Pub Date : 2019-01-01DOI: 10.26907/2541-7746.2019.1.145-151
R. Salimov, I. Volodin, N. F. Nasibullina
In this paper, we continue our research on evaluation of the mean value of the normal distribution with prior information that this parameter is positive and very small. These data are obtained by using a prior exponential distribution with a large intensity parameter. The estimation problem with guaranteed relative error is considered. This issue is more important when small fractions are estimated. In addition to restrictions on the relative error, the procedure must have a given level of d -risk. We suggest a sequential procedure based on the first achieve-ment by posterior probability of estimate reliability of a given level 1 − β . The procedure is adapted to the problem of estimating harmful impurities in food products.
{"title":"Sequential d-guaranteed estimate of the normal mean with bounded relative error","authors":"R. Salimov, I. Volodin, N. F. Nasibullina","doi":"10.26907/2541-7746.2019.1.145-151","DOIUrl":"https://doi.org/10.26907/2541-7746.2019.1.145-151","url":null,"abstract":"In this paper, we continue our research on evaluation of the mean value of the normal distribution with prior information that this parameter is positive and very small. These data are obtained by using a prior exponential distribution with a large intensity parameter. The estimation problem with guaranteed relative error is considered. This issue is more important when small fractions are estimated. In addition to restrictions on the relative error, the procedure must have a given level of d -risk. We suggest a sequential procedure based on the first achieve-ment by posterior probability of estimate reliability of a given level 1 − β . The procedure is adapted to the problem of estimating harmful impurities in food products.","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":"91353650","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: 10.26907/2541-7746.2019.2.230-249
A. Semenov, S. Leonov
{"title":"The Continuous Method of Solution Continuation with Respect to the Best Parameter in the Calculation of Shell Structures","authors":"A. Semenov, S. Leonov","doi":"10.26907/2541-7746.2019.2.230-249","DOIUrl":"https://doi.org/10.26907/2541-7746.2019.2.230-249","url":null,"abstract":"","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"17 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83520794","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: 10.26907/2541-7746.2019.2.191-204
V. Levin, K. M. Zingerman, K. Krapivin, O. Ryabova, A. V. Kukushkin, Moscow Russia Fidesys Llc
A mathematical model of material microstructure formation in the process of selective laser sintering was proposed. The model is based on the stress and strain analysis in a represen-tative volume of a powder that contains some particles. The strains and stresses are caused by contact interaction of particles due to surface tension. It was assumed that the particles are made of elastoplastic material. The material properties were described by the associative Drucker–Prager model with hardening. The nonlinear effects caused by large strains were taken into account. The model permits one to determine the shape of particles in the de-formed state and the shape of pores. The numerical results were presented for the problem of contact interaction between two particles that assume the spherical shape before deformation. The displacements of centers of powder particles were specified as input. The finite-element method was used for computations. The flow rule was integrated using the implicit Euler backward method. The mortar method was used to solve the problem with account of contact interaction. The distribution of contact stresses over the surfaces of powder particles and the distribution of the von Mises plastic strains in the section of these particles were shown as a result of the analysis. The dependence of contact zone radius on the contact displacements of the particles’ centers was investigated. It was analyzed how the radius of contact zone depends on the material parameter characterizing the pressure dependence of plastic flow.
{"title":"A Model of Material Microstructure Formation on Selective Laser Sintering with Allowance for Large Elastoplastic Strains","authors":"V. Levin, K. M. Zingerman, K. Krapivin, O. Ryabova, A. V. Kukushkin, Moscow Russia Fidesys Llc","doi":"10.26907/2541-7746.2019.2.191-204","DOIUrl":"https://doi.org/10.26907/2541-7746.2019.2.191-204","url":null,"abstract":"A mathematical model of material microstructure formation in the process of selective laser sintering was proposed. The model is based on the stress and strain analysis in a represen-tative volume of a powder that contains some particles. The strains and stresses are caused by contact interaction of particles due to surface tension. It was assumed that the particles are made of elastoplastic material. The material properties were described by the associative Drucker–Prager model with hardening. The nonlinear effects caused by large strains were taken into account. The model permits one to determine the shape of particles in the de-formed state and the shape of pores. The numerical results were presented for the problem of contact interaction between two particles that assume the spherical shape before deformation. The displacements of centers of powder particles were specified as input. The finite-element method was used for computations. The flow rule was integrated using the implicit Euler backward method. The mortar method was used to solve the problem with account of contact interaction. The distribution of contact stresses over the surfaces of powder particles and the distribution of the von Mises plastic strains in the section of these particles were shown as a result of the analysis. The dependence of contact zone radius on the contact displacements of the particles’ centers was investigated. It was analyzed how the radius of contact zone depends on the material parameter characterizing the pressure dependence of plastic flow.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"19 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83601555","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: 10.26907/2541-7746.2019.2.250-262
R. Enikeev
{"title":"Real Number Approximation by a Rational Number in the Approximating k-ary Algorithm","authors":"R. Enikeev","doi":"10.26907/2541-7746.2019.2.250-262","DOIUrl":"https://doi.org/10.26907/2541-7746.2019.2.250-262","url":null,"abstract":"","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"21 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78892926","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: 10.26907/2541-7746.2019.3.377-392
I. Tsygvintsev, A. Y. Krukovskiy, Yu.A. Poveshchenk, V. Gasilov, D. S. Boykov, S. B. Popov
{"title":"Homogeneous Difference Schemes for the Coupled Problems of Hydrodynamics and Elasticity","authors":"I. Tsygvintsev, A. Y. Krukovskiy, Yu.A. Poveshchenk, V. Gasilov, D. S. Boykov, S. B. Popov","doi":"10.26907/2541-7746.2019.3.377-392","DOIUrl":"https://doi.org/10.26907/2541-7746.2019.3.377-392","url":null,"abstract":"","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"126 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74487792","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: 10.26907/2541-7746.2019.4.552-568
M. Pavlova, E. Rung
In this paper, we proved the generalized solvability of a problem describing the process of unsteady saturated-unsaturated fluid filtration in a porous medium with the condition of uni-lateral permeability to parts of the boundary. It should be noted that the variational inequality that arises in this case is a variational inequality of a variable type: in the saturated filtration zone – elliptical and parabolic – otherwise. In the generalized formulation of the problem under consideration, a classical transition based on the Kirchhoff transform to an equivalent variational problem that is more convenient for research was used. In this paper, we considered the most interesting case, from the point of applications, when the Kirchhoff transform maps the real axis into a semi-axis bounded below: [ − γ, + ∞ ) . It is assumed that the value of the Kirchhoff transform at a point − γ is zero. Along with the original problem with re-striction, we considered the so-called “predefined problem” without restrictions u ( x, t ) ≥ − γ , the solution of which on the set ( −∞ , − γ ) is assumed to be zero. Definitions of generalized solutions to these problems in the form of variational inequalities were given. The proof of the existence theorem for a generalized solution of the “predefined problem” was carried out using the methods of half-sampling and penalty. In conclusion, it was proved that the solution to the “predetermined problem” is the solution to the original one.
{"title":"On the Solvability of a Variational Inequality in the Filtration Theory","authors":"M. Pavlova, E. Rung","doi":"10.26907/2541-7746.2019.4.552-568","DOIUrl":"https://doi.org/10.26907/2541-7746.2019.4.552-568","url":null,"abstract":"In this paper, we proved the generalized solvability of a problem describing the process of unsteady saturated-unsaturated fluid filtration in a porous medium with the condition of uni-lateral permeability to parts of the boundary. It should be noted that the variational inequality that arises in this case is a variational inequality of a variable type: in the saturated filtration zone – elliptical and parabolic – otherwise. In the generalized formulation of the problem under consideration, a classical transition based on the Kirchhoff transform to an equivalent variational problem that is more convenient for research was used. In this paper, we considered the most interesting case, from the point of applications, when the Kirchhoff transform maps the real axis into a semi-axis bounded below: [ − γ, + ∞ ) . It is assumed that the value of the Kirchhoff transform at a point − γ is zero. Along with the original problem with re-striction, we considered the so-called “predefined problem” without restrictions u ( x, t ) ≥ − γ , the solution of which on the set ( −∞ , − γ ) is assumed to be zero. Definitions of generalized solutions to these problems in the form of variational inequalities were given. The proof of the existence theorem for a generalized solution of the “predefined problem” was carried out using the methods of half-sampling and penalty. In conclusion, it was proved that the solution to the “predetermined problem” is the solution to the original one.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"89 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74869203","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: 10.26907/2541-7746.2019.2.263-273
I. Zabotin, K. Kazaeva
{"title":"A Version of the Penalty Method with Approximationof the Epigraphs of Auxiliary Functions","authors":"I. Zabotin, K. Kazaeva","doi":"10.26907/2541-7746.2019.2.263-273","DOIUrl":"https://doi.org/10.26907/2541-7746.2019.2.263-273","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":"73198951","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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