Research Papers

A Comparative Study of the Formulations and Benchmark Problems for the Topology Optimization of Compliant Mechanisms

[+] Author and Article Information
Sangamesh R. Deepak, M. Dinesh, Deepak K. Sahu

Mechanical Engineering, Indian Institute of Science, Bangalore 560012, India

G. K. Ananthasuresh

Mechanical Engineering, Indian Institute of Science, Bangalore 560012, Indiasuresh@mecheng.iisc.ernet.in




J. Mechanisms Robotics 1(1), 011003 (Jul 30, 2008) (8 pages) doi:10.1115/1.2959094 History: Received April 22, 2008; Revised June 20, 2008; Published July 30, 2008

The topology optimization problem for the synthesis of compliant mechanisms has been formulated in many different ways in the past 15years, but there is not yet a definitive formulation that is universally accepted. Furthermore, there are two unresolved issues in this problem. In this paper, we present a comparative study of five distinctly different formulations that are reported in the literature. Three benchmark examples are solved with these formulations using the same input and output specifications and the same numerical optimization algorithm. A total of 35 different synthesis examples are implemented. The examples are limited to desired instantaneous output direction for prescribed input force direction. Hence, this study is limited to linear elastic modeling with small deformations. Two design parametrizations, namely, the frame element-based ground structure and the density approach using continuum elements, are used. The obtained designs are evaluated with all other objective functions and are compared with each other. The checkerboard patterns, point flexures, and the ability to converge from an unbiased uniform initial guess are analyzed. Some observations and recommendations are noted based on the extensive implementation done in this study. Complete details of the benchmark problems and the results are included. The computer codes related to this study are made available on the internet for ready access.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 1

Specification for a typical compliant mechanism synthesis problem

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Figure 2

A gripper example solved with YINSYN . (a) Problem specifications, (b) optimal topology with output stiffness=1×10−6N∕m, and (c) optimal topology with output stiffness=100N∕m. This example used Young’s modulus of 2×109Pa, Poisson’s ratio of 0.3, 300×150mm2 rectangular design domain with some nondesign hole, out-of-plane thickness of 5mm, 5N input force, a material penalization parameter equal to 3, and a volume fraction of 0.2.

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Figure 3

Design domain and material properties

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Figure 4

Inverter example

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Figure 7

Topology of the inverter obtained with Kin=1×106N∕m and Kout=1×104N∕m

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Figure 8

Topology of the inverter obtained with Kin=1×106N∕m and Kout=1×106N∕m

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Figure 9

Topology of the inverter obtained with Kin=Kout=1×107N∕m




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