GEOMETRIC MODELING OF MULTI-FACTOR PROCESSES BASED ON VARIABLE POINT ALGORITHMS

2021 ◽  
pp. 29-38
Author(s):  
E. V. Konopatskiy ◽  
I. V. Seleznev ◽  
M. V. Lagunova ◽  
A. A. Bezditniy
Keyword(s):  
Geometric Modeling ◽  
Geometric Theory ◽  
Physical And Mechanical Properties ◽  
Multidimensional Space ◽  
Fine Grained ◽  
Variable Approach ◽  
Multidimensional Interpolation ◽  
Geometric Objects ◽  
Variable Point ◽  
Current Point

In this paper, the geometric theory of multidimensional interpolation was further developed. It has been established that the geometric models of multivariate processes obtained using multidimensional interpolation are characterized by variability, which is a consequence of the multiplicity of choice of reference lines in the process of developing a geometric modeling scheme. At the same time, all possible variations of geometric interpolants fully satisfy the initial experimental and statistical data, but have different curvature between the node points of the interpolation. As the dimension of the space increases, the number of variations increases significantly. The variable approach to geometric modeling of multifactorial processes generates a number of scientific problems that require further research, such as: comparison of geometric objects of multidimensional space, development of criteria for choosing the best solutions, construction of averaged geometric objects as one of the tools for optimizing the results of modeling, etc. The article also presents the results of a computational experiment on geometric modeling of the dependence of the physical and mechanical properties of fine-grained concrete on the composition of the combined aggregate based on variable point algorithms with the subsequent construction of an averaged response surface, the current point of which is the center of gravity of a multidimensional tetrahedron, for which the dimension of space depends on the amount possible interpolation options.

GEOMETRIC MODELING OF ADAPTIVE ALGEBRAIC CURVES PASSING THROUGH PREDETERMINED POINTS

2021 ◽  
pp. 26-34
Author(s):  
E. V. Konopatskiy ◽  
I. V. Seleznev ◽  
O. A. Chernysheva ◽  
M. V. Lagunova ◽  
A. A. Bezditnyi
Keyword(s):  
Initial Data ◽  
Geometric Modeling ◽  
Algebraic Curves ◽  
Geometric Theory ◽  
Multidimensional Space ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Multidimensional Interpolation ◽  
Geometric Objects ◽  
Parameter Values

In this paper, the geometric theory of multidimensional interpolation was further developed in terms of modeling and using adaptive curves passing through predetermined points. A feature of the proposed approach to modeling curved lines is the ability to adapt to any initial data for high-quality interpolation, which excludes unplanned oscillations, due to the uneven distribution of parameter values, the source of which are the initial data. This is the improvement of the previously proposed method for constructing and analytically describing arcs of algebraic curves passing through predetermined points, obtained on the basis of Bezier curves, which are compiled taking into account the expansion coefficients of the Newton binomial. The paper gives an example of using adaptive algebraic curves passing through predetermined points for geometric modeling of the stress-strain state of membrane coatings cylindrical shells using two-dimensional interpolation. The given example an illustrative showed the advantages of the proposed adaptation of algebraic curves passing through predetermined points and obtained on the basis of Bezier curves for geometric modeling of multifactor processes and phenomena. The use of such adaptation allows not only to avoid unplanned oscillations, but also self-intersection of geometric objects when generalized to a multidimensional space. Adaptive algebraic curves can also be effectively used as formative elements for constructing geometric objects of multidimensional space, both as guide lines and as generatrix’s.

scholarly journals An Approach to Comparing Multidimensional Geometric Objects

2021 ◽  
Author(s):  
Igor Seleznev ◽  
Evgeniy Konopatskiy ◽  
Olga Voronova ◽  
Oksana Shevchuk ◽  
Andrey Bezditnyi
Keyword(s):  
Mechanical Properties ◽  
Geometric Theory ◽  
Physical And Mechanical Properties ◽  
Coefficient Of Determination ◽  
Discrete Point ◽  
Point Sets ◽  
Geometric Models ◽  
Fine Grained ◽  
Multidimensional Interpolation ◽  
Geometric Objects

The paper proposes an approach to the comparison of multidimensional geometric objects, which is used to assess the variational geometric models of multifactor processes and phenomena obtained using the geometric theory of multidimensional interpolation. The proposed approach consists of two stages, the first of which consists in the discretization of multidimensional geometric objects in the form of a set of discretely given points, and the second is in comparing the obtained discrete point sets using a criterion that is essentially similar to the coefficient of determination. In this case, one of the discrete point sets is taken as a reference for comparison with another point set. For a correct comparison of multidimensional geometric models in the form of point equations, which are reduced to a system of parametric equations, it is necessary to perform interconnection of parameters. A computational experiment was carried out on the example of comparing geometric models of the physical and mechanical properties of fine-grained concrete. It showed the possibility of using the proposed approach for comparing multidimensional geometric objects and the reliability of the results obtained in comparison with scientific visualization methods. On the same example, it was found that for an accurate comparison of the investigated geometric models of the physical and mechanical properties of fine-grained concrete, it is enough to discretize 100 points. A further increase in the set of discrete points of the compared geometric objects has no significant effect on the criterion for assessing their similarity.

scholarly journals VARIATIVE GEOMETRIC ALGORITHMS FOR MODELING MULTIFACTOR PROCESSES

2021 ◽  
pp. 135-145
Author(s):  
I. V. Seleznev ◽  
E. V. Konopatskiy ◽  
O. S. Voronova
Keyword(s):  
Geometric Modeling ◽  
Process Model ◽  
Model Comparison ◽  
Response Surfaces ◽  
Geometric Algorithms ◽  
Computational Experiments ◽  
Geometric Models ◽  
Variable Approach ◽  
Multidimensional Interpolation

The work is investigated by the influence of variable geometric algorithms in modeling multifactor processes using multidimensional interpolation. Geometric models of multifactorial processes obtained using multidimensional interpolation inherent variability, which is a consequence of the multiplicity of the choice of reference lines during the development of geometric modeling schemes. At the same time, all possible variations of geometric interpolyns are fully satisfying the initial data. It has been established that the number of variations of geometric schemes directly depends on the number of current parameters and the dimension of the space in which the simulated geometrical object is located. Thus, a variable approach to geometrical modeling of multifactor processes generates a number of scientific tasks, the main one is the need to determine the effect of the variability of geometric algorithms on the final results of the computational experiment and, as a result, the choice of the best modeling results. To this end, the article presents the studies of variable geometric algorithms and computational experiments on the example of 2-parametric geometric interpolyns. A classification of 2-parametric geometric interpolytesses, which were conditionally divided into 3 types. Depending on the geometric scheme of constructing interpolynta, the square geometric scheme, a rectangular geometric scheme, a mixed geometric scheme. As a result of computational experiments, it was found that for a square geometric scheme, the variability does not affect the final results, in rectangular geometric schemes, the variability has a slight influence, and mixed geometric schemes may have significant differences and require additional research to select the highest quality geometric process model. Comparison of geometric models were performed by the methods of scientific visualization by overlaying the response surfaces on each other.

GEOMETRIC THEORY OF MULTIDIMENSIONAL INTERPOLATION

2020 ◽  
Vol 2020 (1) ◽  
pp. 9-16
Author(s):  
Evgeniy Konopatskiy
Keyword(s):  
Response Function ◽  
Algebraic Curves ◽  
Geometric Theory ◽  
Analytical Description ◽  
Geometric Interpretation ◽  
Affine Geometry ◽  
Mathematical Apparatus ◽  
Multidimensional Interpolation ◽  
Pass Through

The paper presents a geometric theory of multidimensional interpolation based on invariants of affine geometry. The analytical description of geometric interpolants is performed within the framework of the mathematical apparatus BN-calculation using algebraic curves that pass through preset points. A geometric interpretation of the interaction of parameters, factors, and the response function is presented, which makes it possible to generalize the geometric theory of multidimensional interpolation in the direction of increasing the dimension of space. The conceptual principles of forming the tree of the geometric interpolant model as a geometric basis for modeling multi-factor processes and phenomena are described.

Physical and Mechanical Properties of Fine-Grained Soil in the Zhejiang-Fujian Coastal Area, China

2011 ◽  
Vol 29 (4) ◽  
pp. 333-345 ◽  
Author(s):  
Yuan-Qin Xu ◽  
Pei-Ying Li ◽  
Ping Li ◽  
Le-Jun Liu ◽  
Cheng-Xiao Cao ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Coastal Area ◽  
Physical And Mechanical Properties ◽  
Fine Grained ◽  
Fine Grained Soil

scholarly journals Mechanical and physical properties of fine-grained concrete for concrete additive manufacturing

2019 ◽  
Vol 91 ◽  
pp. 02041
Author(s):  
Sergey Udodov ◽  
Yuriy Galkin ◽  
Philip Belov
Keyword(s):  
Mechanical Properties ◽  
Additive Manufacturing ◽  
3D Printing ◽  
Physical Properties ◽  
Crucial Role ◽  
Physical And Mechanical Properties ◽  
Concrete Composition ◽  
Fine Grained ◽  
Mechanical And Physical Properties ◽  
Time Periods

Additive manufacturing (3D printing) is becoming more and more common in the field of modern construction. However, for wider implementation of this technology, it is necessary to solve a number of material-oriented scientific problems related to development of concrete composition with targeted rheological, stress-strain, physical and mechanical properties. It has been established that time periods between successful applications of layers play the crucial role in ensuring monolithic features of the “printed” structures. Application of mathematics planning of the experiment allowed establishing the main principles of formation of basic physical and mechanical properties of fine-grained concrete depending on material composition.

Influence of Physical Properties of B4C Powder on the Strength Properties of the Ceramics Manufactured by SPS Sintering

2015 ◽  
Vol 1085 ◽  
pp. 312-315
Author(s):  
Oleg L. Khasanov ◽  
Edgar S. Dvilis ◽  
Zulfa G. Bikbaeva ◽  
Valentina V. Polisadova ◽  
Alexey O. Khasanov ◽  
...  
Keyword(s):  
Physical Properties ◽  
Boron Carbide ◽  
Physical And Mechanical Properties ◽  
High Strength ◽  
Strength Properties ◽  
Carbide Powder ◽  
Fine Grained ◽  
Fine Grained Structure ◽  
Determining Factor ◽  
Sps Sintering

Ceramics samples in the form of a parallelepiped with high strength characteristics have been made. For the manufacture of the ceramics samples a powder mixture from submicron В4С powder with additives (1 wt%, 5 wt%, 10 wt%) of boron carbide nanopowder was used. The physical properties of the powder mixtures and strength properties of sintered ceramics have been studied. It was shown that the use of submicron fractions of the boron carbide powder together with nanoadditives is a determining factor in the formation of dense fine-grained structure providing improved physical and mechanical properties of the ceramics.

The Comparison between Boron Carbide (B4C) with other Common Inhibitors on Physical and Mechanical Properties of WC/Co

2012 ◽  
Vol 05 ◽  
pp. 102-110 ◽  
Author(s):  
H. Tamizifar ◽  
A.M. Hadian ◽  
M. Tamizifar
Keyword(s):  
Boron Carbide ◽  
Vanadium Carbide ◽  
Sintering Temperature ◽  
Physical And Mechanical Properties ◽  
Growth Inhibitor ◽  
Hard Metal ◽  
Growth Inhibitors ◽  
Fine Grained ◽  
Hard Metals ◽  
Boron Carbide B4c

The hardness, toughness and sum of cracks measurement of fine-grained WC - Co hard metals were studied. Thirty commercial and experimental hard metal grades with different additives such as boron carbide ( B 4 C ), vanadium carbide ( VC ), chromium carbide ( Cr 3 C 2) and silicon carbide ( SiC ) were prepared in a commercial sinter HIP furnace. Physical, mechanical and microstructure properties were investigated to build up a representative hardness/sum of cracks measurement band. This band was then used to estimate the most effective sintering temperature and the amount of each additives. Afterwards, influence of grain growth inhibitors in optimum condition were compared. The results showed that the grades, doped with B 4 C and VC as growth inhibitor exhibits more hardness than other comparable doped alloys. However, Cr 3 C 2 is favorable in toughness improvement.

Technologies of Nanomodification of Low-Carbon Low Alloyed Steels

2010 ◽  
Vol 638-642 ◽  
pp. 3123-3127
Author(s):  
V.A. Malyshevsky ◽  
E.I. Khlusova ◽  
V.V. Orlov
Keyword(s):  
Large Scale ◽  
Physical And Mechanical Properties ◽  
Metallurgical Industry ◽  
Low Alloy Steels ◽  
Scale Production ◽  
Low Carbon ◽  
Fine Grained ◽  
Interphase Boundaries ◽  
Alloy Steels ◽  
High Level

Metallurgical industry can be considered as a field most accommodated for perception of nano-technologies, which in the near future will be able to provide large scale production and high level of investments return. Specially noted should physical and mechanical properties of nano-structured steels and alloys (strength, plasticity, toughness and so on) which will cardinally excel characteristics of respective materials developed using conventional technologies. Investigations have shown that basic principles of selection of a structure up to nano-level for low-carbon low-alloy steels can be put forward, that is: 1) morphological similarity of structural components, pre-domination of globular type structures due to reduction in carbon components and rational alloying; 2) formation of fine-dispersed carbide phase of globular morphology; 3) exclusion of lengthy interphase boundaries; 4) formation of fragmented structure with boundaries close to wide-angle ones, which inherited structure of fine-grained deformed austenite.

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