Semkin V. Packing of convex three-dimensional geometric objects with rotations into connected domains

The research subject is the optimisation process of packing of convex three-dimensional geometric objects. The goal is mathematical and computer modeling of optimisation process of packing of convex three-dimensional geometric objects that allow continuous translations and rotations. The research methods are a Ф-functions method for an analytical representation of geometric objects interaction conditions, methods of geometrical design and analytical geometry for construction of Ф-functions, nonlinear optimisation methods for solving a packing problem. The thesis is the further development of the geometrical design theory. Computer programs "3D layout optimization" and "Dense packing of 3D objects" are developed. Scientific novelty lies in the fact that new mathematical modeling tools of interaction of convex three-dimensional geometric objects that can be derived from a spherocone with account for their continuous translations and rotations as well as shortest distances are developed, namely normalized Ф-functions, quasi-Ф-functions and pseudonormalized quasi-Ф-functions; a mathematical model of a packing problem of the objects is constructed as a nonlinear programming problem, its solution strategy and methods are developed. The research results are planned to be introduced. Application branches are mechanical engineering, building industry, nanotechnologies.