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Lightweight Designs and Improving the Load-Bearing Capacity of Structures by the Method of Aggregation

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  • Michael Todinov

    (School of Engineering, Computing and Mathematics, Oxford Brookes University, Oxford OX33 1HX, UK)

Abstract

The paper introduces a powerful method for developing lightweight designs and enhancing the load-bearing capacity of common structures. The method, referred to as the ‘method of aggregation’, has been derived from reverse engineering of sub-additive and super-additive algebraic inequalities. The essence of the proposed method is consolidating multiple elements loaded in bending into a reduced number of elements with larger cross sections but a smaller total volume of material. This procedure yields a huge reduction in material usage and is the first major contribution of the paper. For instance, when aggregating eight load-carrying beams into two beams supporting the same total load, the material reduction was more than 1.58 times. The second major contribution of the paper is in demonstrating that consolidating multiple elements loaded in bending into a reduced number of elements with larger cross sections but the same total volume of material leads to a big increase in the load-bearing capacity of the structure. For instance, when aggregating eight cantilevered or simply supported beams into two beams with the same volume of material, the load-bearing capacity until a specified tensile stress increased twice. At the same time, the load-bearing capacity until a specified deflection increased four times.

Suggested Citation

  • Michael Todinov, 2024. "Lightweight Designs and Improving the Load-Bearing Capacity of Structures by the Method of Aggregation," Mathematics, MDPI, vol. 12(10), pages 1-20, May.
  • Handle: RePEc:gam:jmathe:v:12:y:2024:i:10:p:1522-:d:1393928
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    References listed on IDEAS

    as
    1. Chanchal Kundu & Amit Ghosh, 2017. "Inequalities involving expectations of selected functions in reliability theory to characterize distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(17), pages 8468-8478, September.
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