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Topology optimization using the finite cell method

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Abstract

Huge effort has been spent over the past decades to develop efficient numerical methods for topology optimization of mechanical structures. Most recent investigations have focused on increasing the efficiency and robustness, improving the optimization schemes and extending them to multidisciplinary objective functions. The vast majority of available methods is based on low order finite elements, assuming one element as the smallest entity which can be assigned material in the optimization process. Whereas the present paper uses only a very simple, heuristic optimization procedure, it investigates in detail the feasibility of high order elements for topology optimization. The Finite Cell Method, an extension of the p-version of FEM is used, which completely separates between the description of the geometry of a structure and cells, where the high order shape functions are defined. Whereas geometry is defined on a (very) fine mesh, the material grid, shape functions live on a much coarser grid of elements, the finite cells. The method takes advantage of the ability of high order elements to accurately approximate even strongly inhomogeneous material distribution within one element and thus boundaries between material and void which pass through the interior of the coarse cells. Very attractive properties of the proposed method can be observed: Due to the high order approach the stress field in the optimized structure is approximated very accurately, no checkerboarding is observed, the iteratively found boundary of the structure is very smooth and the observed number of iterations is in general very small.

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Authors and Affiliations

  1. Department of Industrial Engineering, Isfahan University of Technology, Isfahan, 84156 83111, Iran

    J. Parvizian

  2. Numerische Strukturanalyse mit Anwendungen in der Schiffstechnik (M-10), Technische Universität Hamburg-Harburg, Schwarzenbergstr. 95c, 21073, Hamburg, Germany

    A. Düster

  3. Chair for Computation in Engineering, Faculty of Civil Engineering and Geodesy, Technische Universität München, Arcisstr. 21, 80333, Munich, Germany

    E. Rank

Authors
  1. J. Parvizian
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  2. A. Düster
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  3. E. Rank
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Correspondence to J. Parvizian.

Additional information

This work is the result of an institutional partnership of the three authors being supported by the Alexander von Humboldt Foundation. This support is gratefully acknowledged.

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Parvizian, J., Düster, A. & Rank, E. Topology optimization using the finite cell method. Optim Eng 13, 57–78 (2012). https://doi.org/10.1007/s11081-011-9159-x

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