BSU bulletin
Mathematics, Informatics
LoginРУСENG

BSU bulletin. Mathematics, Informatics

Bibliographic description:
Ausheev T. V.
,
Bulychev R. N.
MODELING OF PARAMETRIC RATIONAL BODIES USING GENERALIZED BEZIER INTERPOLATION // BSU bulletin. Mathematics, Informatics. - 2018. №1. . - С. 83-94.
Title:
MODELING OF PARAMETRIC RATIONAL BODIES USING GENERALIZED BEZIER INTERPOLATION
Financing:
Codes:
DOI: 10.18101/2304-5728-2018-1-83-94UDK: 004.925.8
Annotation:
The process of manufacturing parts by single point incremental forming (SPIF) of sheet blanks can be described by a multilayer structure. Therefore, the most promising method of modeling a multilayer structure is parametric solid modeling. Parametric bodies can model both a shape and an anisotropic interior space. The article deals with the problem of constructing the equation portion of body management using generalized interpolation of Bezier. We de- scribe three types of body portions, often used as initial and boundary condi- tions in numerical simulation. Several portions can be joined together to form a complex compound body. Use of Bezier rational function to describe the body provides additional benefits in the form of its management and internal spaces. The proposed system has been implemented in the program MathCAD. Com- putational experiments show, that it is easy to define and modify the shape and position of intermediate surfaces inside the body.
Keywords:
parametric bodies; generalized Bezier interpolation; incremental sheet forming; multilayer structure.
List of references:
Micari F., Ambrogio G., Filice L. Shape and Dimensionality in Single Point Incremental Forming: State of the Art and Future Trends. Journal of Ma- terials Processing Technology. 2007. V. 191 (1–3). Pp. 390–395.

Kochan A. Dieless Forming. Assembly Automation. 2001. V. 21. Pp. 321–322.

Guangcheng Z., Jinbo X., Xiaofan S., Xun Z., Chuankai L. Forming Process of Automotive Body Panel Based on Incremental Forming. Metallurgi- cal and Mining Industry. 2015. V. 1. I. 12. Pp. 350–357.

Kim T. J., Yang D. Y. Improvement of Formability for the Incremental Sheet Metal Forming Process. International Journal of Mechanical Sciences. 2000. V. 42. I. 7. Pp.1271–1286.

Lanouar B. A., Camille R., Arnaud D., Mohammed N. Simplified Nu- merical Approach for Incremental Sheet Metal Forming Process. Engineering Structures. 2014. V. 62–63. Pp. 75–86.

Ayusheev T. V. Metod postroeniya sploshnykh tel s primeneniem obob- shchennoi interpolyatsii Ermita [Method of Constructing Continuous Bodies Using the Generalized Hermite Interpolation]. Informatsionnye tekhnologii — Information Technologies. 2005. No. 6. Pp. 27–32.

Durikovic R., Czanner S. Modeling with Three Types of Coons Bodies // International Journal of Modeling & Simulation. 2004. V. 24. No. 2. Pp. 97– 101.

Golovanov N. N. Geometricheskoe modelirovanie [Geometric Modeling]. Moscow: Physical and Mathematical Literature Publ., 2002. 472 p.