Heat conduction dynamics are described by partial differential equations. Their approximations with a set of finite number of ordinary differential equations are often required for simpler computations and analyses. R...Heat conduction dynamics are described by partial differential equations. Their approximations with a set of finite number of ordinary differential equations are often required for simpler computations and analyses. Rational approximations of the Laplace solutions such as the Pade approximation can be used for this purpose. For some heat conduction problems appearing in a semi-infinite slab, however, such rational approximations are not easy to obtain because the Laplace solutions are not analytic at the origin. In this article, a continued fraction method has been proposed to obtain rational approximations of such heat conduction dynamics in a semi-infinite slab.展开更多
In this paper,we consider a robust semi-infinite interval-valued optimization problem with inequality constraints having an uncertain parameter.The parametric representation of the aforesaid problem is also considered...In this paper,we consider a robust semi-infinite interval-valued optimization problem with inequality constraints having an uncertain parameter.The parametric representation of the aforesaid problem is also considered in order to derive the necessary and sufficient optimality conditions.Furthermore,we formulate a mixed-type dual problem and derive duality results which associate the robust weak efficient solution of the primal and its dual problems.Several examples are given to illustrate the results in the manuscript.展开更多
The intracontinental subduction of a>200-km-long section of the Tajik-Tarim lithosphere beneath the Pamir Mountains is proposed to explain nearly 30 km of shortening in the Tajik fold-thrust belt and the Pamir upli...The intracontinental subduction of a>200-km-long section of the Tajik-Tarim lithosphere beneath the Pamir Mountains is proposed to explain nearly 30 km of shortening in the Tajik fold-thrust belt and the Pamir uplift.Seismic imaging revealed that the upper slab was scraped and that the lower slab had subducted to a depth of>150 km.These features constitute the tectonic complexity of the Pamirs,as well as the thermal subduction mechanism involved,which remains poorly understood.Hence,in this study,high-resolution three-dimensional(3D)kinematic modeling is applied to investigate the thermal structure and geometry of the subducting slab beneath the Pamirs.The modeled slab configuration reveals distinct along-strike variations,with a steeply dipping slab beneath the southern Pamirs,a more gently inclined slab beneath the northern Pamirs,and apparent upper slab termination at shallow depths beneath the Pamirs.The thermal field reveals a cold slab core after delamination,with temperatures ranging from 400℃to 800℃,enveloped by a hotter mantle reaching~1400℃.The occurrence of intermediate-depth earthquakes aligns primarily with colder slab regions,particularly near the slab tear-off below the southwestern Pamirs,indicating a strong correlation between slab temperature and seismicity.In contrast,the northern Pamirs exhibit reduced seismicity at depth,which is likely associated with thermal weakening and delamination.The central Pamirs show a significant thermal anomaly caused by a concave slab,where the coldest crust does not descend deeply,further suggesting crustal detachment or mechanical failure.The lateral asymmetry in slab temperature possibly explains the mechanism of lateral tearing and differential slab-mantle coupling.展开更多
A complementary method to determine the vibration source intensity,defined as the weighted vertical acceleration level at the tunnel wall,is needed urgently when comparable measurements or database predictions are una...A complementary method to determine the vibration source intensity,defined as the weighted vertical acceleration level at the tunnel wall,is needed urgently when comparable measurements or database predictions are unavailable in empirical predictions.In this study,we present an analytical model designed to quickly and accurately estimate the vibration source intensity produced by moving metro trains,considering both regular and floating slab tracks.The improved periodic pipe-in-pipe(PiP)model with regular or floating slabs affixed to the tunnel invert was developed.The train loads are represented in the frequency-wavenumber domain to apply in the model.Measured track irregularities were applied and the proposed model was validated against the measured results and verified by a tunnel-soil coupled model.The proposed approach effectively and accurately assessed the vibration source intensity generated by underground trains in a prediction time of just 58 s.Track irregularities significantly affect the vibration source intensity,making them a key factor in comparable measurements or database predictions.A floating slab track can reduce the vibration source intensity by about 14 dB.The proposed approach can serve as an additional method to complement comparable measurements or database predictions for determining the vibration source intensity in empirical predictions.展开更多
In this study, a combined experimental, numerical and theoretical investigation is conducted on the penetration of semi-infinite 4340 steel targets by a homogeneous 93 W rod and two types of jacketed rods with strikin...In this study, a combined experimental, numerical and theoretical investigation is conducted on the penetration of semi-infinite 4340 steel targets by a homogeneous 93 W rod and two types of jacketed rods with striking velocities of 0.9-3.3 km/s. The results show that the jacketed rods produced typical“co-erosion” damage at all test velocities, except for the 93 W/1060 Al jacketed rod, which switched from an early “bi-erosion” damage to later “co-erosion” damage at a striking velocity of 936 m/s. However, the homogeneous 93 W rod always forms a large mushroom head during the penetration process. The damage mechanisms of these two types of jacketed rods differ for striking velocities of 0.9-2.0 km/s, but this difference gradually decreases with increased striking velocity. For velocities of 2.0-3.3 km/s, all three types of projectiles exhibit typical hydrodynamic penetration characteristics, and the damage mechanisms of the two types of jacketed rods are almost identical. For the same initial kinetic energy, the penetration performance of the jacketed rods is distinctly superior to that of the homogeneous 93 W rods.Compared with jacket density, jacket strength shows a more significant influence on the damage mechanism and penetration performance of the jacketed rod. Finally, an existing theoretical prediction model of the penetration depth of jacketed rods on semi-infinite targets in the co-erosion mode is modified. It transpires that-in terms of penetration depth-the modified theoretical model is in good agreement with the experimental and numerical observations for 93 W/TC4 and 93 W/1060 Al jacketed rods penetrating semi-infinite 4340 steel targets.展开更多
Based on the fundamental equations of magnetoelectroelastic material and the analytic theory, and using the Muskhelishvili-introduced well-known elastic techniques combined with the superposition principle, the closed...Based on the fundamental equations of magnetoelectroelastic material and the analytic theory, and using the Muskhelishvili-introduced well-known elastic techniques combined with the superposition principle, the closed form solution of the generalized stress field of the interaction between many parallel screw dislocations and a semi-infinite crack in an infinite magnetoelectroelastic solid is obtained, on the assumption that the surface of the crack is impermeable electrically and magnetically. Besides, the Peach-Koehler formula of n parallel screw dislocations is given. Numerical examples show that the generalized stress varies with the position of point z and is related to the material constants. The results indicate that the stress concentration occurs at the dislocation core and the tip of the crack. The result of interaction makes the system stay in a lower energy state.展开更多
The aim of this article is to discuss an asymptotic approximation model and its convergence for the minimax semi-infinite programming problem. An asymptotic surrogate constraints method for the minimax semi-infinite p...The aim of this article is to discuss an asymptotic approximation model and its convergence for the minimax semi-infinite programming problem. An asymptotic surrogate constraints method for the minimax semi-infinite programming problem is presented by making use of two general discrete approximation methods. Simultaneously, the consistence and the epi-convergence of the asymptotic approximation problem are discussed.展开更多
By means of analytic function theory, the problems of interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are studied. The analytic solutions o...By means of analytic function theory, the problems of interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are studied. The analytic solutions of stress fields of the interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are obtained. They indicate that the stress concentration occurs at the dislocation source and the tip of the crack, and the value of the stress increases with the number of the dislocations increasing. These results are the development of interaction among the finitely many defects of quasicrystals, which possesses an important reference value for studying the interaction problems of infinitely many defects in fracture mechanics of quasicrystal.展开更多
This study employs a data-driven methodology that embeds the principle of dimensional invariance into an artificial neural network to automatically identify dominant dimensionless quantities in the penetration of rod ...This study employs a data-driven methodology that embeds the principle of dimensional invariance into an artificial neural network to automatically identify dominant dimensionless quantities in the penetration of rod projectiles into semi-infinite metal targets from experimental measurements.The derived mathematical expressions of dimensionless quantities are simplified by the examination of the exponent matrix and coupling relationships between feature variables.As a physics-based dimension reduction methodology,this way reduces high-dimensional parameter spaces to descriptions involving only a few physically interpretable dimensionless quantities in penetrating cases.Then the relative importance of various dimensionless feature variables on the penetration efficiencies for four impacting conditions is evaluated through feature selection engineering.The results indicate that the selected critical dimensionless feature variables by this synergistic method,without referring to the complex theoretical equations and aiding in the detailed knowledge of penetration mechanics,are in accordance with those reported in the reference.Lastly,the determined dimensionless quantities can be efficiently applied to conduct semi-empirical analysis for the specific penetrating case,and the reliability of regression functions is validated.展开更多
A theoretical study is presented herein on the pen- etration of a semi-infinite target by a spherical-headed long rod for Yp 〉 S, where Yp is the penetrator strength and S is the static target resistance. For Yp 〉 S...A theoretical study is presented herein on the pen- etration of a semi-infinite target by a spherical-headed long rod for Yp 〉 S, where Yp is the penetrator strength and S is the static target resistance. For Yp 〉 S, depending upon initial impact velocity, there exist three types of penetration, namely, penetration by a rigid long rod, penetration by a deforming non-erosive long rod and penetration by an erosive long rod. If the impact velocity of the penetrator is higher than the hydrodynamic velocity （VH）, it will penetrate the target in an erosive mode; if the impact velocity lies between the hydrodynamic velocity （VH） and the rigid body velocity （VR）, it will penetrate the target in a deformable mode; if the impact velocity is less than the rigid body velocity （VR）, it will penetrate the target in a rigid mode. The critical conditions for the transition among these three penetration modes are proposed. It is demonstrated that the present model predictions correlate well with the experimental observations in terms of depth of penetration （DOP） and the critical transition conditions.展开更多
Using the complex variable function method and the technique of the conformal mapping, the fracture problem of a semi-infinite crack in a piezoelectric strip is studied under the anti-plane shear stress and the in-pla...Using the complex variable function method and the technique of the conformal mapping, the fracture problem of a semi-infinite crack in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load. The analytic solutions of the field intensity factors and the mechanical strain energy release rate are presented under the assumption that the surface of the crack is electrically impermeable. When the height of the strip tends to infinity, the analytic solutions of an infinitely large piezoelectric solid with a semi-infinite crack are obtained. Moreover, the present results can be reduced to the well-known solutions for a purely elastic material in the absence of the electric loading. In addition, numerical examples are given to show the influences of the loaded crack length, the height of the strip, and the applied mechanical/electric loads on the mechanical strain energy release rate.展开更多
The problem of a semi-infinite medium subjected to thermal shock on its plane boundary is solved in the context of the dual-phase-lag thermoelastic model. The expressions for temperature, displacement and stress are p...The problem of a semi-infinite medium subjected to thermal shock on its plane boundary is solved in the context of the dual-phase-lag thermoelastic model. The expressions for temperature, displacement and stress are presented. The governing equations are expressed in Laplace transform domain and solved in that domain. The solution of the problem in the physical domain is obtained by using a numerical method for the inversion of the Laplace transforms based on Fourier series expansions. The numerical estimates of the displacement, temperature, stress and strain are obtained for a hypothetical material. The results obtained are presented graphically to show the effect phase-lag of the heat flux and a phase-lag of temperature gradient on displacement, temperature, stress.展开更多
Using the complex variable function method and the conformal mapping technique, the fracture problem of two semi-infinite collinear cracks in a piezoelectric strip is studied under the anti-plane shear stress and the ...Using the complex variable function method and the conformal mapping technique, the fracture problem of two semi-infinite collinear cracks in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load on the partial crack surface. Analytic solutions of the field intensity factors and the mechanical strain energy release rate are derived under the assumption that the surfaces of the crack are electrically impermeable. The results can be reduced to the well-known solutions for a purely elastic material in the absence of an electric load. Moreover, when the distance between the two crack tips tends to infinity, analytic solutions of a semi-infinite crack in a piezoelectric strip can be obtained. Numerical examples are given to show the influence of the loaded crack length, the height of the strip, the distance between the two crack tips, and the applied mechanical/electric loads on the mechanical strain energy release rate. It is shown that the material is easier to fail when the distance between two crack tips becomes shorter, and the mechanical/electric loads have greater influence on the propagation of the left crack than those of the right one.展开更多
In this paper,the bounded traveling wave solutions are examined for a system of partial differential equations with certain boundary conditions.Interestingly,this system can be used to describe the axially symmetric m...In this paper,the bounded traveling wave solutions are examined for a system of partial differential equations with certain boundary conditions.Interestingly,this system can be used to describe the axially symmetric motion of a semi-infinite incompressible hyperelastic cylindrical rod.With the aid of traveling wave transformations,the partial differential equations can be reduced to a traveling wave equation.The implicit analytical expressions determining the traveling waves are derived.Significantly,the influences of material parameters on the qualitative properties are discussed in detail by using the phase portraits of the traveling wave system. Smooth solutions such as the periodic traveling wave solutions and the solitary wave solutions with the peak form are shown.In particular,some interesting singular traveling wave solutions including the solitary cusp wave solutions and the periodic cusp wave solutions with the peak form are obtained.Numerical examples for all these waves are given.展开更多
In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These co...In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These conditions are responsible for the development of duality theory which is an extremely important feature for any class of problems, but the literature available so far lacks these necessary optimality conditions for the stated problem. A lemma is also proved to find the topological dual of as it is required to prove the desired result.展开更多
For the first time, we introduce a fully quantum mechanical Hamiltonian for a semi-infinite chain model of atoms. We then derive the vibration modes of this model by virtue of the ＂invariant eigen-operator＂ method i...For the first time, we introduce a fully quantum mechanical Hamiltonian for a semi-infinite chain model of atoms. We then derive the vibration modes of this model by virtue of the ＂invariant eigen-operator＂ method in two different cases, which is concise and revealing.展开更多
In the present paper reductions of the finite layer mathod once studied in detail by the authors for the elastodvnamics of transverse isotropic bodies are given to several special cases. Two-dimensional problems, axis...In the present paper reductions of the finite layer mathod once studied in detail by the authors for the elastodvnamics of transverse isotropic bodies are given to several special cases. Two-dimensional problems, axisymmetric problems and static problems are discussed, respectively, and this finite layer method is also generalized to the problems in which materials possess viscous properties. Two numerical examples have been presented for the axisymmetric case. From these two examples it can be concluded that the finite layer method can be used to analyse semi-infinite layered soils and to deal with the problem of the interaction between soils and structures.展开更多
In the present paper a finite layer method is studied for the flastodynarnics of transverse isotropic bodies. With this method, semi-infinite soils can be considered as an transverse isotropic half-space, its material...In the present paper a finite layer method is studied for the flastodynarnics of transverse isotropic bodies. With this method, semi-infinite soils can be considered as an transverse isotropic half-space, its material functions varying with depth. Dividing the half-space into a scries of layers in the direction of depth, the material junctions in each layer are simulated by exponential functions Consequently, the fundamental equations to be solved can be simplified if the Fourier transform with repsect to coordinates is used. We have obtained the relationship between the 'layer forces' and 'layer displacements'. This finite layer method, in fact, can also be called a semi-analytical method. It possesses those advantages as the usual semi-analytical methods do, and can be used to analyse the problem of the interaction between soils and structures.展开更多
This paper studies quantum diffusion in semi-infinite one-dimensional periodic lattice and quasiperiodic Fibonacci lattice. It finds that the quantum diffusion in the semi-infinite periodic lattice shows the same prop...This paper studies quantum diffusion in semi-infinite one-dimensional periodic lattice and quasiperiodic Fibonacci lattice. It finds that the quantum diffusion in the semi-infinite periodic lattice shows the same properties as that for the infinite periodic lattice. Different behaviour is found for the semi-infinite Fibonacci lattice. In this case, there are still C（t） - t^-δ and d（t） - t^β. However, it finds that 0 〈δ 〈 1 for smaller time, and δ = 0 for larger time due to the influence of surface localized states. Moreover, β for the semi-infinite Fibonacci lattice is much smaller than that for the infinite Fibonacci lattice. Effects of disorder on the quantum diffusion are also discussed.展开更多
Green’s function for the T-stress near a crack tip is addressed with an analytic function method for a semi-infinite crack lying in an elastical, isotropic, and infinite plate. The cracked plate is loaded by a single...Green’s function for the T-stress near a crack tip is addressed with an analytic function method for a semi-infinite crack lying in an elastical, isotropic, and infinite plate. The cracked plate is loaded by a single inclined concentrated force at an interior point. The complex potentials are obtained based on a superposition principle, which provide the solutions to the plane problems of elasticity. The regular parts of the potentials are extracted in an asymptotic analysis. Based on the regular parts, Green’s function for the T-stress is obtained in a straightforward manner. Furthermore, Green’s functions are derived for a pair of symmetrically and anti-symmetrically concentrated forces by the superimposing method. Then, Green’s function is used to predict the domain-switch-induced T-stress in a ferroelectric double cantilever beam （DCB） test. The T-stress induced by the electromechanical loading is used to judge the stable and unstable crack growth behaviors observed in the test. The prediction results generally agree with the experimental data.展开更多
文摘Heat conduction dynamics are described by partial differential equations. Their approximations with a set of finite number of ordinary differential equations are often required for simpler computations and analyses. Rational approximations of the Laplace solutions such as the Pade approximation can be used for this purpose. For some heat conduction problems appearing in a semi-infinite slab, however, such rational approximations are not easy to obtain because the Laplace solutions are not analytic at the origin. In this article, a continued fraction method has been proposed to obtain rational approximations of such heat conduction dynamics in a semi-infinite slab.
基金supported by the MATRICES,SERB-DST,New Delhi,India(No.MTR/2021/000002).
文摘In this paper,we consider a robust semi-infinite interval-valued optimization problem with inequality constraints having an uncertain parameter.The parametric representation of the aforesaid problem is also considered in order to derive the necessary and sufficient optimality conditions.Furthermore,we formulate a mixed-type dual problem and derive duality results which associate the robust weak efficient solution of the primal and its dual problems.Several examples are given to illustrate the results in the manuscript.
基金the Chinese Academy of Sciences Pioneer Hundred Talents Program and the Second Tibetan Plateau Scientific Expedition and Research Program(Grant No.2019QZKK0708)supported by a MEXT(Ministry of Education,Culture,Sports,Science and Technology)KAKENHI(Grants-in-Aid for Scientific Research)grant(Grant No.21H05203)Kobe University Strategic International Collaborative Research Grant(Type B Fostering Joint Research).
文摘The intracontinental subduction of a>200-km-long section of the Tajik-Tarim lithosphere beneath the Pamir Mountains is proposed to explain nearly 30 km of shortening in the Tajik fold-thrust belt and the Pamir uplift.Seismic imaging revealed that the upper slab was scraped and that the lower slab had subducted to a depth of>150 km.These features constitute the tectonic complexity of the Pamirs,as well as the thermal subduction mechanism involved,which remains poorly understood.Hence,in this study,high-resolution three-dimensional(3D)kinematic modeling is applied to investigate the thermal structure and geometry of the subducting slab beneath the Pamirs.The modeled slab configuration reveals distinct along-strike variations,with a steeply dipping slab beneath the southern Pamirs,a more gently inclined slab beneath the northern Pamirs,and apparent upper slab termination at shallow depths beneath the Pamirs.The thermal field reveals a cold slab core after delamination,with temperatures ranging from 400℃to 800℃,enveloped by a hotter mantle reaching~1400℃.The occurrence of intermediate-depth earthquakes aligns primarily with colder slab regions,particularly near the slab tear-off below the southwestern Pamirs,indicating a strong correlation between slab temperature and seismicity.In contrast,the northern Pamirs exhibit reduced seismicity at depth,which is likely associated with thermal weakening and delamination.The central Pamirs show a significant thermal anomaly caused by a concave slab,where the coldest crust does not descend deeply,further suggesting crustal detachment or mechanical failure.The lateral asymmetry in slab temperature possibly explains the mechanism of lateral tearing and differential slab-mantle coupling.
基金supported by the Natural Science Foundation of Shandong Province of China(No.ZR2024QE071).
文摘A complementary method to determine the vibration source intensity,defined as the weighted vertical acceleration level at the tunnel wall,is needed urgently when comparable measurements or database predictions are unavailable in empirical predictions.In this study,we present an analytical model designed to quickly and accurately estimate the vibration source intensity produced by moving metro trains,considering both regular and floating slab tracks.The improved periodic pipe-in-pipe(PiP)model with regular or floating slabs affixed to the tunnel invert was developed.The train loads are represented in the frequency-wavenumber domain to apply in the model.Measured track irregularities were applied and the proposed model was validated against the measured results and verified by a tunnel-soil coupled model.The proposed approach effectively and accurately assessed the vibration source intensity generated by underground trains in a prediction time of just 58 s.Track irregularities significantly affect the vibration source intensity,making them a key factor in comparable measurements or database predictions.A floating slab track can reduce the vibration source intensity by about 14 dB.The proposed approach can serve as an additional method to complement comparable measurements or database predictions for determining the vibration source intensity in empirical predictions.
基金supported by the National Natural Science Foundation of China(Grant nos.:11672138,11602113)Foundation of National Key Lab.of Transient Physics(Grant no.:6142604180407,JCKYS2020606004).
文摘In this study, a combined experimental, numerical and theoretical investigation is conducted on the penetration of semi-infinite 4340 steel targets by a homogeneous 93 W rod and two types of jacketed rods with striking velocities of 0.9-3.3 km/s. The results show that the jacketed rods produced typical“co-erosion” damage at all test velocities, except for the 93 W/1060 Al jacketed rod, which switched from an early “bi-erosion” damage to later “co-erosion” damage at a striking velocity of 936 m/s. However, the homogeneous 93 W rod always forms a large mushroom head during the penetration process. The damage mechanisms of these two types of jacketed rods differ for striking velocities of 0.9-2.0 km/s, but this difference gradually decreases with increased striking velocity. For velocities of 2.0-3.3 km/s, all three types of projectiles exhibit typical hydrodynamic penetration characteristics, and the damage mechanisms of the two types of jacketed rods are almost identical. For the same initial kinetic energy, the penetration performance of the jacketed rods is distinctly superior to that of the homogeneous 93 W rods.Compared with jacket density, jacket strength shows a more significant influence on the damage mechanism and penetration performance of the jacketed rod. Finally, an existing theoretical prediction model of the penetration depth of jacketed rods on semi-infinite targets in the co-erosion mode is modified. It transpires that-in terms of penetration depth-the modified theoretical model is in good agreement with the experimental and numerical observations for 93 W/TC4 and 93 W/1060 Al jacketed rods penetrating semi-infinite 4340 steel targets.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11262017,11262012,and 11462020)the Natural Science Foundation of Inner Mongolia Autonomous Region,China(Grant No.2015MS0129)+1 种基金the Key Project of Inner Mongolia Normal University,China(Grant No.2014ZD03)the Graduate Research Innovation Project of Inner Mongolia Autonomous Region,China(Grant No.S20171013502)
文摘Based on the fundamental equations of magnetoelectroelastic material and the analytic theory, and using the Muskhelishvili-introduced well-known elastic techniques combined with the superposition principle, the closed form solution of the generalized stress field of the interaction between many parallel screw dislocations and a semi-infinite crack in an infinite magnetoelectroelastic solid is obtained, on the assumption that the surface of the crack is impermeable electrically and magnetically. Besides, the Peach-Koehler formula of n parallel screw dislocations is given. Numerical examples show that the generalized stress varies with the position of point z and is related to the material constants. The results indicate that the stress concentration occurs at the dislocation core and the tip of the crack. The result of interaction makes the system stay in a lower energy state.
基金Supported by the National Key Basic Research Special Fund(2003CB415200)the National Science Foundation(70371032 and 60274048)the Doctoral Foundation of the Ministry of Education(20020486035)
文摘The aim of this article is to discuss an asymptotic approximation model and its convergence for the minimax semi-infinite programming problem. An asymptotic surrogate constraints method for the minimax semi-infinite programming problem is presented by making use of two general discrete approximation methods. Simultaneously, the consistence and the epi-convergence of the asymptotic approximation problem are discussed.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11462020,11262017,and 11262012)the Key Project of Inner Mongolia Normal University,China(Grant No.2014ZD03)
文摘By means of analytic function theory, the problems of interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are studied. The analytic solutions of stress fields of the interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are obtained. They indicate that the stress concentration occurs at the dislocation source and the tip of the crack, and the value of the stress increases with the number of the dislocations increasing. These results are the development of interaction among the finitely many defects of quasicrystals, which possesses an important reference value for studying the interaction problems of infinitely many defects in fracture mechanics of quasicrystal.
基金supported by the National Natural Science Foundation of China(Grant Nos.12272257,12102292,12032006)the special fund for Science and Technology Innovation Teams of Shanxi Province(Nos.202204051002006).
文摘This study employs a data-driven methodology that embeds the principle of dimensional invariance into an artificial neural network to automatically identify dominant dimensionless quantities in the penetration of rod projectiles into semi-infinite metal targets from experimental measurements.The derived mathematical expressions of dimensionless quantities are simplified by the examination of the exponent matrix and coupling relationships between feature variables.As a physics-based dimension reduction methodology,this way reduces high-dimensional parameter spaces to descriptions involving only a few physically interpretable dimensionless quantities in penetrating cases.Then the relative importance of various dimensionless feature variables on the penetration efficiencies for four impacting conditions is evaluated through feature selection engineering.The results indicate that the selected critical dimensionless feature variables by this synergistic method,without referring to the complex theoretical equations and aiding in the detailed knowledge of penetration mechanics,are in accordance with those reported in the reference.Lastly,the determined dimensionless quantities can be efficiently applied to conduct semi-empirical analysis for the specific penetrating case,and the reliability of regression functions is validated.
基金supported by the National Natural Science Foundation of China (10872195)
文摘A theoretical study is presented herein on the pen- etration of a semi-infinite target by a spherical-headed long rod for Yp 〉 S, where Yp is the penetrator strength and S is the static target resistance. For Yp 〉 S, depending upon initial impact velocity, there exist three types of penetration, namely, penetration by a rigid long rod, penetration by a deforming non-erosive long rod and penetration by an erosive long rod. If the impact velocity of the penetrator is higher than the hydrodynamic velocity （VH）, it will penetrate the target in an erosive mode; if the impact velocity lies between the hydrodynamic velocity （VH） and the rigid body velocity （VR）, it will penetrate the target in a deformable mode; if the impact velocity is less than the rigid body velocity （VR）, it will penetrate the target in a rigid mode. The critical conditions for the transition among these three penetration modes are proposed. It is demonstrated that the present model predictions correlate well with the experimental observations in terms of depth of penetration （DOP） and the critical transition conditions.
基金Project supported by the National Natural Science Foundation of China(Nos.10932001 and 11072015)the Scientific Research Key Program of Beijing Municipal Commission of Education (No.KZ201010005003)the Ph.D.Innovation Foundation of Beijing University of Aeronautics and Astronautics(No.300351)
文摘Using the complex variable function method and the technique of the conformal mapping, the fracture problem of a semi-infinite crack in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load. The analytic solutions of the field intensity factors and the mechanical strain energy release rate are presented under the assumption that the surface of the crack is electrically impermeable. When the height of the strip tends to infinity, the analytic solutions of an infinitely large piezoelectric solid with a semi-infinite crack are obtained. Moreover, the present results can be reduced to the well-known solutions for a purely elastic material in the absence of the electric loading. In addition, numerical examples are given to show the influences of the loaded crack length, the height of the strip, and the applied mechanical/electric loads on the mechanical strain energy release rate.
文摘The problem of a semi-infinite medium subjected to thermal shock on its plane boundary is solved in the context of the dual-phase-lag thermoelastic model. The expressions for temperature, displacement and stress are presented. The governing equations are expressed in Laplace transform domain and solved in that domain. The solution of the problem in the physical domain is obtained by using a numerical method for the inversion of the Laplace transforms based on Fourier series expansions. The numerical estimates of the displacement, temperature, stress and strain are obtained for a hypothetical material. The results obtained are presented graphically to show the effect phase-lag of the heat flux and a phase-lag of temperature gradient on displacement, temperature, stress.
基金Project supported by the National Natural Science Foundation of China(Nos.10932001 and 11072015)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20101102110016)
文摘Using the complex variable function method and the conformal mapping technique, the fracture problem of two semi-infinite collinear cracks in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load on the partial crack surface. Analytic solutions of the field intensity factors and the mechanical strain energy release rate are derived under the assumption that the surfaces of the crack are electrically impermeable. The results can be reduced to the well-known solutions for a purely elastic material in the absence of an electric load. Moreover, when the distance between the two crack tips tends to infinity, analytic solutions of a semi-infinite crack in a piezoelectric strip can be obtained. Numerical examples are given to show the influence of the loaded crack length, the height of the strip, the distance between the two crack tips, and the applied mechanical/electric loads on the mechanical strain energy release rate. It is shown that the material is easier to fail when the distance between two crack tips becomes shorter, and the mechanical/electric loads have greater influence on the propagation of the left crack than those of the right one.
基金National Natural Science Foundation of China (Nos.11672069, 11702059,11232003,11672062)the Ph.D.Programs Foundation of Ministry of Education of China (No.20130041110050)+3 种基金the Research Start-up Project Plan for Liaoning Doctors (No.20141119)the Fundamental Research Funds for the Cen- tral Universities (No.DC201502050407,DC201502050203,DC201502050403,20000101)the Natural Science Foundation of Liaoning Province (No.20170540199)and the 111Project (B08014).
文摘In this paper,the bounded traveling wave solutions are examined for a system of partial differential equations with certain boundary conditions.Interestingly,this system can be used to describe the axially symmetric motion of a semi-infinite incompressible hyperelastic cylindrical rod.With the aid of traveling wave transformations,the partial differential equations can be reduced to a traveling wave equation.The implicit analytical expressions determining the traveling waves are derived.Significantly,the influences of material parameters on the qualitative properties are discussed in detail by using the phase portraits of the traveling wave system. Smooth solutions such as the periodic traveling wave solutions and the solitary wave solutions with the peak form are shown.In particular,some interesting singular traveling wave solutions including the solitary cusp wave solutions and the periodic cusp wave solutions with the peak form are obtained.Numerical examples for all these waves are given.
文摘In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These conditions are responsible for the development of duality theory which is an extremely important feature for any class of problems, but the literature available so far lacks these necessary optimality conditions for the stated problem. A lemma is also proved to find the topological dual of as it is required to prove the desired result.
基金The project supported by the President Foundation of the Chinese Academy of Sciences
文摘For the first time, we introduce a fully quantum mechanical Hamiltonian for a semi-infinite chain model of atoms. We then derive the vibration modes of this model by virtue of the ＂invariant eigen-operator＂ method in two different cases, which is concise and revealing.
文摘In the present paper reductions of the finite layer mathod once studied in detail by the authors for the elastodvnamics of transverse isotropic bodies are given to several special cases. Two-dimensional problems, axisymmetric problems and static problems are discussed, respectively, and this finite layer method is also generalized to the problems in which materials possess viscous properties. Two numerical examples have been presented for the axisymmetric case. From these two examples it can be concluded that the finite layer method can be used to analyse semi-infinite layered soils and to deal with the problem of the interaction between soils and structures.
文摘In the present paper a finite layer method is studied for the flastodynarnics of transverse isotropic bodies. With this method, semi-infinite soils can be considered as an transverse isotropic half-space, its material functions varying with depth. Dividing the half-space into a scries of layers in the direction of depth, the material junctions in each layer are simulated by exponential functions Consequently, the fundamental equations to be solved can be simplified if the Fourier transform with repsect to coordinates is used. We have obtained the relationship between the 'layer forces' and 'layer displacements'. This finite layer method, in fact, can also be called a semi-analytical method. It possesses those advantages as the usual semi-analytical methods do, and can be used to analyse the problem of the interaction between soils and structures.
基金Project supported by the National Natural Science Foundation of China(Grant No19674046)the Cheung Kong Scholars Programme of Chinathe Construct Program of the Key Discipline in Hunan Province,China
文摘This paper studies quantum diffusion in semi-infinite one-dimensional periodic lattice and quasiperiodic Fibonacci lattice. It finds that the quantum diffusion in the semi-infinite periodic lattice shows the same properties as that for the infinite periodic lattice. Different behaviour is found for the semi-infinite Fibonacci lattice. In this case, there are still C（t） - t^-δ and d（t） - t^β. However, it finds that 0 〈δ 〈 1 for smaller time, and δ = 0 for larger time due to the influence of surface localized states. Moreover, β for the semi-infinite Fibonacci lattice is much smaller than that for the infinite Fibonacci lattice. Effects of disorder on the quantum diffusion are also discussed.
基金Project supported by the National Natural Science Foundation of China(Nos.10702071 and 11090334)the China Postdoctoral Science Foundation(No.201003281)+2 种基金the Shanghai Postdoctoral Scientific Program(No.10R21415800)the Shanghai Leading Academic Discipline Project(No.B302)sponsored by the"Sino-German Center for Research Promotion"under a project of"Crack Growth in Ferroelectrics Driven by Cyclic Electric Loading"
文摘Green’s function for the T-stress near a crack tip is addressed with an analytic function method for a semi-infinite crack lying in an elastical, isotropic, and infinite plate. The cracked plate is loaded by a single inclined concentrated force at an interior point. The complex potentials are obtained based on a superposition principle, which provide the solutions to the plane problems of elasticity. The regular parts of the potentials are extracted in an asymptotic analysis. Based on the regular parts, Green’s function for the T-stress is obtained in a straightforward manner. Furthermore, Green’s functions are derived for a pair of symmetrically and anti-symmetrically concentrated forces by the superimposing method. Then, Green’s function is used to predict the domain-switch-induced T-stress in a ferroelectric double cantilever beam （DCB） test. The T-stress induced by the electromechanical loading is used to judge the stable and unstable crack growth behaviors observed in the test. The prediction results generally agree with the experimental data.
