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Research Papers: Design Automation

Topology Optimization of Total Femur Structure: Application of Parameterized Level Set Method Under Geometric Constraints

[+] Author and Article Information
Xiaowei Deng

Department of Structural Engineering,
University of California, San Diego,
La Jolla, CA 92093
e-mail: x8deng@eng.ucsd.edu

Yingjun Wang

Department of Structural Engineering,
University of California, San Diego,
La Jolla, CA 92093
e-mail: yiw009@eng.ucsd.edu

Jinhui Yan

Department of Structural Engineering,
University of California, San Diego,
La Jolla, CA 92093
e-mail: jiy071@eng.ucsd.edu

Tao Liu

Wuhan Heavy Duty Machine Tool,
Group Co., Ltd.,
Wuhan 430205, China
e-mail: tower.lau@qq.com

Shuting Wang

Professor
School of Mechanical Science and Engineering,
Huazhong University of Science and Technology,
Wuhan 430074, China
e-mail: wangst@mail.hust.edu.cn

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received December 14, 2014; final manuscript received September 22, 2015; published online November 16, 2015. Assoc. Editor: James K. Guest.

J. Mech. Des 138(1), 011402 (Nov 16, 2015) (8 pages) Paper No: MD-14-1786; doi: 10.1115/1.4031803 History: Received December 14, 2014; Revised September 22, 2015

Optimization of the femur prosthesis is a key issue in femur replacement surgeries that provide a viable option for limb salvage rather than amputation. To overcome the drawback of the conventional techniques that do not support topology optimization of the prosthesis design, a parameterized level set method (LSM) topology optimization with arbitrary geometric constraints is presented. A predefined narrow band along the complex profile of the original femur is preserved by applying the contour method to construct the level set function, while the topology optimization is carried out inside the cavity. The Boolean R-function is adopted to combine the free boundary and geometric constraint level set functions to describe the composite level set function of the design domain. Based on the minimum compliance goal, three different designs of 2D femur prostheses subject to the target cavity fill ratios 34%, 54%, and 74%, respectively, are illustrated.

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Figures

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Fig. 1

Fourteen months postoperative radiograph of a 73-year-old man after total femur replacement [2]

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Fig. 2

A 2D design domain and the level set model

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Fig. 3

Example of complex geometry: snowflake pattern

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Fig. 4

Flowchart of contour function construction

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Fig. 5

Design domain of the femur model

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Fig. 6

Optimization stages of the femur with volume ratio 20%: (a) Initial design, (b) step 2, (c) step 6, (d) step 12, (e) step 16, and (f) step 20 (final result)

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Fig. 7

Convergent histories of the femur optimization

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Fig. 8

Optimized femur results of different volume ratios: (a) 0.15, (b) 0.2, and (c) 0.25

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Fig. 9

Point-domain position relationship for two arbitrary points: (a) Both are inside the domain, (b) one is inside and the other is outside the domain, and (c) both are outside the domain

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