Development of a method for triangulation of inhomogeneous regions represented by functions

Abstract

<p>In the process of designing structures from inhomogeneous materials, there is the need to build discrete models that consider the peculiarities of the geometrical shape of subdomains from different materials. The first stage in the modeling of such structures is the construction of a geometric model. In order to describe the shapes of inhomogeneous structures, we have proposed a functional approach, based on the use of systems of implicit functions and R-functions. The first implicit function defines the shape of a structure. The implicit functions starting from a second one determine the shapes of the subdomains whose boundaries must be considered when building a discrete model. Each implicit function within the system exceeds zero at inner points of the respective domain or subdomain, is equal to zero at the border, and is less than zero at outer points. The result is a possibility to describe the shapes of domains and subdomains of arbitrary complexity.</p><p>We have constructed a method for the triangulation of structures from inhomogeneous materials, whose shape is assigned functionally. The devised method makes it possible to consider the shape of subdomains from different materials used in the structure. The basic idea of the method implies consistent correction of coordinates for the nodes from the primary triangulation of the domain. Primary triangulation can be arbitrary, but it must fully capture the structure. At each step, the boundary of the structure or a subdomain from a particular material is approached by the node closest to the respective boundary. Following the displacement of each node, the coordinates of neighboring nodes are computed by minimizing the functional of exponents in the planes of incident elements. At the same time, for the elements that are incident at nodes and whose coordinates were changed, meeting the Delaunay condition is checked; if necessary, the operation «flip» is performed to change the diagonal. Upon removing the outer nodes, one would obtain a discrete model in which the boundaries of the structure and subdomains from different materials are approximated by nodes and edges of elements.</p>

Authors and Affiliations

Serhii Choporov, Sergii Grebenyuk, Oleksii Kudin

Keywords

Related Articles

Synthesis of Ni(OH)2 by template homogeneous precipitation for application in the binder­free electrode of supercapacitor

Nickel hydroxide is widely used as the active material for hybrid supercapacitors. The most electrochemically active is α-Ni(OH)<sub>2</sub>, synthesized using template homogeneous precipitation. The disadvantage of temp...

Development of a method for the probabilistic inference of sequences of a business process activities to support the business process management

<p class="a"><span lang="EN-US">Models of temporal rules of execution of the business process actions were proposed for the use in absence in the process model of complete information on the reasons for execution of thes...

Development of an intelligent agent for analysis of nonfunctional characteristics in specifications of software requirements

<p>One of the urgent present-day tasks consists in ensuring an automated analysis of specifications of software requirements for sufficiency of information on nonfunctional component characteristics of software quality....

Studying the railroad track geometry deterioration as a result of an uneven subsidence of the ballast layer

<p>A method for calculating impairment of the track geometry under influence of dynamic loads in the course of passing the track unevenness by the rolling stock was developed. The method takes into consideration interrel...

Development of a technology for utilizing the electroplating wastes by applying a ferritization method to the alkaline­activated materials

The study reported in this paper reveals the effective way of recycling water treatment products by using them as a component of alkaline cements and concretes based on them. Large-scale utilization of products from wast...

Download PDF file
  • EP ID EP666832
  • DOI 10.15587/1729-4061.2019.174010
  • Views 91
  • Downloads 0

How To Cite

Serhii Choporov, Sergii Grebenyuk, Oleksii Kudin (2019). Development of a method for triangulation of inhomogeneous regions represented by functions. Восточно-Европейский журнал передовых технологий, 4(4), 21-27. https://europub.co.uk/articles/-A-666832