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Construction of a body with layered structure using Bézier boundary surfaces
Abstract.The object of the study is a numerical simulation of the process of incremental forming of sheet metal in the manufacture of thin-walled parts on equipment with numerical program control. Particular attention is paid to the problem of constructing the surface of deformation of a sheet blank, under the influence of a working tool.The subject of the study is the solution of the problem of constructing a smooth three-parameter body with a layered structure using Bézier boundary surfaces from given interpolation nodes. The body is built on a frame, consisting of a set of curvilinear octagonal portions, in which the opposite boundaries have different parametric lengths.The method of investigation is a method for constructing a three-parameter body with a layered structure using Bezier boundary surfaces using the technology of parametric solid modeling. The novelty of the study is to develop a method for constructing a smooth three-parameter body of a layered structure on an arbitrary frame in the form of Bézier.Main conclusions. The use of the cubic Bézier function with parameterization along the length of the arc for describing the body of a multilayer structure provides additional advantages in controlling the shape and internal space of the body than the construction constructed using the generalized Hermite interpolation.Parametric three-dimensional bodies of this type can be effectively used in finite elements with irregular boundaries to avoid difficulties in constructing a model for such structures.
Keywords: lamellar deformation, Bézier surface, Bézier curve, interpolation, lamellar body, body portion, three-parameter body, solid modeling, incremental forming, multilayer structure
Article was received:16-05-2018
This article written in Russian. You can find full text of article in Russian here .