UDC 519.85

Modeling densely packed systems of three-dimensional objects

The paper represents the concept of Ф-functions and quasi Ф-functions as an efficient tool for mathematical modeling of three-dimensional packing problems for convex geometrical objects with continuous translations and rotations. A mathematical model of packing convex geometrical objects is formulated and its basic properties are considered. A method is proposed to solve it, which includes the following stages: construction of starting points, computation of local extrema, and a jump from one local minimum to another. The computating experiments have shown that the solution approach is efficient to solve optimization packing problems. Numerical examples are given. Fig.: 1. Refs: 15 titles.

Keywords:

packing, mathematical modeling, optimization, quasi Φ-function, convex three-dimensional objects, translation, rotation.


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About author(s):

Стоян Юрий Григорьевич, чл.-кор. НАН Украины, доктор техн. наук, профессор, заведующий отделом Института проблем машиностроения им. А.Н. Подгорного НАН Украины, Харьков,
e-mail: stoyan@ipmach.kharkov.ua

Сёмкин Владимир Владимирович, аспирант Института проблем машиностроения им. А.Н. Подгорного НАН Украины, Харьков,
e-mail: vl.semkin@gmail.com

Чугай Андрей Михайлович, кандидат техн. наук, старший начный сотрудник Института проблем машиностроения им. А.Н. Подгорного НАН Украины, Харьков,
e-mail: cam508@ukr.net