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A coupled meshless element-free Galerkin and radial basis functions method for level set-based topology optimization

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Abstract

This paper presents a meshless element-free Galerkin method coupled with the radial basis functions (RBFs)-based level set algorithm for topology optimization. The meshless approach provides the structural response and corresponding sensitivities at nodal/grid points, and the solution of RBFs-based level set formulation updates the structural geometry accordingly. Thus, this unique and novel approach allows solution of the optimization problems using a single discretization scheme for both the meshless and the level set methods. A special technique is proposed for the identification of meshless nodal points within the solid and void regions of the structural geometry. The present method handles the appropriate topological modifications, i.e. hole creation, splitting, merging, etc., affectively. Optimal solutions of the benchmark problems suggest reliability and compatibility of the proposed approach versus the mesh-based techniques available within the structural optimization literature.

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Acknowledgements

The data that support the findings of this study are available from the authors, upon reasonable request. Finally, the authors confirm that there are no relevant financial or non-financial competing interests to report.

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Authors and Affiliations

  1. Department of Basic Sciences, Faculty of Architecture, Allied Sciences and Humanities, University of Engineering and Technology, Peshawar, Pakistan

    Baseer Ullah, Wajid Khan &  Siraj-ul-Islam

  2. Advanced Composites Research Group, School of Mechanical and Aerospace Engineering, Queen’s University, Belfast, Ashby Building, Belfast, BT9 5AH, UK

    Zahur Ullah

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Ullah, B., Khan, W., Siraj-ul-Islam et al. A coupled meshless element-free Galerkin and radial basis functions method for level set-based topology optimization. J Braz. Soc. Mech. Sci. Eng. 44, 89 (2022). https://doi.org/10.1007/s40430-022-03382-5

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