Continuous density-based topology optimization of cracked structures using peridynamics
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RESEARCH PAPER
Continuous density-based topology optimization of cracked structures using peridynamics A. Sohouli 1 & A. Kefal 2,3,4,5 & A. Abdelhamid 1 & M. Yildiz 2,3,4 & A. Suleman 1,6 Received: 10 June 2019 / Revised: 8 January 2020 / Accepted: 12 April 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Peridynamics (PD) is a meshless approach that addresses some of the difficulties and limitations associated with mesh-based topology optimization (TO) methods. This study investigates topology optimization of structures with and without embedded cracks using peridynamics (PD-TO). To this end, PD is coupled with two different continuous density-based topology optimization methods, namely the optimality criteria and the proportional optimization. The optimization results are compared for a continuous definition of the design variables, which are the relative densities defined for PD particles. The checkerboard issue has been removed using filtering schemes. The accuracy of the proposed PD-TO approach is validated by solving benchmark problems and comparing the optimal topologies with those obtained using a FEM-based topology optimization. Various problems are solved with and without defects (cracks) under different loading and constraint boundary conditions. Topology optimization for an unstructured discretization problem has also been investigated applied to a complex geometry. The optimal topology of a cracked structure may change for different optimization methods. The numerical results demonstrate the accuracy, high efficiency, and robustness of the PD-TO approach. Keywords Topology optimization . Peridynamics . Continuous density-based topology optimization . Cracked structures . Unstructured discretization
1 Introduction Responsible Editor: Hyunsun Alicia Kim Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00158-020-02608-1) contains supplementary material, which is available to authorized users. * A. Suleman [email protected] 1
Department of Mechanical Engineering, University of Victoria, Victoria, British Columbia, Canada
2
Faculty of Engineering and Natural Sciences, Sabanci University, Tuzla, 34956 Istanbul, Turkey
3
Integrated Manufacturing Technologies Research and Application Center, Sabanci University, Tuzla, 34956 Istanbul, Turkey
4
Composite Technologies Center of Excellence, Istanbul Technology Development Zone, Sabanci University-Kordsa, Pendik, 34906 Istanbul, Turkey
5
Faculty of Naval Architecture and Ocean Engineering, Istanbul Technical University, Maslak-Sariyer, 34469 Istanbul, Turkey
6
CCTAE-LAETA, Instituto Superior Tecnico, 1049-001 Lisbon, Portugal
Lightweight structures designed for high structural performance are commonly required in a wide range of engineering disciplines, particularly in automotive (Yang and Chahande 1995; Forsberg and Nilsson 2007; Cavazzuti et al. 2011) and aerospace (Inoyama et al. 2008; Zhu et al. 2016; Maute and Allen 2004) applications. Structural optimization methods, which ar
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