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Research Papers: Design Automation

Application of a Ground Beam-Joint Topology Optimization Method for Multi-Piece Frame Structure Design

[+] Author and Article Information
Myung-Jin Kim

School of Mechanical and Aerospace Engineering and National Creative Research Initiatives Center for Multiscale Design,  Seoul National University, Seoul 151-742, Koreadootoomi@idealab.snu.ac.kr

Gang-Won Jang

School of Mechanical Engineering, Kunsan National University, Kunsan, Chonbuk 573-701, Koreagangwon@kunsan.ac.kr

Yoon Young Kim

School of Mechanical and Aerospace Engineering and National Creative Research Initiatives Center for Multiscale Design,  Seoul National University, Seoul 151-742, Koreayykim@snu.ac.kr

In this paper, we discriminate between “intersection” and “joint.” The intersection means the spatial common position where the neighboring beam elements connect, and the joint is an infinitesimal part from the intersection to the connected beam element. One intersection has as many joints as the connected beam elements.

J. Mech. Des 130(8), 081401 (Jul 10, 2008) (9 pages) doi:10.1115/1.2936930 History: Received November 23, 2006; Revised August 29, 2007; Published July 10, 2008

When a multipiece frame structure is designed, not only its topological layout but also assembly locations should be determined. This paper presents a compliance-minimizing topology optimization technique to determine an optimal layout configuration and to suggest candidate assembly locations. The technique employs a ground beam-joint model and places candidate assembly joints where the values of joint stiffness are relatively small. The zero-length joint elements have varying stiffness controlled by real-valued design variables. Because joint stiffness values at the converged state can be utilized to select candidate assembly locations along with their strengths, the technique is extremely useful in multipiece frame structure design. Because structural properties of ground beams can have only discrete values or remain unchanged for optimization process, no poststructural modification is required in an actual manufacturing step.

Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Comparison of ground beam models: (a) the conventional beam-only model using variable beam sections and (b) the proposed model with flexible joint springs with variable spring stiffness

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Figure 2

Beam intersection with intermediate nodes

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Figure 3

The effect of κ on joint stiffness (a) beam element with a tip force, and (b) the displacements at the tip for both models (δspring, tip deflection by the joint-beam model; δno-spring, tip deflection by the jointless beam model)

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Figure 4

Layout optimization of a simply supported frame structure (E=210GPa, A=1.9635×10−3m2, Iz=3.0680×10−7m4, and F=1000N)

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Figure 5

Optimized topologies for various values of t in Eq. 4: (a) t=0.35, (b) t=0.5, (c), t=1, and (d) t=2

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Figure 6

Optimum topology of the simply supported frame structure for t=0.35: (a) joint labeling and (b) their JSIs

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Figure 7

A suggested assembly according to the JSI (⋯, Class A assembly; ⋅⋅, Class B assembly; ⋅, Class C assembly)

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Figure 8

Layout for an automobile sub-frame assembly problem

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Figure 9

Beam and joint labeling of a subframe with physical dimensions (unit: mm)

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Figure 10

JSI of a subframe in Fig. 9

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Figure 11

Optimum assembly of the subframe according to the JSI (⋯, Class A assembly; ⋅⋅, Class B assembly; ⋅, Class C assembly)

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Figure 12

Layout optimization involving multiple cross sections for (a) a torsion load (T=100Nm, L=6m, and W=4m) and (b) a bending load (F=100N)

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Figure 13

Available beam sections: (a) Section 1 (a1=30mm, b1=60mm, t1=10mm) and (b) Section 2 (a2=50mm, b2=20mm, t2=10mm)

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Figure 14

Results for the torsion load case: (a) optimum topology with JSIS and (b) optimum assembly (⋯, Class A assembly. ⋅⋅, Class B assembly; ⋅, Class C assembly)

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Figure 15

Results for the bending load case: (a) optimum topology with JSIS and (b) suggested assembly (⋯, Class A assembly. ⋅⋅, Class B assembly; ⋅, Class C assembly)

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Figure 16

Available beam sections: (a) Section 1 (a1=100mm, b1=80mm, t1=10mm) and (b) Section 2 (a2=80mm, b2=100mm, t2=10mm)

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Figure 17

Layout optimization involving multiple cross sections for a force couple (F=100N and 10% mass usage)

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Figure 18

Results for a force couple case in Fig. 1: (a) optimum topology with JSIs and (b) suggested assembly (⋯, Class A assembly; ⋅⋅, Class B assembly; ⋅, Class C assembly)

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