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Volume 57 >>> № 4 JULY — AUGUST 2021
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UDC 519.85
Y.G. Stoyan1, T.E. Romanova2, O.V. Pankratov3, P.I. Stetsyuk4, Y.E. Stoian5


1 A. Pidgorny Institute of Mechanical Engineering Problems,
National Academy of Sciences of Ukraine, Kharkiv, Ukraine

 yustoyan19@gmail.com

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

 tarom27@yahoo.com

3 A. Pidgorny Institute of Mechanical Engineering Problems,
National Academy of Sciences of Ukraine, Kharkiv, Ukraine

 pankratov2001@yahoo.com

4 V.M. Glushkov Institute of Cybernetics, National Academy
of Sciences of Ukraine, Kyiv, Ukraine

 stetsyukp@gmail.com

5 A. Pidgorny Institute of Mechanical Engineering Problems,
National Academy of Sciences of Ukraine, Kharkiv, Ukraine

 urikpostg@gmail.com

SPARSE BALANCED DISTRIBUTION OF SPHERICAL VOIDS
IN THREE-DIMENSIONAL DOMAINS

Abstract. The paper considers the optimization problem of generating spherical voids in three-dimensional domains bounded by cylindrical and spherical surfaces and planes. The problem is reduced to the problem of arranging spherical objects in a composite container, taking into account constraints on “sparseness” of the objects and balancing conditions (a location of the gravity center of the system). A mathematical model in the form of a nonlinear programming problem is provided. A fast method of finding allowable solutions based on the balanced homothetic transformations of 3D objects and methods of finding locally optimal solutions using the decomposition algorithm and r -algorithm are proposed. The results of numerical experiments are given.

Keywords: sparse layout, spherical objects, phi-function, nonlinear programming, r -algorithm.



FULL TEXT

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