Pub Date : 2022-03-30DOI: 10.18287/2541-7525-2021-27-2-80-90
A. Perevaryukha
Our ongoing research is devoted to various aspects of predicting invasive processes in unstable biosystems. Extreme events are interesting for modeling. The purpose of this work is to describe in a computational experiment a scenario of active counteraction, which temporarily suppresses the development of an aggressive invasive process. The impact in a situation of slow regulation begins to affect not the small initial group N(0) L of individuals of the invading species, but only when the critical population threshold is reached. Relevance let us consider in the model a scenario that can be interpreted as an artificially created resistance in case of delayed immune activation. In most cases, after invasion, the presence of the species remains, but below its biological optimum. Method a modification of the equation with two delays is used. Novelty a model has been obtained where it is possible to overcome the crisis or the death of the population, depending on the time of activation of the impact. The oscillatory scenario is not observed in the model. The equation with a threshold reaction assumes further expansion and use in the composition of multicomponent polymodel complexes.
{"title":"SCENARIOS MODEL OF THE EFFECT OF A TEMPORARY SHARP REDUCTION OF POPULATION WITH A LARGE REPRODUCTIVE PARAMETER","authors":"A. Perevaryukha","doi":"10.18287/2541-7525-2021-27-2-80-90","DOIUrl":"https://doi.org/10.18287/2541-7525-2021-27-2-80-90","url":null,"abstract":"Our ongoing research is devoted to various aspects of predicting invasive processes in unstable biosystems. Extreme events are interesting for modeling. The purpose of this work is to describe in a computational experiment a scenario of active counteraction, which temporarily suppresses the development of an aggressive invasive process. The impact in a situation of slow regulation begins to affect not the small initial group N(0) L of individuals of the invading species, but only when the critical population threshold is reached. Relevance let us consider in the model a scenario that can be interpreted as an artificially created resistance in case of delayed immune activation. In most cases, after invasion, the presence of the species remains, but below its biological optimum. Method a modification of the equation with two delays is used. Novelty a model has been obtained where it is possible to overcome the crisis or the death of the population, depending on the time of activation of the impact. The oscillatory scenario is not observed in the model. The equation with a threshold reaction assumes further expansion and use in the composition of multicomponent polymodel complexes.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122330750","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 : 2021-11-29DOI: 10.18287/2541-7525-2021-27-1-15-28
V. Dmitriev
The aim of this paper is to study the solvability of solution of non-local problem with integral condition in spatial variables for high-order linear equation in the classe of regular solutions (which have all the squaredderivatives generalized by S.L. Sobolev that are included in the corresponding equation). It is indicated that at first similar problems were studied for high-order equations either in the one-dimensional case, or under certain conditions of smallness by the value of T. A list of new works for the multidimensional case is also given. In this paper, we present new results on the solvability of non-local problem with integral spatial variables for high-order equation a) in the multidimensional case with respect to spatial variables; b) in the absence of smallness conditions by the value T; however, this condition exists for the kernel K(x; y; t). The research method is based on obtaining a priori estimates of the solution of the problem, which implies its existence and uniqueness in a given space.
{"title":"BOUNDARY VALUE PROBLEM WITH A NONLOCAL BOUNDARY CONDITION OF INTEGRAL FORM FOR A MULTIDIMENSIONAL EQUATION OF IV ORDER","authors":"V. Dmitriev","doi":"10.18287/2541-7525-2021-27-1-15-28","DOIUrl":"https://doi.org/10.18287/2541-7525-2021-27-1-15-28","url":null,"abstract":"The aim of this paper is to study the solvability of solution of non-local problem with integral condition in spatial variables for high-order linear equation in the classe of regular solutions (which have all the squaredderivatives generalized by S.L. Sobolev that are included in the corresponding equation). It is indicated that at first similar problems were studied for high-order equations either in the one-dimensional case, or under certain conditions of smallness by the value of T. A list of new works for the multidimensional case is also given. In this paper, we present new results on the solvability of non-local problem with integral spatial variables for high-order equation a) in the multidimensional case with respect to spatial variables; b) in the absence of smallness conditions by the value T; however, this condition exists for the kernel K(x; y; t). The research method is based on obtaining a priori estimates of the solution of the problem, which implies its existence and uniqueness in a given space.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114046492","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 : 2021-11-29DOI: 10.18287/2541-7525-2021-27-1-62-73
S. M. Ratseev, O. Cherevatenko, V. A. Chernyavskaya
In 1978 McEliece built the first public key cryptosystem based on error-correcting codes. At the same time, effective attacks on the secret keys of this cryptosystem have not yet been found. The work describes the classical and modernized cryptosystems of McEliece and Niederreiter, also examples of their practical application based on Goppa codes using the Patterson algorithm. Also the algorithms of two-step authentication protocols with zero disclosure based on error-correcting codes are given.
{"title":"ON SOME CRYPTOSYSTEMS BASED ON ALGEBRAIC CODES","authors":"S. M. Ratseev, O. Cherevatenko, V. A. Chernyavskaya","doi":"10.18287/2541-7525-2021-27-1-62-73","DOIUrl":"https://doi.org/10.18287/2541-7525-2021-27-1-62-73","url":null,"abstract":"In 1978 McEliece built the first public key cryptosystem based on error-correcting codes. At the same time, effective attacks on the secret keys of this cryptosystem have not yet been found. The work describes the classical and modernized cryptosystems of McEliece and Niederreiter, also examples of their practical application based on Goppa codes using the Patterson algorithm. Also the algorithms of two-step authentication protocols with zero disclosure based on error-correcting codes are given.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"146 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114951595","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 : 2021-11-29DOI: 10.18287/2541-7525-2021-27-1-74-80
Maxim V. Shamolin
Proposed work is the sixth work of the cycle on differential and topological diagnostics. It is shown that the diagnostics in the case of trajectorial measurements corrupted by noise, which is a stochastic process of the normal white noise type with zero mean value and bounded spectrum, can be performed by using the diagnostic algorithms obtained in [5], i.e., the results of this section remain valid even in this rather general case; moreover, the diagnostic functional, which was introduced in the theorem of [5] a priori, is now obtained a posteriori.
{"title":"PROBLEMS OF DIFFERENTIAL AND TOPOLOGICAL DIAGNOSTICS. PART 6. STATISTICAL SOLVING OF THE PROBLEM OF DIFFERENTIAL DIAGNOSTICS","authors":"Maxim V. Shamolin","doi":"10.18287/2541-7525-2021-27-1-74-80","DOIUrl":"https://doi.org/10.18287/2541-7525-2021-27-1-74-80","url":null,"abstract":"Proposed work is the sixth work of the cycle on differential and topological diagnostics. It is shown that the diagnostics in the case of trajectorial measurements corrupted by noise, which is a stochastic process of the normal white noise type with zero mean value and bounded spectrum, can be performed by using the diagnostic algorithms obtained in [5], i.e., the results of this section remain valid even in this rather general case; moreover, the diagnostic functional, which was introduced in the theorem of [5] a priori, is now obtained a posteriori.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130011065","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 : 2021-11-29DOI: 10.18287/2541-7525-2021-27-1-7-14
A. V. Bogatov
In this paper, we study the problem with a dynamic nonlocal condition for the one-dimensional hyperbolic equation, which occurs in the study of rod vibrations. This problem may be used as a mathematical model oflongitudinal vibration in a thick short bar and illustrates a nonlocal approach to such processes. Conditions have been obtained for input data, providing unambiguous resolution of the task, proof of the existence and singularity of the problem in the space of Sobolev. The proof is based on the a priori estimates obtained in this paper, Galerkins procedure and the properties of the Sobolev spaces.
{"title":"A PROBLEM WITH NONLOCAL CONDITION FOR ONE-DIMENSIONAL HYPERBOLIC EQUATION","authors":"A. V. Bogatov","doi":"10.18287/2541-7525-2021-27-1-7-14","DOIUrl":"https://doi.org/10.18287/2541-7525-2021-27-1-7-14","url":null,"abstract":"In this paper, we study the problem with a dynamic nonlocal condition for the one-dimensional hyperbolic equation, which occurs in the study of rod vibrations. This problem may be used as a mathematical model oflongitudinal vibration in a thick short bar and illustrates a nonlocal approach to such processes. Conditions have been obtained for input data, providing unambiguous resolution of the task, proof of the existence and singularity of the problem in the space of Sobolev. The proof is based on the a priori estimates obtained in this paper, Galerkins procedure and the properties of the Sobolev spaces.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127438313","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 : 2021-11-29DOI: 10.18287/2541-7525-2021-27-1-29-43
E. Providas, L. S. Pulkina, I. Parasidis
The solvability condition and the unique exact solution by the universal factorization (decomposition) method for a class of the abstract operator equations of the type B1u = Au S(A0u) GF(Au) = f, u D(B1),where A,A0 are linear abstract operators, G, S are linear vectors and , F are linear functional vectors is investigagted. This class is useful for solving Boundary Value Problems (BVPs) with Integro-Differential Equations (IDEs), where A,A0 are differential operators and F(Au), (A0u) are Fredholm integrals. It was shown that the operators of the type B1 can be factorized in the some cases in the product of two moresimple operators BG, BG0 of special form, which are derived analytically. Further the solvability condition and the unique exact solution for B1u = f easily follow from the solvability condition and the unique exact solutions for the equations BGv = f and BG0u = v.
研究了一类B1u = Au S(A0u) GF(Au) = f, u D(B1)型抽象算子方程的可解性条件和唯一精确解，其中a,A0为线性抽象算子，G, S为线性泛函向量，f为线性泛函向量。该类对于求解积分-微分方程边值问题(bvp)非常有用，其中A,A0为微分算子，F(Au)， (A0u)为Fredholm积分。证明了B1型算子在某些情况下可以分解为两个更简单的特殊形式的算子BG, BG0的乘积，并给出了它们的解析表达式。进一步，由方程BGv = f和bgu = v的可解条件和精确唯一解可以很容易地推导出B1u = f的可解条件和精确唯一解。
{"title":"FACTORIZATION OF ORDINARY AND HYPERBOLIC INTEGRO-DIFFERENTIAL EQUATIONS WITH INTEGRAL BOUNDARY CONDITIONS IN A BANACH SPACE","authors":"E. Providas, L. S. Pulkina, I. Parasidis","doi":"10.18287/2541-7525-2021-27-1-29-43","DOIUrl":"https://doi.org/10.18287/2541-7525-2021-27-1-29-43","url":null,"abstract":"The solvability condition and the unique exact solution by the universal factorization (decomposition) method for a class of the abstract operator equations of the type B1u = Au S(A0u) GF(Au) = f, u D(B1),where A,A0 are linear abstract operators, G, S are linear vectors and , F are linear functional vectors is investigagted. This class is useful for solving Boundary Value Problems (BVPs) with Integro-Differential Equations (IDEs), where A,A0 are differential operators and F(Au), (A0u) are Fredholm integrals. It was shown that the operators of the type B1 can be factorized in the some cases in the product of two moresimple operators BG, BG0 of special form, which are derived analytically. Further the solvability condition and the unique exact solution for B1u = f easily follow from the solvability condition and the unique exact solutions for the equations BGv = f and BG0u = v.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126434341","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 : 2021-11-29DOI: 10.18287/2541-7525-2021-27-1-104-110
A. Kuznetsova, V. Saleev
The article discusses the production of prompt isolated photons with large transverse momenta at the LHC at energies s = 8 and 13 TeV in the parton Reggeization approach, which is based on the factorizationtheorem for hard processes at high energies and the effective theory of Reggeized gluons and quarks by L.N. Lipatov. Unintegrated parton distributions in the parton Reggeization approach were obtained in the modified KimberMartinRyskin model proposed earlier by the authors of the article. In numerical calculations, only the contribution of the main parton process, R +Q( Q) + q(q), is taken into account,since the contribution of other processes does not exceed 510 %. The calculation results are compared with the predictions obtained in the collinear parton model. Good agreement of calculations in the partonReggeization approach with experimental data obtained by the ATLAS collaboration is shown.
{"title":"PRODUCTION OF ISOLATED PHOTONS WITH LARGE TRANSVERSE MOMENTA AT LHC IN THE REGGE LIMIT OF QCD","authors":"A. Kuznetsova, V. Saleev","doi":"10.18287/2541-7525-2021-27-1-104-110","DOIUrl":"https://doi.org/10.18287/2541-7525-2021-27-1-104-110","url":null,"abstract":"The article discusses the production of prompt isolated photons with large transverse momenta at the LHC at energies s = 8 and 13 TeV in the parton Reggeization approach, which is based on the factorizationtheorem for hard processes at high energies and the effective theory of Reggeized gluons and quarks by L.N. Lipatov. Unintegrated parton distributions in the parton Reggeization approach were obtained in the modified KimberMartinRyskin model proposed earlier by the authors of the article. In numerical calculations, only the contribution of the main parton process, R +Q( Q) + q(q), is taken into account,since the contribution of other processes does not exceed 510 %. The calculation results are compared with the predictions obtained in the collinear parton model. Good agreement of calculations in the partonReggeization approach with experimental data obtained by the ATLAS collaboration is shown.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129947247","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 : 2021-11-29DOI: 10.18287/2541-7525-2021-27-1-44-61
S. Ratseev, A. D. Lavrinenko, E. A. Stepanova
The paper is devoted to the Berlekamp Masssey algorithm and its equivalent version based on the extended Euclidean algorithm. An optimized Berlekamp Massey algorithm is also given for the case ofa field of characteristic 2. The Berlekamp Massey algorithm has a quadratic complexity and is used, for example, to solve systems of linear equations in which the matrix of the system is the Toeplitz matrix. In particular, such systems of equations appear in algorithms for the syndrome decoding of BCH codes, Reed Solomon codes, generalized Reed Solomon codes, and Goppa codes. Algorithms for decoding the listed codes based on the Berlekamp Massey algorithm are given.
{"title":"ON THE BERLEKAMP — MASSEY ALGORITHM AND ITS APPLICATION FOR DECODING ALGORITHMS","authors":"S. Ratseev, A. D. Lavrinenko, E. A. Stepanova","doi":"10.18287/2541-7525-2021-27-1-44-61","DOIUrl":"https://doi.org/10.18287/2541-7525-2021-27-1-44-61","url":null,"abstract":"The paper is devoted to the Berlekamp Masssey algorithm and its equivalent version based on the extended Euclidean algorithm. An optimized Berlekamp Massey algorithm is also given for the case ofa field of characteristic 2. The Berlekamp Massey algorithm has a quadratic complexity and is used, for example, to solve systems of linear equations in which the matrix of the system is the Toeplitz matrix. In particular, such systems of equations appear in algorithms for the syndrome decoding of BCH codes, Reed Solomon codes, generalized Reed Solomon codes, and Goppa codes. Algorithms for decoding the listed codes based on the Berlekamp Massey algorithm are given.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130334773","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 : 2021-11-29DOI: 10.18287/2541-7525-2021-27-1-81-103
S. Lychev, K. Koifman, A. V. Digilov
The present paper develops a general approach to deriving nonlinear equations of motion for solids whose material points possess additional degrees of freedom. The essential characteristic of this approach is theaccount of incompatible deformations that may occur in the body due to distributed defects or in the result of the some kind of process like growth or remodelling. The mathematical formalism is based on least action principle and Noether symmetries. The peculiarity of such formalism is in formal description of reference shape of the body, which in the case of incompatible deformations has to be regarded either as a continual family of shapes or some shape embedded into non-Euclidean space. Although the general approach yields equations for Cosserat-type solids, micromorphic bodies and shells, the latter differ significantly in the formal description of enhanced geometric structures upon which the action integral has to be defined. Detailed discussion of this disparity is given.
{"title":"NONLINEAR DYNAMIC EQUATIONS FOR ELASTIC MICROMORPHIC SOLIDS AND SHELLS. PART I","authors":"S. Lychev, K. Koifman, A. V. Digilov","doi":"10.18287/2541-7525-2021-27-1-81-103","DOIUrl":"https://doi.org/10.18287/2541-7525-2021-27-1-81-103","url":null,"abstract":"The present paper develops a general approach to deriving nonlinear equations of motion for solids whose material points possess additional degrees of freedom. The essential characteristic of this approach is theaccount of incompatible deformations that may occur in the body due to distributed defects or in the result of the some kind of process like growth or remodelling. The mathematical formalism is based on least action principle and Noether symmetries. The peculiarity of such formalism is in formal description of reference shape of the body, which in the case of incompatible deformations has to be regarded either as a continual family of shapes or some shape embedded into non-Euclidean space. Although the general approach yields equations for Cosserat-type solids, micromorphic bodies and shells, the latter differ significantly in the formal description of enhanced geometric structures upon which the action integral has to be defined. Detailed discussion of this disparity is given.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121655439","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 : 2021-08-17DOI: 10.18287/2541-7525-2020-26-4-56-67
L. Stepanova, K. N. Aldebeneva
In this work, digital photoelasticity method is applied for assessment of the crack tip linear fracture mechanics parameters for a plate with double edge notches and different other crack configurations. The overarching objective of the study is to obtain the coefficients of the Williams series expansion for the stress and displacement fields in the vicinity of the crack tip by the digital photoelasticity technique for the double edge notched plate. The digital image processing tool for experimental data obtained from the photoelasticity experiments is developed and utilized. The digital image processing tool is based on the Ramesh approach but allows us to scan the image in any direction and to analyse the image after any number of logical operations. In the digital image processing isochromatic fringe analysis, the optical data contained in the transmission photoelastic isochromatics were converted into text file and then the points of isochromatic fringes with minimum light intensity were used for evaluating fracture mechanics parameters. The multi-parameter stress field approximation is used. The mixed mode fracture parameters, especially stress intensity factors (SIF) are estimated for specimen configurations like double edge notches and inclined center crack using the proposed algorithm based on the classical over-deterministic method. The effects of higher-order terms in the Williams expansion were analysed for different cracked specimens. It is shown that the higher order terms are needed for accurate characterization of the stress field in the vicinity of the crack tip. The experimental SIF values estimated using the proposed method are compared with analytical / finite element analysis (FEA) results, and are found to be in good agreement.
{"title":"Photoelastic study of a double edge notched plate for determination of the Williams series expansion","authors":"L. Stepanova, K. N. Aldebeneva","doi":"10.18287/2541-7525-2020-26-4-56-67","DOIUrl":"https://doi.org/10.18287/2541-7525-2020-26-4-56-67","url":null,"abstract":"In this work, digital photoelasticity method is applied for assessment of the crack tip linear fracture mechanics parameters for a plate with double edge notches and different other crack configurations. The overarching objective of the study is to obtain the coefficients of the Williams series expansion for the stress and displacement fields in the vicinity of the crack tip by the digital photoelasticity technique for the double edge notched plate. The digital image processing tool for experimental data obtained from the photoelasticity experiments is developed and utilized. The digital image processing tool is based on the Ramesh approach but allows us to scan the image in any direction and to analyse the image after any number of logical operations. In the digital image processing isochromatic fringe analysis, the optical data contained in the transmission photoelastic isochromatics were converted into text file and then the points of isochromatic fringes with minimum light intensity were used for evaluating fracture mechanics parameters. The multi-parameter stress field approximation is used. The mixed mode fracture parameters, especially stress intensity factors (SIF) are estimated for specimen configurations like double edge notches and inclined center crack using the proposed algorithm based on the classical over-deterministic method. The effects of higher-order terms in the Williams expansion were analysed for different cracked specimens. It is shown that the higher order terms are needed for accurate characterization of the stress field in the vicinity of the crack tip. The experimental SIF values estimated using the proposed method are compared with analytical / finite element analysis (FEA) results, and are found to be in good agreement.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"532 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133355351","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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