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TECHNICAL PAPERS

Decomposition-Based Assembly Synthesis of a Three-Dimensional Body-in-White Model for Structural Stiffness

[+] Author and Article Information
Naesung Lyu, Kazuhiro Saitou

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109-2125

J. Mech. Des 127(1), 34-48 (Mar 02, 2005) (15 pages) doi:10.1115/1.1799551 History: Received July 01, 2003; Revised March 01, 2004; Online March 02, 2005
Copyright © 2005 by ASME
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References

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Lee,  B., and Saitou,  K., 2003, “Decomposition-Based Assembly Synthesis for In-Process Dimensional Adjustability,” ASME J. Mech. Des., 125, pp. 464–473.
Lyu,  N., and Saitou,  K., 2002, “Decomposition-Based Assembly Synthesis for Structural Stiffness,” ASME J. Mech. Des., 125, pp. 452–463.
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Figures

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(a) A simple structure with a plate reinforced by a beam, and (b) decomposition with two beam and three plate components
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(a) Overall structure, (b) beam substructure, and (c) plate substructure separated from (a), (d) four basic members (B0–B3) defined in (b), and (e) six basic members (P0–P5) defined in (c)
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Constructing structural topology graph for each substructure. (a) Basic members of beam substructure, (b) structural topology graph GB of (a), (c) basic members of plate substructure, and (d) topology graph GP of (c). In (b) and (d), JD* represents the joint design at each potential joint position defined for each edge.
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(a) Beam and plate basic members, (b) entire structural topology graph GE, and (c) joint designs between beam and plate basic members [thick edges in (b)]
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Sample decomposition of structural topology graph of (a) beam substructure and (b) corresponding components set with joint designs, of (c) plate substructure and (d) corresponding components set with joint designs, (e) assignment of joint properties between beam and plate components, and (f) resulting component set
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(a) Physical location of joints. (b) Entire structural graph GE. (c) Table of joint points and corresponding edges in GE.
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“Graph-based” crossover operation by plane A. (a) Parent structures P1 cut into S1/S2, (b) another parent structure P2 cut into S3/S4, (c) child C1 made of S1/S4, and (d) child C2 made of S3/S2.
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Flowchart of multicomponent structure synthesis
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FE model of a four door passenger vehicle BIW composed of beam and plate elements
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Global bending condition used for case studies I and II. Two downward loads of 4900 [N] (1/4 of total weight) are applied at nodes on the rocker at the 1/3 distance between the supports.
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(a) Side frame portion of the FE model made of beam elements, (b) selected 21 basic members, and (c) corresponding entire structural topology graph GE with 21 nodes and 24 edges
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(a) Side frame before deformation and (b) after deformation, and (c) calculation of front door frame distortion. Black line, front door shape in (a) and gray line, front door shape in (b). DISPLACEMENTS will be the maximum distance between Ai and Bi (i=0,1,2,3).
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GUI of the optimization software used in case study I
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Function values at the terminal generation (generation number=100). Points in the plots are the Pareto optimal designs.
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Design R1 (best fstiffness). (a) Four components, (b) structural topology graph, and (c) joint designs.
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Design R2 (best fmanufac). (a) Five components (b) structural topology graph, and (c) joint designs.
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Design R3 (best fassemble). (a) One component, (b) structural topology graph, and (c) joint designs: not available (no joints).
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Design R4. (a) Five components, (b) structural topology graph, and (c) joint designs.
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Spider diagram of the four representative designs from the Pareto front in case study I, normalized within these four designs. Design R1, R2, and R3 show the best results only considering fstiffness value, fmanufac value, and fassemble value, respectively. Design R4 shows balanced results in all three objective functions.
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Side/floor frame and floor panel in BIW model used in case study II
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(a ) Entire structure to be decomposed (right half only), (b) beam substructure, and (c) plate substructure
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(a) 37 basic members in beam substructure and (b) corresponding structural topology graph GB with 37 nodes and 46 edges
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(a) 28 basic members in plate substructure and (b) corresponding structural topology graph GP with 28 nodes and 45 edges
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Entire structural graph GE with 65 nodes and 120 edges. In GE, 29 edges (edge 91–edge 119) are used to connect beam basic member and plate basic member.
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Points for measuring deflection of floor panel
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GUI of the optimization software used in case study II
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Function values at the terminal generation (generation number=100). Points in the plots are the Pareto optimal designs.
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Design R1 (best fstiffness) (a) Six components in beam substructure, (b) GB, (c) one component in plate substructure, (d) GP, (e) joint designs (selected from seven joints) in beam substructure, (f) joint designs in plate substructure: not available (no joints), and (g) joint designs (selected from 29 joints) between beam and plate substructures
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Design R2 (best fmanufac). (a) Eight components in beam substructure, (b) GB, (c) two components in plate structure, (d) GP, (e) three joint designs (selected from 10 joints) in beam substructure, (f) three joint designs (selected from four joints) in plate substructure, (g) three joint designs (selected from 29 joints) between beam and plate structures.
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Design R3 (best fassemble). (a) Four components in beam substructure, (b) GB, (c) one component in plate substructure, (d) GP, (e) three joint designs (selected from six joints) in beam substructure, (f) joint designs in plate substructure: not available (no joints), (g) three joint designs (selected from 29 joints) between beam and plate structures.
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Design R4. (a) Seven components in beam substructure, (b) GB, (c) three components in plate substructure, (d) GP, (e) three joint designs (selected from nine joints) in beam substructure, (f) three joint designs (selected from 11 joints) in plate substructure, and (g) three joint designs (selected from 29 joints) between beam and plate structures.
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Spider diagram of the four representative designs from the Pareto front in case study II, normalized within these four designs. Design R4 shows balanced results in all three objective functions.

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