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Multiobjective topology optimization of truss structures with kinematic stability repair

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Abstract

This paper addresses single and multiobjective topology optimization of truss-like structures using genetic algorithms (GA’s). In order to improve the performance of the GA’s (despite the presence of binary topology variables) a novel approach based on kinematic stability repair (KSR) is proposed. The methodology consists of two parts, namely the creation of a number of kinematically stable individuals in the initial population (IP) and a chromosome repair procedure. The proposed method is developed for both 2D and 3D structures and is shown to produce (in the single-objective case) results which are better than, or equal to, those found in the literature, while significantly increasing the rate of convergence of the algorithm. In the multiobjective case, the proposed modifications produce superior results compared to the unmodified GA. Finally the algorithm is successfully applied to a cantilevered 3D structure.

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Notes

  1. DOF = dn − m − n s , where d is the dimension, n is the number of nodes, m the number of bar members and n s the number of degrees of freedom constrained by the supports. It should be verified that DOF is not positive.

  2. This does not include unconnected nodes.

  3. Note that the structures conform to the Chebyshev–Grübler–Kutzbach criterion.

  4. During collinear/planar repair, it is ensured that the number of elements removed does not lead to the node connected to one or two elements, respectively in 2D and 3D problems. This is to avoid connectivity violations, while technically satisfying the collinear/planar check.

  5. Note that the problem of singular topologies is eliminated through the presence of the topology variable.

  6. In the figures one of the two overlapping members is drawn below or above the other to avoid confusion. These members are connected to the nodes above or below them at the end points only.

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Acknowledgement

The first author would like to thank the Fonds de la Recherche Scientifique (FNRS) for financial support of this research.

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Authors and Affiliations

  1. BATir - Building, Architecture and Town Planning, Brussels School of Engineering, Université Libre de Bruxelles, 50 avenue Fr. D. Roosevelt (CP 194/02), 1050, Brussels, Belgium

    James N. Richardson, Philippe Bouillard & Rajan Filomeno Coelho

  2. MEMC - Mechanics of Materials and Construction, Faculty of Engineering Sciences, Vrije Universiteit Brussel, Pleinlaan 2, 1050, Brussels, Belgium

    Sigrid Adriaenssens

  3. Department of Civil and Environmental Engineering, Princeton University, Engineering Quadrangle E332, Princeton, NJ, USA

    Sigrid Adriaenssens

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  1. James N. Richardson
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  2. Sigrid Adriaenssens
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  4. Rajan Filomeno Coelho
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Correspondence to James N. Richardson.

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Richardson, J.N., Adriaenssens, S., Bouillard, P. et al. Multiobjective topology optimization of truss structures with kinematic stability repair. Struct Multidisc Optim 46, 513–532 (2012). https://doi.org/10.1007/s00158-012-0777-5

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  • DOI: https://doi.org/10.1007/s00158-012-0777-5

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