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Adaptive Finite Element Methods for Shape Optimization of Linearly Elastic Structures

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The Optimum Shape

Part of the book series: General Motors Research Laboratories Symposia Series ((RLSS))

Abstract

In this paper the application of adaptive grid methods with automatic remeshing schemes is discussed to solve shape optimization problems of linearly elastic structures.

After demonstrating that the final optimal shape of a structure strongly depends on the shape of finite elements near the design boundary, we briefly review the discretization error due to finite element approximations. More precisely, we derive the interpolation error to quantify the effect of distortion of the finite elements. Based on the above, an adaptive finite element grid design problem is defined using the idea of structural optimization. A necessary condition is obtained that defines a manner to adapt a given finite element grid.

Since the domain to be discretized in shape optimization problems changes its shape and size very drastically during the iterative process to find the optimal solution, remeshing must be performed at certain design stages in order to maintain the quality of finite elements of undesirable geometrical distortion. However, remeshing must be implemented without interruption of the computing process to obtain the optimal shape. This leads to numerical grid generation and adaptive methods being combined with automatic remeshing schemes.

Several shape optimization problems are solved to demonstrate the capability of the proposed method.

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Author information

Authors and Affiliations

  1. The University of Michigan, Ann Arbor, Michigan, USA

    N. Kikuchi, K. Y. Chung, T. Torigaki & J. E. Taylor

Authors
  1. N. Kikuchi
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  2. K. Y. Chung
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  3. T. Torigaki
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  4. J. E. Taylor
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Editor information

Editors and Affiliations

  1. General Motors Research Laboratories, USA

    J. A. Bennett  & M. E. Botkin  & 

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© 1986 Plenum Press, New York

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Kikuchi, N., Chung, K.Y., Torigaki, T., Taylor, J.E. (1986). Adaptive Finite Element Methods for Shape Optimization of Linearly Elastic Structures. In: Bennett, J.A., Botkin, M.E. (eds) The Optimum Shape. General Motors Research Laboratories Symposia Series. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-9483-3_6

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  • DOI: https://doi.org/10.1007/978-1-4615-9483-3_6

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4615-9485-7

  • Online ISBN: 978-1-4615-9483-3

  • eBook Packages: Springer Book Archive

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