Pub Date : 2023-05-03DOI: 10.37394/232011.2023.18.5
A. S. Sumbatov
For the Lagrange equations of the 2nd kind the problem of the existence of the conditionally linear in the velocities integral, which possesses the property that its total time derivative is identically proportional to the integral itself, is considered. The Lagrange function is assumed to be given in arbitrary generalized coordinates. The conditions for the existence of such integral are reduced to the study of the compatibility of two equations in partial derivatives of the 2nd order for one unknown function of two independent arguments. These equations are written in the invariant form in an arbitrary system of generalized coordinates and the problem is transformed into the investigation of the set of Pfaffian equations.
{"title":"On the Existence of the Conditionally Linear Integral in Conservative Holonomic Systems with Two Degrees of Freedom","authors":"A. S. Sumbatov","doi":"10.37394/232011.2023.18.5","DOIUrl":"https://doi.org/10.37394/232011.2023.18.5","url":null,"abstract":"For the Lagrange equations of the 2nd kind the problem of the existence of the conditionally linear in the velocities integral, which possesses the property that its total time derivative is identically proportional to the integral itself, is considered. The Lagrange function is assumed to be given in arbitrary generalized coordinates. The conditions for the existence of such integral are reduced to the study of the compatibility of two equations in partial derivatives of the 2nd order for one unknown function of two independent arguments. These equations are written in the invariant form in an arbitrary system of generalized coordinates and the problem is transformed into the investigation of the set of Pfaffian equations.","PeriodicalId":53603,"journal":{"name":"WSEAS Transactions on Applied and Theoretical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45146300","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 : 2023-04-04DOI: 10.37394/232011.2023.18.4
José Luís Miranda Dias
Buildings are subjected to deformations of their reinforced concrete structure due to vertical loads that can lead, in certain cases, to the significant cracking of the unreinforced masonry (URM) infill walls, therefore requiring the development of specific knowledge of these types of deformations in order to minimise them. Aiming the evaluation of buildings with reinforced concrete structures subjected to vertical deformations, the mechanical characteristics of their infill masonry walls, as well as of their interface with the supporting concrete elements, are here analysed. The basic compression behaviour of brick masonry is assessed particularly through the previous analysis of a vertical compression test of a masonry specimen. The mechanical behaviour characteristics of the constituents (bricks, and mortar joints) are analysed to account for their influence on the compression behaviour of masonry infill, aiming particularly for the prevision of their cracking in case of vertical deformations of the supporting reinforced concrete (RC) elements. Based on that evaluation, the analysis of masonry walls subjected to vertical deformations of their supports is made through the assessment of the relevant characteristic behaviour of masonry wall-beam/slab assembly in case of vertical load. A general modelling approach of the behaviour of URM infills and the interaction with their supports is generally accessed. Finally, the preventive control of deformations of masonry wall-beam/slab assembly is discussed.
{"title":"Damage of Infill Masonry Walls due to Vertical Loads in Buildings with Reinforced Concrete Structure","authors":"José Luís Miranda Dias","doi":"10.37394/232011.2023.18.4","DOIUrl":"https://doi.org/10.37394/232011.2023.18.4","url":null,"abstract":"Buildings are subjected to deformations of their reinforced concrete structure due to vertical loads that can lead, in certain cases, to the significant cracking of the unreinforced masonry (URM) infill walls, therefore requiring the development of specific knowledge of these types of deformations in order to minimise them. Aiming the evaluation of buildings with reinforced concrete structures subjected to vertical deformations, the mechanical characteristics of their infill masonry walls, as well as of their interface with the supporting concrete elements, are here analysed. The basic compression behaviour of brick masonry is assessed particularly through the previous analysis of a vertical compression test of a masonry specimen. The mechanical behaviour characteristics of the constituents (bricks, and mortar joints) are analysed to account for their influence on the compression behaviour of masonry infill, aiming particularly for the prevision of their cracking in case of vertical deformations of the supporting reinforced concrete (RC) elements. Based on that evaluation, the analysis of masonry walls subjected to vertical deformations of their supports is made through the assessment of the relevant characteristic behaviour of masonry wall-beam/slab assembly in case of vertical load. A general modelling approach of the behaviour of URM infills and the interaction with their supports is generally accessed. Finally, the preventive control of deformations of masonry wall-beam/slab assembly is discussed.","PeriodicalId":53603,"journal":{"name":"WSEAS Transactions on Applied and Theoretical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48809378","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 : 2023-03-20DOI: 10.37394/232011.2023.18.3
K. Giannakos
The Railway track, is simulated as a beam on elastic foundation with damping. The motion of a vehicle is simulated by the 2nd order differential equation of motion; the input to the system “vehicle-rail” is the form of the Track Geometry which “acts” as a “signal”. The defects with short and long wavelength influence the value of the dynamic component of the acting loads on the railway track and they are recorded in the frame of the Quality Control of the Railway Track, which presents a determined Confidence Interval depending on its “measurement-base”.
{"title":"Influence of Track Defects on the Track-Loads and Confidence Interval of a Track Recording Car","authors":"K. Giannakos","doi":"10.37394/232011.2023.18.3","DOIUrl":"https://doi.org/10.37394/232011.2023.18.3","url":null,"abstract":"The Railway track, is simulated as a beam on elastic foundation with damping. The motion of a vehicle is simulated by the 2nd order differential equation of motion; the input to the system “vehicle-rail” is the form of the Track Geometry which “acts” as a “signal”. The defects with short and long wavelength influence the value of the dynamic component of the acting loads on the railway track and they are recorded in the frame of the Quality Control of the Railway Track, which presents a determined Confidence Interval depending on its “measurement-base”.","PeriodicalId":53603,"journal":{"name":"WSEAS Transactions on Applied and Theoretical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46634179","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 : 2023-03-16DOI: 10.37394/232011.2023.18.2
W. A. Ahmood, Marwa Mohamed Ismaeel
In our work, we constructed a numerical approximations method to deal with approximations of a linear differential equation. We explained the general framework of the projection method which helps to clarify the basic ideas of the Kantorovich methods. We applied the iterative projection methods and presented a theorem to show the convergence of the constructed solutions to the exact solution. Also, most of the expressions encountered earlier can be used to define functions. Here are some illustrations. A great deal of information can be learned about a functioning relationship by studying its graph. A fundamental objective of section 4, is to acquaint with the graphs of some important functions and develop basic graphing procedures.
{"title":"An Approximation Solution of Linear Differential Equation using Kantorovich Methods","authors":"W. A. Ahmood, Marwa Mohamed Ismaeel","doi":"10.37394/232011.2023.18.2","DOIUrl":"https://doi.org/10.37394/232011.2023.18.2","url":null,"abstract":"In our work, we constructed a numerical approximations method to deal with approximations of a linear differential equation. We explained the general framework of the projection method which helps to clarify the basic ideas of the Kantorovich methods. We applied the iterative projection methods and presented a theorem to show the convergence of the constructed solutions to the exact solution. Also, most of the expressions encountered earlier can be used to define functions. Here are some illustrations. A great deal of information can be learned about a functioning relationship by studying its graph. A fundamental objective of section 4, is to acquaint with the graphs of some important functions and develop basic graphing procedures.","PeriodicalId":53603,"journal":{"name":"WSEAS Transactions on Applied and Theoretical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45706122","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 : 2023-01-30DOI: 10.37394/232011.2023.18.1
Larysa Shcherbyna, A. Bobrakov, Dmytro Saveliev, S. Braichenko, Oleksandr Nikolaievskyi
The goals of the study were the formation of a model of concentrated plasticity based on spherical graphite fibers. The goal was to present indicators of the cyclic behavior of structural elements due to the lack of consideration in modern scientific research of the issue of increasing the technical level and reliability of structures due to the addition of innovative materials during the development of structural elements. Taking into account the fundamental shortcomings in construction in the conditions of installing an excess amount of reinforcement, as one of the main mechanisms for achieving strength and reliability. The aim of the study was to develop a method of improving the quality of structural elements using innovative materials through building spring hinge models. The study involved the mathematical simulation, comparison, and system analysis. The result of the work is a developed spring hinge model for simulating reinforced concrete structural elements. The work emphasizes that the obtained experimental model converges to reference data and does not reflect a significant error with the increased number of cycles. It is emphasized that the model degrades with significant calibration, while the numerical strength and hysteresis behaviour matches the experimental data at higher deformation levels. The model of concentrated plasticity based on spherical graphite fibers was developed for the range of indicators of the cyclic behaviour of structural elements. The main characteristics of the reinforced concrete structural elements under consideration in the framework of the study are provided in a table in order to visually separate the groups of structures according to the main parameters. A non-linear model of a spring hinge is graphically shown, which shows the moment of movement of the spring when a monotonous load is applied. An urgent need to build a system of indicators of the structural elements’ cyclic behaviour was emphasized. A concentrated plasticity model based on spherical graphite fibers was built for this purpose. A beam-column was chosen as a reinforced concrete structure, which is based on a zero-length spring pivot hinge at the end of each individual element. This spring pivot hinge is a uniaxial material model with a moment-rotation dependency. Such a dependency is the fundamental basis of the spring hinge model used to simulate reinforced concrete structural elements. The comparison chart of reference and cyclic strength of a spherical graphite reinforced concrete beam is presented graphically. Prospects for further research involve the development of an empirical system of equations depending on the section geometry and the properties of the structure material based on prognostic variables from the list of potential variable characteristics.
{"title":"Development of Spring Hinge Models to Simulate Structural Elements of Spherical Graphite Reinforced Concrete","authors":"Larysa Shcherbyna, A. Bobrakov, Dmytro Saveliev, S. Braichenko, Oleksandr Nikolaievskyi","doi":"10.37394/232011.2023.18.1","DOIUrl":"https://doi.org/10.37394/232011.2023.18.1","url":null,"abstract":"The goals of the study were the formation of a model of concentrated plasticity based on spherical graphite fibers. The goal was to present indicators of the cyclic behavior of structural elements due to the lack of consideration in modern scientific research of the issue of increasing the technical level and reliability of structures due to the addition of innovative materials during the development of structural elements. Taking into account the fundamental shortcomings in construction in the conditions of installing an excess amount of reinforcement, as one of the main mechanisms for achieving strength and reliability. The aim of the study was to develop a method of improving the quality of structural elements using innovative materials through building spring hinge models. The study involved the mathematical simulation, comparison, and system analysis. The result of the work is a developed spring hinge model for simulating reinforced concrete structural elements. The work emphasizes that the obtained experimental model converges to reference data and does not reflect a significant error with the increased number of cycles. It is emphasized that the model degrades with significant calibration, while the numerical strength and hysteresis behaviour matches the experimental data at higher deformation levels. The model of concentrated plasticity based on spherical graphite fibers was developed for the range of indicators of the cyclic behaviour of structural elements. The main characteristics of the reinforced concrete structural elements under consideration in the framework of the study are provided in a table in order to visually separate the groups of structures according to the main parameters. A non-linear model of a spring hinge is graphically shown, which shows the moment of movement of the spring when a monotonous load is applied. An urgent need to build a system of indicators of the structural elements’ cyclic behaviour was emphasized. A concentrated plasticity model based on spherical graphite fibers was built for this purpose. A beam-column was chosen as a reinforced concrete structure, which is based on a zero-length spring pivot hinge at the end of each individual element. This spring pivot hinge is a uniaxial material model with a moment-rotation dependency. Such a dependency is the fundamental basis of the spring hinge model used to simulate reinforced concrete structural elements. The comparison chart of reference and cyclic strength of a spherical graphite reinforced concrete beam is presented graphically. Prospects for further research involve the development of an empirical system of equations depending on the section geometry and the properties of the structure material based on prognostic variables from the list of potential variable characteristics.","PeriodicalId":53603,"journal":{"name":"WSEAS Transactions on Applied and Theoretical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48302099","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}
We revisit the notion of discrete control by M. Asch considering the case where the control is discreet. This point of view leads to problems of controllability with or without constraints on the control. This article focuses on the case of hyperbolic equations although similar developments can be done for other PDE’s. The main tool used is the HUM method which is "adapted" to the constraints.
{"title":"A Revision of M. Asch Notion of Discrete Control","authors":"Benbrahim Abdelouahab, Rezzoug Imad, Necib Abdelhalim","doi":"10.37394/232011.2022.17.29","DOIUrl":"https://doi.org/10.37394/232011.2022.17.29","url":null,"abstract":"We revisit the notion of discrete control by M. Asch considering the case where the control is discreet. This point of view leads to problems of controllability with or without constraints on the control. This article focuses on the case of hyperbolic equations although similar developments can be done for other PDE’s. The main tool used is the HUM method which is \"adapted\" to the constraints.","PeriodicalId":53603,"journal":{"name":"WSEAS Transactions on Applied and Theoretical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45378479","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 : 2022-12-31DOI: 10.37394/232011.2022.17.27
E. E. El Bahloul, H. Aissaoui, M. Diany, E. Boudaia, S. Touairi
he variety of applications, in all industrial fields, whether for routine use or a specific application, requires the design of increasingly efficient sealing systems. O-rings are fundamental elements in many industrial devices and machines, thanks to advantages such as low cost, small size, cleanliness, and ease of assembly. Moreover, the O-ring is available in thousands of dimensions. In this work, the analysis of the mechanical and leakage behavior of the O-ring seal, when installed either in a groove or between two plates, is presented. The behavior of the assemblies in both scenarios when the clamping force and fluid pressure are applied is investigated using two numerical models generated with Ansys software. The numerical model findings are compared to the analytical approach based on Hertz contact theory and other researchers' experimental results. This study shows that the use of a groove to ensure the mounting of elastomeric O-rings is important in pressurized installations. Furthermore, for different pressure conditions, the reliability of the O-ring strongly depends on three parameters: compression ratio of the seal, the hardness of the seal, and the friction coefficient.
{"title":"Finite Element Analysis of the O-ring Behavior Under Uniform Squeeze Levels and Internal Pressure","authors":"E. E. El Bahloul, H. Aissaoui, M. Diany, E. Boudaia, S. Touairi","doi":"10.37394/232011.2022.17.27","DOIUrl":"https://doi.org/10.37394/232011.2022.17.27","url":null,"abstract":"he variety of applications, in all industrial fields, whether for routine use or a specific application, requires the design of increasingly efficient sealing systems. O-rings are fundamental elements in many industrial devices and machines, thanks to advantages such as low cost, small size, cleanliness, and ease of assembly. Moreover, the O-ring is available in thousands of dimensions. In this work, the analysis of the mechanical and leakage behavior of the O-ring seal, when installed either in a groove or between two plates, is presented. The behavior of the assemblies in both scenarios when the clamping force and fluid pressure are applied is investigated using two numerical models generated with Ansys software. The numerical model findings are compared to the analytical approach based on Hertz contact theory and other researchers' experimental results. This study shows that the use of a groove to ensure the mounting of elastomeric O-rings is important in pressurized installations. Furthermore, for different pressure conditions, the reliability of the O-ring strongly depends on three parameters: compression ratio of the seal, the hardness of the seal, and the friction coefficient.","PeriodicalId":53603,"journal":{"name":"WSEAS Transactions on Applied and Theoretical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45647450","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 : 2022-12-31DOI: 10.37394/232011.2022.17.28
E. Karash
The financial and societal consequences of the sudden failure of various mechanical structures and components can occasionally be severe. As a result, there has been extensive research done on fatigue failure in both the scientific and industrial fields. The impact of stress ratio adjustments on the rates of fatigue fracture propagation for an aluminum alloy has been investigated in the current study. This aluminum alloy was extracted from a Russian MI25 helicopter's primary blade. The stress intensity factor was calculated and employed by creating an initial crack in the test specimens after a specimen of MI25 blade was cut into testing specimens with standard dimensions. A special program was written specifically for this purpose to draw a graph of the stress intensity factor range (k) with value of the propagation of fatigue cracks (da / dN) at each stress ratio (R); Propagation of fatigue cracks has been studied. Finally, the relationship between the two different stress ratios has been discovered. Between the two, a comparison has been established. The findings indicated that when the stress ratio rises, so too does the rate at which fatigue cracks form. Conversely, with a negative stress ratio, the negative increase leads to a reduction in the rate at which fatigue cracks grow. The data have been examined, and during the second stage of crack propagation, where (R = 0.0), pertinent equations that are compatible with the Paris equation have been discovered.
{"title":"The Effect of Stress Ratio on Fatigue Cracks Growth Rate in Aluminum Alloy","authors":"E. Karash","doi":"10.37394/232011.2022.17.28","DOIUrl":"https://doi.org/10.37394/232011.2022.17.28","url":null,"abstract":"The financial and societal consequences of the sudden failure of various mechanical structures and components can occasionally be severe. As a result, there has been extensive research done on fatigue failure in both the scientific and industrial fields. The impact of stress ratio adjustments on the rates of fatigue fracture propagation for an aluminum alloy has been investigated in the current study. This aluminum alloy was extracted from a Russian MI25 helicopter's primary blade. The stress intensity factor was calculated and employed by creating an initial crack in the test specimens after a specimen of MI25 blade was cut into testing specimens with standard dimensions. A special program was written specifically for this purpose to draw a graph of the stress intensity factor range (k) with value of the propagation of fatigue cracks (da / dN) at each stress ratio (R); Propagation of fatigue cracks has been studied. Finally, the relationship between the two different stress ratios has been discovered. Between the two, a comparison has been established. The findings indicated that when the stress ratio rises, so too does the rate at which fatigue cracks form. Conversely, with a negative stress ratio, the negative increase leads to a reduction in the rate at which fatigue cracks grow. The data have been examined, and during the second stage of crack propagation, where (R = 0.0), pertinent equations that are compatible with the Paris equation have been discovered.","PeriodicalId":53603,"journal":{"name":"WSEAS Transactions on Applied and Theoretical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43018187","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 : 2022-12-31DOI: 10.37394/232011.2022.17.32
E. Kormaníková, K. Kotrasová
Sandwich panel with laminate faces is used for free vibration analysis. The periodic microstructure and Mori- Tanaka model are used for homogenization of unidirectional fiber reinforced composite. The Shear Deformation Theory is considered for analytical and numerical analysis. FEM in ANSYS is used for numerical analysis. The effect of sandwich design parameters such as panel length, core thickness and fiber reinforced angle on vibration response is investigated. Natural frequencies of sandwich panel versus sandwich design parameters are presented in graphical form. From the results can be concluded that sandwich design parameters affect the natural frequencies of sandwich panels, and this effect is important for designing of sandwich panels under dynamic load.
{"title":"Dynamic Behavior of Composite Sandwich Panel with CFRP Outer Layers","authors":"E. Kormaníková, K. Kotrasová","doi":"10.37394/232011.2022.17.32","DOIUrl":"https://doi.org/10.37394/232011.2022.17.32","url":null,"abstract":"Sandwich panel with laminate faces is used for free vibration analysis. The periodic microstructure and Mori- Tanaka model are used for homogenization of unidirectional fiber reinforced composite. The Shear Deformation Theory is considered for analytical and numerical analysis. FEM in ANSYS is used for numerical analysis. The effect of sandwich design parameters such as panel length, core thickness and fiber reinforced angle on vibration response is investigated. Natural frequencies of sandwich panel versus sandwich design parameters are presented in graphical form. From the results can be concluded that sandwich design parameters affect the natural frequencies of sandwich panels, and this effect is important for designing of sandwich panels under dynamic load.","PeriodicalId":53603,"journal":{"name":"WSEAS Transactions on Applied and Theoretical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44936696","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 : 2022-12-31DOI: 10.37394/232011.2022.17.31
I. Burova, G. O. Alcybeev
Splines are an important mathematical tool in Applied and Theoretical Mechanics. Several Problems in Mechanics are modeled with Differential Equations the solution of which demands Finite Elements and Splines. In this paper, we consider the construction of computational schemes for the numerical solution of integral equations of the second kind with a weak singularity. To construct the numerical schemes, local polynomial quadratic spline approximations and second-order nonpolynomial spline approximations are used. The results of the numerical experiments are given. This methodology has many applications in problems in Applied and Theoretical Mechanics
{"title":"Solution of Integral Equations Using Local Splines of the Second Order","authors":"I. Burova, G. O. Alcybeev","doi":"10.37394/232011.2022.17.31","DOIUrl":"https://doi.org/10.37394/232011.2022.17.31","url":null,"abstract":"Splines are an important mathematical tool in Applied and Theoretical Mechanics. Several Problems in Mechanics are modeled with Differential Equations the solution of which demands Finite Elements and Splines. In this paper, we consider the construction of computational schemes for the numerical solution of integral equations of the second kind with a weak singularity. To construct the numerical schemes, local polynomial quadratic spline approximations and second-order nonpolynomial spline approximations are used. The results of the numerical experiments are given. This methodology has many applications in problems in Applied and Theoretical Mechanics","PeriodicalId":53603,"journal":{"name":"WSEAS Transactions on Applied and Theoretical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45006379","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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