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Shape optimization for a link mechanism

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Abstract

This paper presents a numerical solution for shape optimization problems for link mechanisms, such as a piston-crank mechanism. The dynamic behavior of a link mechanism is described by a differential-algebraic equation (DAE) system consisting of motion equations for each single body and constraints of linkages and rigid motions. In a shape optimization problem, the objective function to maximize is constructed from the external work done by a given external force, which agrees with the kinetic energy of the link mechanism, for an assigned time interval, and the total volume of all the links forms the constraint function. The Fréchet derivatives of these cost functions with respect to the domain variation, which we call the shape derivatives of these cost functions, are evaluated theoretically. A scheme to solve the shape optimization problem is presented using the H 1 gradient method (the traction method) proposed by the authors as a reshaping algorithm, since it retains the smoothness of the boundary. A numerical example shows that reasonable shapes for each link such that mobility of the link mechanism is improved are obtained by this approach.

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References

  • Adams RA, Fournier JJF (2003) Sobolev spaces, 2nd edn. Academic, New York

    MATH  Google Scholar 

  • Amirouche F (2006) Fundamentals of multibody dynamics: theory and applications. Birkhäuser, Boston

    Google Scholar 

  • Armijo L (1966) Minimization of functions having Lipschitz-continuous first partial derivatives. Pac J Math 16:1–3

    Article  MathSciNet  MATH  Google Scholar 

  • Azegami H, Takeuchi K (2006) A smoothing method for shape optimization: traction method using the Robin condition. Int J Comput Methods 3(1):21–33

    Article  MathSciNet  MATH  Google Scholar 

  • Azegami H, Kaizu S, Takeuchi K (2011) Regular solution to topology optimization problems of continua. JSIAM Lett 3:1–4

    MathSciNet  Google Scholar 

  • Azegami H, Fukumoto S, Aoyama T (2012) Shape optimization of continua using NURBS as basis functions. Struct Multidisc Optim 47(2):247–258

    Article  Google Scholar 

  • Bremer H (2008) Elastic multibody dynamics: a direct Ritz approach. Springer, New York

    Book  Google Scholar 

  • Featherstone R (2008) Rigid body dynamics algorithms. Springer, New York

    Book  MATH  Google Scholar 

  • Nocedal J, Wright SJ (2006) Numerical optimization. Springer, New York

    MATH  Google Scholar 

  • Sokolowski J, Zolésio JP (1992) Introduction to shape optimization: shape sensitivity analysis. Springer, New York

    Book  MATH  Google Scholar 

  • Wolfe P (1969) Convergence conditions for ascent methods. SIAM Rev 11:226–235

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgement

The present study was supported by JSPS KAKENHI (20540113).

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Authors and Affiliations

  1. Graduate School of Information Science, Nagoya University, A4-2 (780) Furo-cho, Chikusa-ku, Nagoya, 464-8601, Japan

    Hideyuki Azegami, Liren Zhou, Kimihiro Umemura & Naoya Kondo

Authors
  1. Hideyuki Azegami
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  2. Liren Zhou
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  3. Kimihiro Umemura
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  4. Naoya Kondo
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Corresponding author

Correspondence to Hideyuki Azegami.

Additional information

This paper was presented at CJK-OSM 7, 18–21 June 2012, Huangshan, China.

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Azegami, H., Zhou, L., Umemura, K. et al. Shape optimization for a link mechanism. Struct Multidisc Optim 48, 115–125 (2013). https://doi.org/10.1007/s00158-013-0886-9

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  • DOI: https://doi.org/10.1007/s00158-013-0886-9

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