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Research Papers

Topology Synthesis of Multicomponent Structural Assemblies in Continuum Domains

[+] Author and Article Information
Ali R. Yildiz1

Department of Automotive Engineering, Uludag University, 16059 Bursa, Turkeyaliriza@uludag.edu.tr

Kazuhiro Saitou

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

Assuming the weld material is less stiff than the structural material, which is the case for spot welded sheet metal assemblies.

1

Corresponding author.

J. Mech. Des. 133(1), 011008 (Jan 06, 2011) (9 pages) doi:10.1115/1.4003038 History: Received August 19, 2009; Revised November 05, 2010; Published January 06, 2011; Online January 06, 2011

This paper presents a new method for synthesizing structural assemblies directly from the design specifications, without going through the two-step process. Given an extended design domain with boundary and loading conditions, the method simultaneously optimizes the topology and geometry of an entire structure and the location and configuration of joints, considering structural performance, manufacturability, and assembleability. As a relaxation of our previous work utilizing a beam-based ground structure, this paper presents a new formulation in a continuum design domain, which enhances the ability to represent complex structural geometry observed in real-world products. A multiobjective genetic algorithm is used to obtain Pareto optimal solutions that exhibit trade-offs among stiffness, weight, manufacturability, and assembleability. Case studies with a cantilever and a simplified automotive floor frame under multiple loadings are examined to show the effectiveness of the proposed method. Representative designs are selected from the Pareto front and trade-offs among the multiple criteria are discussed.

Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Two approaches for (single-component) structural topology optimization: (a) discrete element (ground structure) and (b) continuum, adopted from Ref. 4

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Figure 2

Two approaches for multicomponent structural topology optimization (26-29): (a) with predefined component boundaries and (b) without predefined component boundaries (1)

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Figure 3

Outline of the approach: (a) continuum design domain, (b) discretized design domain, (c) ground topology graph G0, (d) product topology graph G, (e) multicomponent structure with empty diagonal joint elements, and (f) repaired multicomponent structure

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Figure 4

Constraint 1: (a) feasible structure, (b) infeasible structure (disconnected by missing structure), and (c) infeasible structure (disconnected by missing joint)

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Figure 5

Constraint 2: (a) feasible structure, (b) infeasible structure (unattached boundary condition point), and (c) infeasible structure (unattached loading point)

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Figure 6

Constraint 3: (a) feasible structure, (b) infeasible structure (void in component), and (c) infeasible structure (disconnected weld line)

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Figure 7

Repair rules for constraint 3: Gray elements indicate that they are filled with structural or weld materials, and hatched elements indicate that they are filled with either structural or weld materials or void. All gray elements in a rule must be filled with the same material, whereas hatched elements can be filled with different material types including void.

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Figure 8

Unnatural features not excluded by the repair rules in Fig. 7: (a) truncated weld and (b) stand alone weld

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Figure 9

Convex hull as an estimation of die usable area: (a) component, (b) centroids of diagonal joint elements, (c) extracted vertices, (d) convex hull vertices, (e) convex hull, and (f) area of convex hull

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Figure 10

Plane area correction factor flw versus bounding box area Ab (in cm2) (36)

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Figure 11

Basic manufacturing points Mp0 versus die complexity index Xp(36)

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Figure 12

Multicomponent structure synthesis using MOGA

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Figure 13

Chromosome representation of design variables x and y where the elements of these vectors are simply laid out to form a linear chromosome of length |V|+|E|

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Figure 14

A FE model for calculating Young’s modulus for weld material

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Figure 15

Case 1 design domain and boundary conditions

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Figure 16

Convergence history of MOGA for case 1

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Figure 17

Distribution of designs at generation=100 for case 1: In all plots, the utopia points are at the upper right corner. Three representative Pareto optimal designs R1, R2, and R3 are shown in Fig. 1.

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Figure 18

Representative Pareto optimal designs for case 1: (a) R1, (b) R2, and (c) R3. R1, R2, and R3 have 3, 4, and 1 components, respectively.

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Figure 19

A radar chart for the objective function values of designs R1, R2, and R3. Note that R2 shows a balanced performance in all four objective functions.

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Figure 20

Design domain of case study 2 with boundary conditions.

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Figure 21

Representative Pareto optimal designs: (a) R1, (b) R2, (c) R3, (d) R4, and (e) R5 have 6, 6, 8, 5, and 1 components, respectively.

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Figure 22

A radar chart for the objective function values of the representative Pareto optimal designs (R1–R5) in case 2. Note that R4 shows a balanced performance in all six objective functions.

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