Development of a method for triangulation of inhomogeneous regions represented by functions
Journal Title: Восточно-Европейский журнал передовых технологий - Year 2019, Vol 4, Issue 4
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
- EP ID EP666832
- DOI 10.15587/1729-4061.2019.174010
- Views 69
- Downloads 0
Using Markov chains for predicting collective motivation of students.
Predicting students' motivation hot topic for research in higher education. In previous work had created a comprehensive model for evaluating students' motivation. As part of the floor is the algorithm of the forecast av...
Influence of the thermal factor on the composition of electronbeam highentropy ALTiVCrNbMo coatings
<p>This paper reports results of studying the element and phase compositions of electron-beam coatings based on the high-entropy alloy AlTiVCrNbMo, depending on the deposition temperature (in the range of 300...700 °С).<...
Algorithmic tools for optimizing the temperature regime of evaporator at absorption-refrigeration units of ammonia production
<p>We analyzed evaporators at absorption-refrigeration plants in a secondary condensation unit of ammonia production as control objects. Coordinates of the vectors of state, control and external perturbations were determ...
Improvement of the structure of floating docks based on the study into the stresseddeformed state of pontoon
<p>We have investigated the stressed-deformed state of reinforced concrete slabs of the composite dock pontoon with a reduced number of framing sets. A refined estimation scheme was applied in the calculation of bending...
Development of portable dc voltage calibrators with additive offsets adjusting
<p>Improvement of portable equipment for controlling the DC voltage measuring channels of cyber-physical systems at the operating sites is proposed. Additive offsets and drifts make a dominant contribution to the error o...