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RESEARCH PAPERS

Decomposition-Based Assembly Synthesis of Space Frame Structures Using Joint Library

[+] Author and Article Information
Naesung Lyu

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

Kazuhiro Saitou1

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109-2125kazu@umich.edu

1

Corresponding author.

J. Mech. Des 128(1), 57-65 (Nov 25, 2004) (9 pages) doi:10.1115/1.1909203 History: Received June 13, 2004; Revised November 25, 2004

This paper presents a method for identifying the optimal designs of components and joints in the space frame body structures of passenger vehicles considering structural characteristics, manufacturability, and assembleability. Dissimilar to our previous work based on graph decomposition, the problem is posed as a simultaneous determination of the locations and types of joints in a structure and the cross sections of the joined structural frames, selected from a predefined joint library. The joint library is a set of joint designs containing the geometry of the feasible joints at each potential joint location and the cross sections of the joined frames, associated with their structural characteristics as equivalent torsional springs obtained from the finite element analyses of the detailed joint geometry. Structural characteristics of the entire structure are evaluated by finite element analyses of a beam-spring model constructed from the selected joints and joined frames. Manufacturability and assembleability are evaluated as the manufacturing and assembly costs estimated from the geometry of the components and joints, respectively. The optimization problem is solved by a multiobjective genetic algorithm using a direct crossover. A case study on an aluminum space frame of a midsize passenger vehicle is discussed.

Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) Audi A2 and (b) ASF (20)

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Figure 2

Approaches used in this paper

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Figure 3

(a) Sample space frame structure and (b) decomposed structure with joints (welded cast sleeves)

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Figure 4

Specified six potential joint locations (0–5, colored as gray boxes) and possible configurations (types) for each joint

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Figure 5

(a) Seven basic members (m0–m6) and (b) structural topology graph with seven nodes (n0–n6) and ten edges (e0–e9)

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Figure 6

Selected joint types and topology graph with the corresponding edges removed

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Figure 7

(a) Three subgraphs and (b) corresponding three components

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Figure 8

(a) Frames with connected by a T-joint and (b) their FE model with beam elements (solid lines) and torsional spring elements (gray lines)

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Figure 9

(a) Detailed 3D solid model of a joint and (b) its FE model with plate elements for beams, solid elements for casting, and plate elements for welding

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Figure 10

Estimating torsional spring rates using FE analysis

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Figure 11

(a) Sample design, (b) three components with three bends (shown as shaded spheres), and (c) four cast sleeves for joining

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Figure 12

(a) ASF for Audi A8 (20) and (b) simplified frame model used in the case study. Extruded and cast components are shaded dark and light, respectively.

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Figure 13

(a) Possible joint locations and (b) feasible joint types at each location

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Figure 14

(a) Resulting 42 basic members and (b) constructed structural topology graph with 42 nodes and 66 edges

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Figure 15

Definitions of the beam cross-section design and welding design: (a) (thicki,0,thicki,1)∊FSi, the ith beam cross-section design used to define variable y (upper/lower thickness thicki,0 and side thickness thicki,1 and (b) (weldi,0,weldi,1)∊Wi, the ith potential joint location welding design used to define variable z (weld thickness for component 0, weldi,0 and for component 1, weldi,1)

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Figure 16

Loading and boundary conditions (33)

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Figure 17

Radial basis networks. In this case study, R=6, S1=1250 and S2=1 (adapted from (35)).

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Figure 18

Convergence trend of the optimization run for case study using 100 numbers of generation with 1000 numbers of population. Note that after a certain number of generation, number of individuals in the Pareto set converges to about 70% of the entire population.

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Figure 19

(a) Pareto solutions at generation=100. Total 656 individuals among 1000 population are in the Pareto set. (b) Pareto solutions near fassm=−57.5. (c) Pareto solutions near fmfg=−380.0. (d) Pareto solutions near fstiff=−2.4×10−3. Utopian points are located at the upper right corner of each graph.

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Figure 20

Designs selected in the Pareto results in Fig. 1: (a) Design A (14 components) with good stiffness and assembleability, (b) design B (12 components) with good manufacturability, and (c) design C (12 components) balanced in all three objectives

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