Pub Date : 2024-08-21DOI: 10.1134/S0021894424010073
L. R. Gareev, O. O. Ivanov, V. V. Vedeneev, D. A. Ashurov
This paper touches upon the effect of an amplitude of a deflector introduced into a laminar jet flow on the linear change coefficient of the radial component of a stationary perturbation. Methods for introducing and measuring the perturbations are described. It is shown that a decrease in the deflector amplitude has no effect on the flow pattern, cannot prevent an algebraic growth mechanism, and causes a proportional decrease in the radial component of the stationary velocity perturbation. Turbulence is established after reaching some radial expansion value that is independent of the initial perturbation amplitude.
{"title":"EFFECT OF THE AMPLITUDE OF A STATIONARY PERTURBATION ON ITS NON-MODAL GROWTH IN A LAMINAR SUBMERGED JET","authors":"L. R. Gareev, O. O. Ivanov, V. V. Vedeneev, D. A. Ashurov","doi":"10.1134/S0021894424010073","DOIUrl":"10.1134/S0021894424010073","url":null,"abstract":"<p>This paper touches upon the effect of an amplitude of a deflector introduced into a laminar jet flow on the linear change coefficient of the radial component of a stationary perturbation. Methods for introducing and measuring the perturbations are described. It is shown that a decrease in the deflector amplitude has no effect on the flow pattern, cannot prevent an algebraic growth mechanism, and causes a proportional decrease in the radial component of the stationary velocity perturbation. Turbulence is established after reaching some radial expansion value that is independent of the initial perturbation amplitude.</p>","PeriodicalId":608,"journal":{"name":"Journal of Applied Mechanics and Technical Physics","volume":"65 1","pages":"61 - 65"},"PeriodicalIF":0.5,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142200218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-21DOI: 10.1134/S0021894424010140
I. S. Nikitin, A. D. Nikitin, B. A. Stratula
Previously obtained analytical formulas for natural frequencies and vibration modes of inhomogeneous hourglass-shaped rods are applied to obtain geometric and elastic characteristics of samples and to estimate the amplitudes of axial stresses obtained during experimental studies of fatigue strength of metal alloys under high-frequency cyclic loading. A numerical method based on a multi-regime fatigue failure model is proposed for calculating damage kinetics under high-frequency cyclic tension-compression loading of hourglass-shaped specimens at different stress ratios. The calculations based on the proposed model are compared with the results of experiments on hourglass-shaped titanium alloy samples. The proposed model and calculation method make it possible to construct fatigue curves with sufficient accuracy for various cyclic loading conditions and stress ratios. This problem requires knowing the base points of the bimodal fatigue curve for a fully reverse cycle.
{"title":"MODEL AND METHOD FOR CALCULATING CYCLIC DAMAGE UNDER HIGH-FREQUENCY LOADING OF HOURGLASS-SHAPED SAMPLES","authors":"I. S. Nikitin, A. D. Nikitin, B. A. Stratula","doi":"10.1134/S0021894424010140","DOIUrl":"10.1134/S0021894424010140","url":null,"abstract":"<p>Previously obtained analytical formulas for natural frequencies and vibration modes of inhomogeneous hourglass-shaped rods are applied to obtain geometric and elastic characteristics of samples and to estimate the amplitudes of axial stresses obtained during experimental studies of fatigue strength of metal alloys under high-frequency cyclic loading. A numerical method based on a multi-regime fatigue failure model is proposed for calculating damage kinetics under high-frequency cyclic tension-compression loading of hourglass-shaped specimens at different stress ratios. The calculations based on the proposed model are compared with the results of experiments on hourglass-shaped titanium alloy samples. The proposed model and calculation method make it possible to construct fatigue curves with sufficient accuracy for various cyclic loading conditions and stress ratios. This problem requires knowing the base points of the bimodal fatigue curve for a fully reverse cycle.</p>","PeriodicalId":608,"journal":{"name":"Journal of Applied Mechanics and Technical Physics","volume":"65 1","pages":"121 - 133"},"PeriodicalIF":0.5,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142200226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-21DOI: 10.1134/S0021894424010176
V. N. Paimushin, V. M. Shishkin
This paper presents a solution to the problem of forced bending vibrations of a flat rod with two cantilevers and a finite-length fixed region on one of the outer surfaces. The cantilever deformation processes are described using the Timoshenko model with no account for transverse compression and the fixed region: the same deformation model with allowance for transverse compression, modified by considering the presence of an unmoving fixed region. Conditions for the kinematic coupling of the cantilevers and the fixed region are formulated. The Hamilton–Ostrogradsky variational principle serves as a basis for equations of motion, boundary conditions, and force conditions for the coupling of the rod regions. Exact analytical solutions to the equations of motion under the influence of a harmonic transverse force at the end of one of the cantilevers are obtained. The passage of resonant vibrations through a finite-length fixed region in duralumin and fiber composite rods with and without account for the transverse compression of the fixed region is studied in numerical experiments. There is a significant increase in the vibration amplitude of the end of the unloaded cantilever of a duralumin rod due to transverse compression of the fixed region. The vibration amplitude for the composite rod increases slightly.
{"title":"REFINED MODEL OF DYNAMIC DEFORMATION OF A FLAT ROD WITH A FINITE-LENGTH FIXED REGION ON AN OUTER SURFACE","authors":"V. N. Paimushin, V. M. Shishkin","doi":"10.1134/S0021894424010176","DOIUrl":"10.1134/S0021894424010176","url":null,"abstract":"<p>This paper presents a solution to the problem of forced bending vibrations of a flat rod with two cantilevers and a finite-length fixed region on one of the outer surfaces. The cantilever deformation processes are described using the Timoshenko model with no account for transverse compression and the fixed region: the same deformation model with allowance for transverse compression, modified by considering the presence of an unmoving fixed region. Conditions for the kinematic coupling of the cantilevers and the fixed region are formulated. The Hamilton–Ostrogradsky variational principle serves as a basis for equations of motion, boundary conditions, and force conditions for the coupling of the rod regions. Exact analytical solutions to the equations of motion under the influence of a harmonic transverse force at the end of one of the cantilevers are obtained. The passage of resonant vibrations through a finite-length fixed region in duralumin and fiber composite rods with and without account for the transverse compression of the fixed region is studied in numerical experiments. There is a significant increase in the vibration amplitude of the end of the unloaded cantilever of a duralumin rod due to transverse compression of the fixed region. The vibration amplitude for the composite rod increases slightly.</p>","PeriodicalId":608,"journal":{"name":"Journal of Applied Mechanics and Technical Physics","volume":"65 1","pages":"161 - 175"},"PeriodicalIF":0.5,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142200232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-21DOI: 10.1134/S0021894424010103
M. A. Pakhomov
The local flow structure in a turbulent gas-droplet flow behind a single obstacle has been studied numerically with varying initial mass fraction and diameter of dispersed particles. The effect of evaporating droplets flowing over a single square obstacle on the local mean and fluctuating flow structure and dispersed-phase propagation has been analyzed. The mean longitudinal velocity profiles for the gas and dispersed phases are similar to those for single-phase flow. The gas velocity in the gas-droplet flow is insignificantly (less than 3%) higher than that in single-phase flow. The turbulence kinetic energy increases in approaching the obstacle. Maximum gas-phase turbulence was obtained on the obstacle at (x/h= -1{-}0), and it is more than 50% higher than the turbulence kinetic energy before and after the obstacle.
{"title":"MODELING OF A TURBULENT DROPLET-LADEN FLOW BEHIND AN OBSTACLE","authors":"M. A. Pakhomov","doi":"10.1134/S0021894424010103","DOIUrl":"10.1134/S0021894424010103","url":null,"abstract":"<p>The local flow structure in a turbulent gas-droplet flow behind a single obstacle has been studied numerically with varying initial mass fraction and diameter of dispersed particles. The effect of evaporating droplets flowing over a single square obstacle on the local mean and fluctuating flow structure and dispersed-phase propagation has been analyzed. The mean longitudinal velocity profiles for the gas and dispersed phases are similar to those for single-phase flow. The gas velocity in the gas-droplet flow is insignificantly (less than 3%) higher than that in single-phase flow. The turbulence kinetic energy increases in approaching the obstacle. Maximum gas-phase turbulence was obtained on the obstacle at <span>(x/h= -1{-}0)</span>, and it is more than 50% higher than the turbulence kinetic energy before and after the obstacle.</p>","PeriodicalId":608,"journal":{"name":"Journal of Applied Mechanics and Technical Physics","volume":"65 1","pages":"80 - 91"},"PeriodicalIF":0.5,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142200222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-21DOI: 10.1134/S0021894424010036
V. B. Shulyatyev, M. A. Gulov, E. V. Karpov, A. G. Malikov, A. A. Filippov
Results of tensile and low-cycle fatigue testing of samples made of an aluminum–lithium alloy of the Al–Mg–Li system obtained by plasma-assisted laser cutting performed by a pulsed CO2 laser in an argon jet with the laser beam and optical discharge plasma simultaneously affecting the material are reported. Low-cycle fatigue tests show that the number of loading cycles survived by the sample obtained by plasma-assisted laser cutting is more than twice greater than the number of cycles survived by the samples obtained by conventional laser cutting with a continuous beam.
{"title":"MECHANICAL PROPERTIES OF AVIATION ALUMINUM–LITHIUM ALLOY SAMPLES OBTAINED BY PLASMA-ASSISTED LASER CUTTING","authors":"V. B. Shulyatyev, M. A. Gulov, E. V. Karpov, A. G. Malikov, A. A. Filippov","doi":"10.1134/S0021894424010036","DOIUrl":"10.1134/S0021894424010036","url":null,"abstract":"<p>Results of tensile and low-cycle fatigue testing of samples made of an aluminum–lithium alloy of the Al–Mg–Li system obtained by plasma-assisted laser cutting performed by a pulsed CO<sub>2</sub> laser in an argon jet with the laser beam and optical discharge plasma simultaneously affecting the material are reported. Low-cycle fatigue tests show that the number of loading cycles survived by the sample obtained by plasma-assisted laser cutting is more than twice greater than the number of cycles survived by the samples obtained by conventional laser cutting with a continuous beam.</p>","PeriodicalId":608,"journal":{"name":"Journal of Applied Mechanics and Technical Physics","volume":"65 1","pages":"18 - 25"},"PeriodicalIF":0.5,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142200215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-21DOI: 10.1134/S002189442401005X
I. S. Tsyryulnikov, N. A. Maslov, S. G. Mironov, T. V. Poplavskaya
The influence of the jet pressure ratio ((n=1.18{-}3.35)) in a nonisobaric supersonic jet of a vibrationally excited gas SF6 exhausting from a convergent axisymmetric nozzle 0.25 mm in diameter is studied numerically and experimentally. The experiments aimed at studying the gas-dynamic structure of the jets are performed in a specially designed jet setup of the Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences. The numerical simulations are performed by solving two-dimensional Navier–Stokes equations within the framework of the ANSYS Fluent software and the thermally perfect gas model. The influence of excitation of vibrational degrees of freedom of the SF6 gas is studied in both an equilibrium gas and a vibrationally nonequilibrium gas. The nonequilibrium state of vibrational degrees of freedom is simulated with the use of a two-temperature model of relaxation flows. It is shown that the jet pressure ratio of the SF6 gas affects the cell length of the wave structure, which is responsible for the change in the vibrational relaxation rate. The coefficient of density amplitude reduction in gas-dynamic cells is derived as a function of the jet pressure ratio.
Abstract The impact of the jet pressure ratio ((n=1.18{-}3.35)) in a nonisobaric supersonic jet of a vibrational excited gas SF6 exhausting from a convergent axisymm nozzle 0.25 mm in diameter is studied numerically and experimentsally.旨在研究射流气体动力结构的实验是在俄罗斯科学院西伯利亚分院克里斯蒂安诺维奇理论与应用力学研究所专门设计的射流装置中进行的。数值模拟是在 ANSYS Fluent 软件和热完美气体模型的框架内,通过求解二维纳维-斯托克斯方程进行的。在平衡气体和振动非平衡气体中研究了激发 SF6 气体振动自由度的影响。利用双温弛豫流模型模拟了振动自由度的非平衡状态。结果表明,SF6 气体的喷射压力比会影响波结构的单元长度,从而导致振动弛豫速率的变化。气体动力单元中的密度振幅降低系数是喷射压力比的函数。
{"title":"EFFECT OF THE JET PRESSURE RATIO IN SUPERSONIC AXISYMMETRIC JETS OF A POLYATOMIC GAS SF6 ON THEIR GAS-DYNAMIC STRUCTURE","authors":"I. S. Tsyryulnikov, N. A. Maslov, S. G. Mironov, T. V. Poplavskaya","doi":"10.1134/S002189442401005X","DOIUrl":"10.1134/S002189442401005X","url":null,"abstract":"<p>The influence of the jet pressure ratio (<span>(n=1.18{-}3.35)</span>) in a nonisobaric supersonic jet of a vibrationally excited gas SF<sub>6</sub> exhausting from a convergent axisymmetric nozzle 0.25 mm in diameter is studied numerically and experimentally. The experiments aimed at studying the gas-dynamic structure of the jets are performed in a specially designed jet setup of the Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences. The numerical simulations are performed by solving two-dimensional Navier–Stokes equations within the framework of the ANSYS Fluent software and the thermally perfect gas model. The influence of excitation of vibrational degrees of freedom of the SF<sub>6</sub> gas is studied in both an equilibrium gas and a vibrationally nonequilibrium gas. The nonequilibrium state of vibrational degrees of freedom is simulated with the use of a two-temperature model of relaxation flows. It is shown that the jet pressure ratio of the SF<sub>6</sub> gas affects the cell length of the wave structure, which is responsible for the change in the vibrational relaxation rate. The coefficient of density amplitude reduction in gas-dynamic cells is derived as a function of the jet pressure ratio.</p>","PeriodicalId":608,"journal":{"name":"Journal of Applied Mechanics and Technical Physics","volume":"65 1","pages":"40 - 49"},"PeriodicalIF":0.5,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142200217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-21DOI: 10.1134/S0021894424010085
A. M. Pavlenko, B. Yu. Zanin, E. A. Melnik, N. S. Alpatskiy
The paper presents the results of an experimental study of the influence of distributed engines mounted downstream of the trailing edge on the structure of a separated flow around a trapezoidal model of a flying wing in a subsonic wind tunnel. Visualization patterns of the near-wall flow on the leeward side of the model are obtained in the modes of blocked engines and for the rotational speed of the impeller of 32800 rpm in the range of angles of attack of the wing (alpha = 5{-}20^circ). The studies also take into account the location of distributed propulsion relative to the level of the trailing edge, where the axis of rotation of the engine impeller coincided with the continuation of the wing chord line or is higher than that. The possibility of controlling a separated flow by using sources of stationary disturbances in the form of cones and ribs locally mounted at singular points on the wing surface is studied.
{"title":"INVESTIGATION OF THE INFLUENCE OF DISTRIBUTED PROPULSION ON THE STRUCTURE OF A SEPARATED FLOW AROUND A TRAPEZOIDAL MODEL OF A FLYING WING","authors":"A. M. Pavlenko, B. Yu. Zanin, E. A. Melnik, N. S. Alpatskiy","doi":"10.1134/S0021894424010085","DOIUrl":"10.1134/S0021894424010085","url":null,"abstract":"<p>The paper presents the results of an experimental study of the influence of distributed engines mounted downstream of the trailing edge on the structure of a separated flow around a trapezoidal model of a flying wing in a subsonic wind tunnel. Visualization patterns of the near-wall flow on the leeward side of the model are obtained in the modes of blocked engines and for the rotational speed of the impeller of 32800 rpm in the range of angles of attack of the wing <span>(alpha = 5{-}20^circ)</span>. The studies also take into account the location of distributed propulsion relative to the level of the trailing edge, where the axis of rotation of the engine impeller coincided with the continuation of the wing chord line or is higher than that. The possibility of controlling a separated flow by using sources of stationary disturbances in the form of cones and ribs locally mounted at singular points on the wing surface is studied.</p>","PeriodicalId":608,"journal":{"name":"Journal of Applied Mechanics and Technical Physics","volume":"65 1","pages":"66 - 75"},"PeriodicalIF":0.5,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142200220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-25DOI: 10.1134/S002189442402010X
Wu Yan, Sun Guofeng, Liu Xuhui, Li Zhaoyang, Han Shizhan
The feasibility of joining of the 6061 aluminum alloy to double-layer oxygen-free copper (TU1) by laser welding technology is reported. The weld formation and microstructure of the Cu–Cu–Al welding joint for various technological parameters are analyzed. The assessment of experimental results is based on macro- and microstructure observations of the weld using the Axio Observer D1M and Gemini SEM 300 scanning electron microscopes. The width and depth of the molten pool and the mechanical properties of the Cu–Cu–Al welding joint are tested by the Eagle-MD semi-automatic image measuring instrument and the YH-9002 computerized tension and compression machine. Among the nine tested samples, the most favorable weld parameters values are obtained with a laser power at 1600 W and a welding speed of 90 mm/s. The aluminum side area has a richer metallographic structure than the copper side area after welding.
{"title":"EFFECT OF COPPER-TO-ALUMINUM LASER WELDING PARAMETERS ON THE WELD FORMATION AND MICROSTRUCTURE CHARACTERISTICS","authors":"Wu Yan, Sun Guofeng, Liu Xuhui, Li Zhaoyang, Han Shizhan","doi":"10.1134/S002189442402010X","DOIUrl":"10.1134/S002189442402010X","url":null,"abstract":"<p>The feasibility of joining of the 6061 aluminum alloy to double-layer oxygen-free copper (TU1) by laser welding technology is reported. The weld formation and microstructure of the Cu–Cu–Al welding joint for various technological parameters are analyzed. The assessment of experimental results is based on macro- and microstructure observations of the weld using the Axio Observer D1M and Gemini SEM 300 scanning electron microscopes. The width and depth of the molten pool and the mechanical properties of the Cu–Cu–Al welding joint are tested by the Eagle-MD semi-automatic image measuring instrument and the YH-9002 computerized tension and compression machine. Among the nine tested samples, the most favorable weld parameters values are obtained with a laser power at 1600 W and a welding speed of 90 mm/s. The aluminum side area has a richer metallographic structure than the copper side area after welding.</p>","PeriodicalId":608,"journal":{"name":"Journal of Applied Mechanics and Technical Physics","volume":"65 2","pages":"279 - 289"},"PeriodicalIF":0.5,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141510570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-25DOI: 10.1134/S0021894424010152
H. Moosazadeh, M. M. Mohammadi
Nonlinear vibrations, buckling, and aeroelasticity of a thin nonlinear orthotropic composite plate have been analyzed. The types of symmetric and antisymmetric sheet layering, the number of layers, the fiber angle ranging from 0 to 90°, the effect of constant and variable thermal loads, the temperature dependence of the specific heat coefficient and the elastic modulus of the material, along with the local geometric defects have been investigated. Using Galerkin’s weighted residual theory, partial differential equations have been transformed into nonlinear ordinary differential equations, which are solved by the Runge–Kutta method.
{"title":"ANALYSIS OF THE DYNAMIC BEHAVIOR, BUCKLING, AND AEROELASTICITY OF A THIN COMPOSITE PLATE WITH THE EFFECT OF GENERAL AND LOCAL GEOMETRIC DEFECTS","authors":"H. Moosazadeh, M. M. Mohammadi","doi":"10.1134/S0021894424010152","DOIUrl":"10.1134/S0021894424010152","url":null,"abstract":"<p>Nonlinear vibrations, buckling, and aeroelasticity of a thin nonlinear orthotropic composite plate have been analyzed. The types of symmetric and antisymmetric sheet layering, the number of layers, the fiber angle ranging from 0 to 90°, the effect of constant and variable thermal loads, the temperature dependence of the specific heat coefficient and the elastic modulus of the material, along with the local geometric defects have been investigated. Using Galerkin’s weighted residual theory, partial differential equations have been transformed into nonlinear ordinary differential equations, which are solved by the Runge–Kutta method.</p>","PeriodicalId":608,"journal":{"name":"Journal of Applied Mechanics and Technical Physics","volume":"65 1","pages":"134 - 151"},"PeriodicalIF":0.5,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141510573","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-25DOI: 10.1134/S0021894424020172
P. Drygaś, N. Rylko
The stress-strain elastic field in a square array of (N) non-overlapping circular inclusions is described by approximate analytical formulas. In particular, soft inclusions are studied by an asymptotic analysis. The case with (N = 1) yields a regular square array of disks of radius (r) embedded in an elastic matrix. The computations of Natanzon and Filshtinsky are based on an infinite system of linear algebraic equations solved by the truncation method. The infinite system determines the Taylor series coefficients of the Kolosov–Muskhelishvili complex potentials. A method of functional equations is used to write the series coefficients in symbolic form up to terms of the order of (O(r^{2s})) at a fixed value of (s). Approximate analytical formulas for local elastic fields are derived.
摘要 由 N 个非重叠圆形夹杂物组成的正方形阵列中的应力-应变弹性场是用近似分析公式描述的。特别是通过渐近分析研究了软夹杂物。在 N = 1 的情况下,会产生一个嵌入弹性矩阵的半径为 r 的规则方形圆盘阵列。Natanzon 和 Filshtinsky 的计算基于截断法求解的线性代数方程的无限系统。这个无限系统决定了 Kolosov-Muskhelishvili 复势的泰勒级数系数。利用函数方程的方法,以符号形式写出了在 s 的固定值下直到 O(r2s)阶项的系列系数。
{"title":"PLANE-STRAIN ELASTIC PROBLEM FOR A SQUARE ARRAY OF DISKS. I. ELASTIC FIELD IN A COMPOSITE WITH SOFT INCLUSIONS","authors":"P. Drygaś, N. Rylko","doi":"10.1134/S0021894424020172","DOIUrl":"10.1134/S0021894424020172","url":null,"abstract":"<p>The stress-strain elastic field in a square array of <span>(N)</span> non-overlapping circular inclusions is described by approximate analytical formulas. In particular, soft inclusions are studied by an asymptotic analysis. The case with <span>(N = 1)</span> yields a regular square array of disks of radius <span>(r)</span> embedded in an elastic matrix. The computations of Natanzon and Filshtinsky are based on an infinite system of linear algebraic equations solved by the truncation method. The infinite system determines the Taylor series coefficients of the Kolosov–Muskhelishvili complex potentials. A method of functional equations is used to write the series coefficients in symbolic form up to terms of the order of <span>(O(r^{2s}))</span> at a fixed value of <span>(s)</span>. Approximate analytical formulas for local elastic fields are derived.</p>","PeriodicalId":608,"journal":{"name":"Journal of Applied Mechanics and Technical Physics","volume":"65 2","pages":"354 - 367"},"PeriodicalIF":0.5,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141510568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}