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Journal: Academic Journal "Industrial Machine Building, Civil Engineering" (Vol.3, No. 45)

Publication Date:

Authors : ; ;

Page : 28-39

Keywords : discrete modeling; discrete analogs; recurrent formulas; numerical sequences; functional load; geometrical apparatus of superpositions.;

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Designing the systems of automated engineering and preproduction is impossible without mathematical modeling of facilities and production processes. Except mathematical description geometric modeling gives a visual representation of the object or process. One of the most complex processes of geometrical modeling is the design and restoration of surfaces with complex forms that must meet a number of specified criteria. Modeling of such surfaces is an up-to-date problem in many construction and engineering industries such as aircraft building, machine building, hydraulic machinery construction and shipbuilding. Discrete representation of any engineering object or process has significant advantages over the continuous one. It is the only possible representation in some practical problems. As a kind of mathematical modeling, discrete geometric modeling sets the same goals and objectives. It is based on mathematical methods and uses mathematical symbols. However, the geometrical model always has a property of visualization and could be reflected graphically. The classical method of finite differences, static-geometrical method, mathematical apparatus of numerical sequences and geometrical apparatus of superpositions give different representations of the same mathematical apparatus. Each of the methods has its advantages and disadvantages to solve specific problems. The geometrical apparatus of superpositions allows to obtain formulas linking values of finite series of constant terms sequences from initial data (coordinates of nonadjacent terms of given sequences). It is possible due to the variation of coefficient values of superposition and the choice of the distribution function of the external load. Thus it significantly saves computational resource. Control the form of discrete represented curve (DRC) in the static-geometrical method can be carried out not only with varying of functional external load, but also with coefficients in computing stencil which are the basis for making up the finite-difference equations of forming the DRC and show an partial participation of adjacent nodes in the formation of required result. The article determines the influence of superposition coefficients as adjacent as arbitrary nodes of numerical sequences on the formation of discrete analogues of polynomial functional dependencies. This article does research to determine the discrete analogues of geometrical images of designing objects in the form of one-dimensional numerical sequences including functional load from initial data based on geometrical apparatus of superpositions. The discrete analogs of polynomial functional dependencies formed with superpositions of point sets including external load. have been studied.

Last modified: 2016-07-25 19:41:22