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On optimization of lightweight planar frame structures: an evolving ground structure approach

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Abstract

We consider the problem of designing lightweight, load-bearing planar frame structures for additive manufacturing, which can be formulated as a nonlinear, non-convex mathematical programming problems. Even using state-of-the-art commercial solvers, exact methods are only capable of solving small unrealistic instances (with very few variables). In this paper, we develop a heuristic method which is fast and capable of solving the design problem for larger-scale, weight-optimized, planar frame structures for additive manufacturing. The approach explicitly considers manufacturability constraints stemming from the use of additive manufacturing technology and leverages the problem structure imposed by these constraints. The proposed heuristic method is based on iteratively resolving a relaxed master problem on a reduced ground structure. The approach differs from the existing methods in two important aspects. First, we consider planar frame optimization master problem directly (instead of simpler but less relevant truss optimization). Secondly, we employ both element and node addition, which allows us to enforce additive manufacturability constraints without using binary variables (and hence, avoiding the need for computationally expensive integer programming).

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Acknowledgements

The authors are grateful to the National Center for Additive Manufacturing Excellence (NCAME) at Auburn University and especially Dr. Nima Shamsaei for the guidance and support provided.

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Authors and Affiliations

  1. Mechanical, Robotics and Industrial Engineering, Lawrence Technological University, Southfield, MI, USA

    Oguz Toragay

  2. Industrial and Systems Engineering, Auburn University, Auburn, AL, USA

    Daniel F. Silva & Alexander Vinel

Authors
  1. Oguz Toragay
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  2. Daniel F. Silva
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  3. Alexander Vinel
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Correspondence to Oguz Toragay.

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Replication of results

The results that we mentioned in this paper can be replicated using the codes which are shared in the first author’s Github account https://github.com/oguztoragay/AMPAP2.8.

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Responsible Editor: Matthew Gilbert

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Toragay, O., Silva, D.F. & Vinel, A. On optimization of lightweight planar frame structures: an evolving ground structure approach. Struct Multidisc Optim 67, 79 (2024). https://doi.org/10.1007/s00158-024-03796-w

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