Pub Date : 2019-01-01DOI: 10.26907/2541-7746.2019.2.165-180
A. Aganin, T. Guseva, L. A. Kosolapova, N. A. Khimatullina
{"title":"Dependence of Cavitation Bubble Impact onto a Body on Liquid Pressure","authors":"A. Aganin, T. Guseva, L. A. Kosolapova, N. A. Khimatullina","doi":"10.26907/2541-7746.2019.2.165-180","DOIUrl":"https://doi.org/10.26907/2541-7746.2019.2.165-180","url":null,"abstract":"","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"60 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81621999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.26907/2541-7746.2019.4.569-590
V. Paimushin, S. Kholmogorov, N. Polyakova, M. A. Shishov
Analytical solutions to the linearized problems on possible macroscale buckling modes of sandwich specimens made from fiber-reinforced plastics with lay-up sequence [0 ◦ ] s ( s is the number of laminas) under axial compression were analyzed. Materials characterized by a physically nonlinear dependence only between the transverse shear stresses and the corre-sponding shear strains were considered. Linearized equations of equilibrium in a perturbed state obtained on the basis of the previously constructed geometrically nonlinear equations of the theory of sandwich shells with a transversely flexible core were used. The linearized equations are based on the use of S.P. Timoshenko’s refined model for the facing layers, which takes into account the transverse compression, as well as on the use of three-dimensional equations of the theory of elasticity, which are simplified by the model of the transversely flexible layer, for the core. The latter allow integration over the thickness with the introduction of two un-known functions (transverse tangential stresses). In the linearized equations used, the physical nonlinearity of the material of the facing layers was taken into account in accordance with the Shanley concept based on the introduction of the tangential transverse shear modulus. In the equations used, there are degenerate terms that correspond to the implementation of purely transverse-shear buckling modes during compression of the specimen in the axial direction (along the fibers). The implementation of these buckling modes is possible for specimens with a considerable relative thickness of the layers package. Based on the analysis of the results obtained, it was shown that failure for these specimens is most likely due to the buckling in such a macroscale flexural-shear mode, which is predominantly transverse-shear and is real-ized when the compressive stress averaged over the thickness of the facing layers is equal to the shear modulus of the transverse shear of the composite in the vicinity of the end section of the working length of the specimen in its unperturbed state.
{"title":"Investigation of Buckling Modes of Sandwich Specimens with Facing Layers from [0°]s Fiber-Reinforced Plastic under Axial Compression","authors":"V. Paimushin, S. Kholmogorov, N. Polyakova, M. A. Shishov","doi":"10.26907/2541-7746.2019.4.569-590","DOIUrl":"https://doi.org/10.26907/2541-7746.2019.4.569-590","url":null,"abstract":"Analytical solutions to the linearized problems on possible macroscale buckling modes of sandwich specimens made from fiber-reinforced plastics with lay-up sequence [0 ◦ ] s ( s is the number of laminas) under axial compression were analyzed. Materials characterized by a physically nonlinear dependence only between the transverse shear stresses and the corre-sponding shear strains were considered. Linearized equations of equilibrium in a perturbed state obtained on the basis of the previously constructed geometrically nonlinear equations of the theory of sandwich shells with a transversely flexible core were used. The linearized equations are based on the use of S.P. Timoshenko’s refined model for the facing layers, which takes into account the transverse compression, as well as on the use of three-dimensional equations of the theory of elasticity, which are simplified by the model of the transversely flexible layer, for the core. The latter allow integration over the thickness with the introduction of two un-known functions (transverse tangential stresses). In the linearized equations used, the physical nonlinearity of the material of the facing layers was taken into account in accordance with the Shanley concept based on the introduction of the tangential transverse shear modulus. In the equations used, there are degenerate terms that correspond to the implementation of purely transverse-shear buckling modes during compression of the specimen in the axial direction (along the fibers). The implementation of these buckling modes is possible for specimens with a considerable relative thickness of the layers package. Based on the analysis of the results obtained, it was shown that failure for these specimens is most likely due to the buckling in such a macroscale flexural-shear mode, which is predominantly transverse-shear and is real-ized when the compressive stress averaged over the thickness of the facing layers is equal to the shear modulus of the transverse shear of the composite in the vicinity of the end section of the working length of the specimen in its unperturbed state.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83097238","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.26907/2541-7746.2019.2.181-190
M. N. Afanaseva, E. Kuznetsov
{"title":"The Numerical Solution of the Nonlinear Boundary Value Problem with Singularity for the System of Delay Integrodifferential-Algebraic Equations","authors":"M. N. Afanaseva, E. Kuznetsov","doi":"10.26907/2541-7746.2019.2.181-190","DOIUrl":"https://doi.org/10.26907/2541-7746.2019.2.181-190","url":null,"abstract":"","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"33 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85149809","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.26907/2541-7746.2019.2.292-300
V. Kugurakov, A. Gainutdinova, V. Dubrovin
{"title":"About Permutations on the Sets of Tuples from Elements of the Finite Field","authors":"V. Kugurakov, A. Gainutdinova, V. Dubrovin","doi":"10.26907/2541-7746.2019.2.292-300","DOIUrl":"https://doi.org/10.26907/2541-7746.2019.2.292-300","url":null,"abstract":"","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"26 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87829426","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.26907/2541-7746.2019.3.365-376
V. Levin, K. Zingerman, A. Vershinin, I. A. Podpruzhnikov
{"title":"An Approach to the Analysis of Propagation of Elastic Waves in Grids Made of Rods of Varying Curvature","authors":"V. Levin, K. Zingerman, A. Vershinin, I. A. Podpruzhnikov","doi":"10.26907/2541-7746.2019.3.365-376","DOIUrl":"https://doi.org/10.26907/2541-7746.2019.3.365-376","url":null,"abstract":"","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"16 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73729795","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.26907/2541-7746.2019.4.591-605
P. Troshin
This paper discusses a new algorithm for construction of regular tessellation of the Lobachevskii plane. The problems of combinatorial and topological arrangement of regular tessellations, finding the number of tiles in each layer of such tessellation, and implementation of the algorithm in the modern computer programming language were studied. The relevance of the study is determined, on the one hand, by the unceasing interest in hyperbolic geometry and, in particular, in tessellations within it. On the other hand, the relevance is due to the insufficient number of published algorithm descriptions and their implementations. The following methods were used: ● implementation of the basic knowledge in the group of motions of the Lobachevskii plane in the Beltrami–Klein model, its trigonometry and isometries to the other known models to construct a prototile and tessellation layers; ● splitting the tessellation by layers and layers by subclasses of tiles, studying the arrangement of each layer with respect to the previous one, finding the number of tiles in the layers with the help of mathematical induction; ● devising an algorithm in the form of a pseudocode and in the programming language of Wolfram Mathematica. In the course of the study, the following results were obtained: ● an algorithm for regular tessellation of the Lobachevskii plane, which produces the tessellation layer by layer, without repetition of the tiles, by means of proper rigid motions applied to the initial prototile; ● the algorithm implemented in the programming language of Wolfram Mathematica; ● formulas for estimation of the number of tiles in layers for the suggested algorithm. The obtained results and observations made in this paper are important for construction of tessellations in hyperbolic geometry.
{"title":"Regular Tessellation of the Lobachevskii Plane","authors":"P. Troshin","doi":"10.26907/2541-7746.2019.4.591-605","DOIUrl":"https://doi.org/10.26907/2541-7746.2019.4.591-605","url":null,"abstract":"This paper discusses a new algorithm for construction of regular tessellation of the Lobachevskii plane. The problems of combinatorial and topological arrangement of regular tessellations, finding the number of tiles in each layer of such tessellation, and implementation of the algorithm in the modern computer programming language were studied. The relevance of the study is determined, on the one hand, by the unceasing interest in hyperbolic geometry and, in particular, in tessellations within it. On the other hand, the relevance is due to the insufficient number of published algorithm descriptions and their implementations. The following methods were used: ● implementation of the basic knowledge in the group of motions of the Lobachevskii plane in the Beltrami–Klein model, its trigonometry and isometries to the other known models to construct a prototile and tessellation layers; ● splitting the tessellation by layers and layers by subclasses of tiles, studying the arrangement of each layer with respect to the previous one, finding the number of tiles in the layers with the help of mathematical induction; ● devising an algorithm in the form of a pseudocode and in the programming language of Wolfram Mathematica. In the course of the study, the following results were obtained: ● an algorithm for regular tessellation of the Lobachevskii plane, which produces the tessellation layer by layer, without repetition of the tiles, by means of proper rigid motions applied to the initial prototile; ● the algorithm implemented in the programming language of Wolfram Mathematica; ● formulas for estimation of the number of tiles in layers for the suggested algorithm. The obtained results and observations made in this paper are important for construction of tessellations in hyperbolic geometry.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"16 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83372548","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.26907/2541-7746.2019.1.66-74
F. M. Kadyrov, A. Kosterin, E. Skvortsov
The process of seepage consolidation of an elastic saturated body under the normal load that is instantly applied to its surface has been considered. An equality obtained using the con-ditions of compatibility of deformations has been added to the well-known spatial consolidation scheme. It has been shown that the sum of effective normal stresses satisfies the heat equation and can be found as a solution to the corresponding boundary value problem. A pressure-rela-ted auxiliary function that satisfies the Laplace equation has been introduced. The boundary condition for it is determined by the boundary condition for the above sum. The proposed scheme for studying the consolidation of an elastic body has been illustrated by the example of uniform normal loading on the surface of an elastic porous sphere. In the analytical form, the pressure of the fluid, the total and effective normal stresses of the skeleton, the displace-ment of points of the sphere and its surface in the process of consolidation have been found. It has been demonstrated that the pressure of the fluid at each fixed point inside the sphere decreases with increasing time.
{"title":"Seepage Consolidation during Elastic Body Deformation under Normal Load","authors":"F. M. Kadyrov, A. Kosterin, E. Skvortsov","doi":"10.26907/2541-7746.2019.1.66-74","DOIUrl":"https://doi.org/10.26907/2541-7746.2019.1.66-74","url":null,"abstract":"The process of seepage consolidation of an elastic saturated body under the normal load that is instantly applied to its surface has been considered. An equality obtained using the con-ditions of compatibility of deformations has been added to the well-known spatial consolidation scheme. It has been shown that the sum of effective normal stresses satisfies the heat equation and can be found as a solution to the corresponding boundary value problem. A pressure-rela-ted auxiliary function that satisfies the Laplace equation has been introduced. The boundary condition for it is determined by the boundary condition for the above sum. The proposed scheme for studying the consolidation of an elastic body has been illustrated by the example of uniform normal loading on the surface of an elastic porous sphere. In the analytical form, the pressure of the fluid, the total and effective normal stresses of the skeleton, the displace-ment of points of the sphere and its surface in the process of consolidation have been found. It has been demonstrated that the pressure of the fluid at each fixed point inside the sphere decreases with increasing time.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"31 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82168827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.26907/2541-7746.2019.4.526-535
A. Kazantsev
It was established that if the left-hand side of the Gakhov equation is bounded by the constant 2, then this equation has exactly one root in the unit disk, where the constant is sharp and the root is not necessarily zero. We revealed two aspects arising with regard to this connection. The first aspect concerns the pre-Schwarzian immersion of the Gakhov class into the space of bounded holomorphic functions. It was shown that the width of this immersion is equal to 2; the full description was done for the intersection of the boundary of the immersion with the ball of the radius 2 centered at the origin. The second aspect is connected with maintenance of the uniqueness of the root when the linear or fractional linear actions on the pre-Schwarzian with multiplying by the unit disk variable are bounded. Some uniqueness conditions were constructed in the form of S.N. Kudryashov’s univalence criteria.
{"title":"Root Uniqueness of the Gakhov Equation in the Classes of Functions with the Bounded Pre-Schwarzian","authors":"A. Kazantsev","doi":"10.26907/2541-7746.2019.4.526-535","DOIUrl":"https://doi.org/10.26907/2541-7746.2019.4.526-535","url":null,"abstract":"It was established that if the left-hand side of the Gakhov equation is bounded by the constant 2, then this equation has exactly one root in the unit disk, where the constant is sharp and the root is not necessarily zero. We revealed two aspects arising with regard to this connection. The first aspect concerns the pre-Schwarzian immersion of the Gakhov class into the space of bounded holomorphic functions. It was shown that the width of this immersion is equal to 2; the full description was done for the intersection of the boundary of the immersion with the ball of the radius 2 centered at the origin. The second aspect is connected with maintenance of the uniqueness of the root when the linear or fractional linear actions on the pre-Schwarzian with multiplying by the unit disk variable are bounded. Some uniqueness conditions were constructed in the form of S.N. Kudryashov’s univalence criteria.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"37 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73223564","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.26907/2541-7746.2019.3.341-354
Yu. V. Zuev
{"title":"About the Use of the Stokes Number for Mathematical Modeling of Two-Phase Jet Flows","authors":"Yu. V. Zuev","doi":"10.26907/2541-7746.2019.3.341-354","DOIUrl":"https://doi.org/10.26907/2541-7746.2019.3.341-354","url":null,"abstract":"","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"3 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77445580","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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