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A truly meshless approach to structural topology optimization based on the Direct Meshless Local Petrov–Galerkin (DMLPG) method

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Abstract

With a wide applicability in several types of engineering problems, topology optimization is one of the most interesting fields of structural optimization. Many meshless methods have been developed, however, they were less explored in topology optimization compared to other methods, as the Finite Element Method (FEM). The Direct Meshless Local Petrov–Galerkin (DMLPG) is characterized as a truly meshless method since it does not use a mesh at any stage of its development. It has been applied to solve many boundary value problems, achieving results with good precision and computational efficiency. Instead of performing the numerical integral of complicated shape functions, the DMLPG considers low-degree polynomials. The new topology optimization approach proposed in this work couples the DMLPG method with a Bi-Directional Evolutionary Structural Optimization (BESO) method. DMLPG is used to obtain smooth nodal displacements, strains, and stresses, and BESO updates the structural geometry based on design sensitivity values. Numerical examples performed were compared with the results obtained with FEM and with other works in the literature, showing the applicability and validity of the technique.

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Acknowledgements

The present research benefited from BESO MATLAB code made available by the researchers at the Centre for Innovative Structures and Materials. We would like to thank our colleagues from the Federal University of Ceará and from the State University of Piauí who provided insight and expertise.

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The authors did not receive funds, grants or other support from any organization for the submitted work.

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Authors and Affiliations

  1. Federal University of Ceará - Crateús Campus, Professora Machadinha Lima Avenue, Crateús, Ceará, 63708-825, Brazil

    Laise Sousa

  2. State University of Piauí, BR-343, Paraíso, Floriano, Piauí, 64800-000, Brazil

    Suzana Oliveira

  3. Department of Computing, Federal University of Ceará, Block 910 - Pici Campus, Fortaleza, Ceará, 60440-900, Brazil

    Creto Vidal & Joaquim Cavalcante-Neto

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  1. Laise Sousa
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Contributions

L.S, S.O. and C.V developed the theory. All authors conceived and planned the experiments. L.S and S.O. carried out the experiments. L.S and S.O. wrote the manuscript with support from C.V. C.V. and J.CN. supervised the project. All authors reviewed the manuscript.

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Correspondence to Laise Sousa.

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Sousa, L., Oliveira, S., Vidal, C. et al. A truly meshless approach to structural topology optimization based on the Direct Meshless Local Petrov–Galerkin (DMLPG) method. Struct Multidisc Optim 67, 110 (2024). https://doi.org/10.1007/s00158-024-03813-y

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