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An extension of the natural force density method to 3D problems

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Abstract

This paper introduces the 3DNFDM method, which extends the natural force density method (NFDM) to three-dimensional problems. The NFDM was first proposed by Pauletti in 2006, as a method for finding configurations of membranes and funicular shell structures, providing viable equilibrium geometries in a single linear equilibrium analysis (Pauletti, in: Proceedings of the IASS symposium/APCS conference—New Olympics, New Shell and Spacial Structures, Beijing, 2006; Pauletti and Pimenta Comput Methods Appl Mech Eng 197(49):4419–4428, 2008. https://doi.org/10.1016/j.cma.2008.05.017). It is an extension of the force density method (FDM), which was originally proposed by Linkwitz (IASS Pacific symposium on tension structures and space frame, Tokyo, pp 145–158, 1971), Linkwitz and Schek (Ingenieur-Archiv, 40:145–158, 1971. https://doi.org/10.1007/BF005321463) for the shape finding of cable nets and has since become ubiquitous in the field of membrane design. Directly treating the continuous membrane problem, the NFDM overcomes limitations of the original FDM, by dealing with irregular meshes and accurately representing continuous surface stress fields. The 3DNFDM represents a further extension of the FDM to three-dimensional problems, which allows for the exploration of a novel class of shape finding problems, generating relevant viable volumetric shapes. Some of these shapes may not be readily interpreted by common sense, but we believe that the 3DNFDM unveils new possibilities for shape finding, as demonstrated by the elementary problems investigated in this foundational paper.

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Funding

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) – Finance Code 001.

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Authors and Affiliations

  1. Department of Structural and Geotechnical Engineering, Polytechnic School at the University of Sāo Paulo, Av. Prof. Almeida Prado - Trav. 2, 83, Sāo Paulo, 05508-070, Brazil

    Ruy Marcelo O. Pauletti

  2. College of Civil Engineering, University of Campinas, Campinas, Brazil

    Vinicius F. Arcaro

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  1. Ruy Marcelo O. Pauletti
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  2. Vinicius F. Arcaro
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Contributions

RMOP conceived and implemented the new method (3DNFDM), based on his previous research on the NFDM, generated the presented data and wrote the manuscript. VFA reviewed the formulation and developed an independent computer implementation, also based on his own independent research on shape finding problems, which validated the consistency of the new method.

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Correspondence to Ruy Marcelo O. Pauletti.

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Pauletti, R.M.O., Arcaro, V.F. An extension of the natural force density method to 3D problems. Arch Appl Mech (2024). https://doi.org/10.1007/s00419-024-02580-y

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