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Author: search.filters.author.Pankratov, Alexander

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    Optimized Filling of a Given Cuboid with Spherical Powders for Additive Manufacturing
    (2020)
    Duriagina, Zoya
    ;
    Lemishka, Igor
    ;
    Litvinchev, Igor
    ;
    Durán Márquez, Mariana
    ;
    Pankratov, Alexander
    In additive manufacturing (also known as 3D printing), a layer-by-layer buildup process is used for manufacturing parts. Modern laser 3D printers can work with various materials including metal powders. In particular, mixing various-sized spherical powders of titanium alloys is considered most promising for the aerospace industry. To achieve desired mechanical properties of the final product, it is necessary to maintain a certain proportional ratio between different powder fractions. In this paper, a modeling approach for filling up a rectangular 3D volume by unequal spheres in a layer-by-layer manner is proposed. A relative number of spheres of a given radius (relative frequency) are known and have to be fulfilled in the final packing. A fast heuristic has been developed to solve this special packing problem. Numerical results are compared with experimental findings for titanium alloy spherical powders. The relative frequencies obtained by using the imposed algorithm are very close to those obtained by the experiment. This provides an opportunity for using a cheap numerical modeling instead of expensive experimental study. © Springer Nature
    Scopus© Citations 31  7  1
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    An Optimized Covering Spheroids by Spheres
    (2020)
    Pankratov, Alexander
    ;
    Romanova, Tatiana
    ;
    Litvinchev, Igor
    ;
    Serrano Bautista, Ramona
    Covering spheroids (ellipsoids of revolution) by different spheres is studied. The research is motivated by packing non-spherical particles arising in natural sciences, e.g., in powder technologies. The concept of an ε-cover is introduced as an outer multi-spherical approximation of the spheroid with the proximity ε. A fast heuristic algorithm is proposed to construct an optimized ε-cover giving a reasonable balance between the value of the proximity parameter ε and the number of spheres used. Computational results are provided to demonstrate the efficiency of the approach.
    Scopus© Citations 14  14  1