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Numerical Verification of the Positive Gaussian Curvature Shell Topological Optimization Approach

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Smart Technologies in Urban Engineering (STUE 2023)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 807))

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Abstract

The article considers the approach of bionic-energetic optimization of structures using the example of topological optimization of the shell of positive Gaussian curvature. This method provides formation of uniformly strong structures with a stepped structure based on energy criteria. Using the finite element method and additional applications, a calculation model of the shell is developed and an algorithm for transforming the original structure into an isoenergetic one with positive parameters is given. A numerical experiment was conducted with the use of a spherical shell on a rectangular plan and the unification of the thicknesses of the finite elements by height in 10 different belts. Based on the results of the iterative process, the average shell thicknesses for each belt were obtained. At each step of the iteration, the magnitudes of strain energy, strain energy density, frequencies and periods of natural oscillations, as well as displacements and stresses were evaluated. It is noted that the attractor in this case was the increase of the strain energy value and the equalization of the isofields of strain energy density to obtain an equal strength element, which was followed already at the first steps of the iterative process. In addition, the controlled parameters, such as tension and displacement, did not exceed the limit values. According to the results of optimization, the starting thickness of the shell decreased by 2.5 times. The proposed method and algorithm of numerical calculation allows its use for a wide range of building structures, in particular, not only for shells of positive, but also arbitrary Gaussian curvature. Further research is aimed at refining the algorithms for calculating the structure according to this method.

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Authors and Affiliations

  1. O.M. Beketov National University of Urban Economy in Kharkiv, 17 Marshal Bazhanov Str., Kharkiv, 61002, Ukraine

    Olena Lugchenko, Petro Reznik, Olena Petrova & Vladyslav Tenesesku

Authors
  1. Olena Lugchenko
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  2. Petro Reznik
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  3. Olena Petrova
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  4. Vladyslav Tenesesku
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Corresponding author

Correspondence to Olena Petrova .

Editor information

Editors and Affiliations

  1. O.M. Beketov National University of Urban Economy in Kharkiv, Kharkiv, Ukraine

    Olga Arsenyeva

  2. A. Pidhornyi Institute of Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine

    Tetyana Romanova

  3. O.M. Beketov National University of Urban Economy in Kharkiv, Kharkiv, Ukraine

    Maria Sukhonos

  4. O.M. Beketov National University of Urban Economy in Kharkiv, Kharkiv, Ukraine

    Ihor Biletskyi

  5. O.M. Beketov National University of Urban Economy in Kharkiv, Kharkiv, Ukraine

    Yevgen Tsegelnyk

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© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

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Lugchenko, O., Reznik, P., Petrova, O., Tenesesku, V. (2023). Numerical Verification of the Positive Gaussian Curvature Shell Topological Optimization Approach. In: Arsenyeva, O., Romanova, T., Sukhonos, M., Biletskyi, I., Tsegelnyk, Y. (eds) Smart Technologies in Urban Engineering. STUE 2023. Lecture Notes in Networks and Systems, vol 807. Springer, Cham. https://doi.org/10.1007/978-3-031-46874-2_15

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