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Information × Registration Number 0221U107235, 0121U109846 , R & D reports Title Mathematical and computer modelling of optimization problems of packing geometric objects popup.stage_title Head Chugai Andrii M., Доктор технічних наук Registration Date 29-12-2021 Organization A. Podgorny Institute of Mechanical Engineering Problems of the National Academy of Sciences of Ukraine popup.description2  The object of research is the process of optimal layout of geometric objects taking into account technological limitations. The aim of the work is to increase the efficiency of solving problems of placement of two- and three-dimensional geometric objects on the basis of constructive means of mathematical and computer modeling, mathematical models, effective optimization methods and modern NLP-solvers (software for solving nonlinear programming problems ). Research methods - methods of geometric design, methods of analytical and computational geometry, the method of F-functions, methods of discrete and continuous nonlinear optimization, statistical probability methods, methods of theoretical mechanics, mathematical analysis. The following fundamental and applied tasks were solved during the research: - the problem of optimizing the topology of products in additive manufacturing due to the optimal placement of circular holes is considered. The task is reduced to packing a set of circles of variable radii, set within the limits set by 3D printing standards; a two-criteria formulation is proposed, which takes into account the packing factor and the maximum mechanical stress of the products; the method of the main criterion is used to find a compromise solution of the problem; a new approach based on the modified method of Apollonian packing of circles and nonlinear optimization is developed; - developed a methodology for the use of parallel computing technologies to solve problems of optimization of geometric design, which reduced the cost of time in solving problems of finding the optimal location of objects using modern NLP solvers; - the effective method of search of local extremums of problems of packing of three-dimensional geometrical objects is developed; - a study of the effectiveness of different approaches to solving different problems of packaging three-dimensional geometric objects; - the corresponding algorithmic and software is developed. Product Description popup.authors popup.nrat_date 2022-03-09 Close