a) sedan model and (b) wagon model. Upward and downward forces of 4000 [N] each are applied at the locations indicated by two arrows.
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Objective function values of the ten Pareto optimal solutions for global torsion. (a) number of modules and force on welds, and (b) number of welds and manufacturing cost.
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Decomposition results for solution 1 in the global torsion condition. Identified modules are annotated with “s.”
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Decomposition results for solution 10 in the global torsion condition. Identified modules are annotated with “s.”
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Example of two product variants 9: (a) design domain and boundary conditions, and (b) two topologically optimal structures to be decomposed. Note that the product, variants do not have to be topologically optimal.

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