The dynamic behavior of a rectangular crack in a three-dimensional （3D） orthotropic elastic medium is investigated under a harmonic stress wave based on the non-local theory. The two-dimensional （2D） Fourier trans...The dynamic behavior of a rectangular crack in a three-dimensional （3D） orthotropic elastic medium is investigated under a harmonic stress wave based on the non-local theory. The two-dimensional （2D） Fourier transform is applied, and the mixed- boundary value problems are converted into three pairs of dual integral equations with the unknown variables being the displacement jumps across the crack surfaces. The effects of the geometric shape of the rectangular crack, the circular frequency of the incident waves, and the lattice parameter of the orthotropic elastic medium on the dynamic stress field near the crack edges are analyzed. The present solution exhibits no stress singularity at the rectangular crack edges, and the dynamic stress field near the rectangular crack edges is finite.展开更多
In this paper, the scattering of harmonic anti-plane shear wavesby a finite crack in infinitely long strip is studied using thenon-local theory. The Fourier transform is applied and a mixedboundary value problem is fo...In this paper, the scattering of harmonic anti-plane shear wavesby a finite crack in infinitely long strip is studied using thenon-local theory. The Fourier transform is applied and a mixedboundary value problem is formulated. Then a set of dual integralequations is solved using the Schmidt method instead of the first orthe second integral equation method. A one-dimensional non-localkernel is used instead of a two-di- mensional one for the anti-planedynamic problem to obtain the stress occurring at the crack tips.Contrary to the classical elasticity solution, it is found that nostress singularity is present at the crack tip. The non-local dynamicelastic solutions yield a finite hoop stress at the crack tip, thusallowing for a fracture criterion based on the maximum dynamic stresshypothesis. The finite hoop stress at the crack tip depends on thecrack length, the width of the strip and the lattice parameters.展开更多
The behavior as t→∞ of solutions of the linear system of elastic equations defined on anon-star-tshaped exterior domains in Rn (n≥3) is discussed.It has showed that the local energydecays with arate of t-1+H (0≤H...The behavior as t→∞ of solutions of the linear system of elastic equations defined on anon-star-tshaped exterior domains in Rn (n≥3) is discussed.It has showed that the local energydecays with arate of t-1+H (0≤H≤1),nonuniformly with respect to the geometrical propertiesof the obstacle.and when n is odd the local energy decays exponentially.For the classical elasticwave,when n=3,the behavior of the solution of the nonhomogeneous system with a right sideterm periodical with respect to time t is discussed.展开更多
In this work,we first use momentum density studies to understand strongly correlated electron behavior,which is typically seen in transition metal oxides.We observe that correlated electron behavior as seen in bulk Ni...In this work,we first use momentum density studies to understand strongly correlated electron behavior,which is typically seen in transition metal oxides.We observe that correlated electron behavior as seen in bulk NiO is due to the Fermi break located in the middle of overlapping spectral functions obtained from a GW（G is Green’s function and W is the screened Coulomb interaction） approximation（GWA） calculation while in the case of TiO2 we can see that the origin of the constant momentum distribution in lower momenta is due to a pile up of spectra before the Fermi energy.These observations are then used to compare our calculated Compton profiles with previous experimental studies of Fukamachi and Limandri.Our calculations for NiO are observed to follow the same trend as the experimental profile but it is seen to have a wide difference in the case of TiO2 before the Fermi break.The ground state momentum densities differ significantly from the quasiparticle momentum density,thus stressing the importance of the quasiparticle wave function as the input for the study of charge density and the electron localization function.Finally we perform a calculation of the quasiparticle renormalization function,giving a quantitative description of the discontinuity of the GWA momentum density.展开更多
The wave method is introduced to vibration analysis of the fluid-conveying carbon nanotube. The constitutive relation of carbon nanotube on micro-scale is founded using the non- local elastic theory. The governing equ...The wave method is introduced to vibration analysis of the fluid-conveying carbon nanotube. The constitutive relation of carbon nanotube on micro-scale is founded using the non- local elastic theory. The governing equation on micro-scale is obtained. And the first five orders of the natural frequency of the carbon nanotube conveying fluid with various speeds are calculated through the wave method. Besides, the critical flow velocity when the carbon nanotube loses stability is obtained. Meanwhile, a contrast is made between the result obtained through tile wave method and that in previous researches.展开更多
The elasticity-based Locally Exact Homogenization Theory(LEHT) is extended to study the mechanical-hygrothermal behaviors of unidirectionally-reinforced composites. Based on the framework developed previously, thermal...The elasticity-based Locally Exact Homogenization Theory(LEHT) is extended to study the mechanical-hygrothermal behaviors of unidirectionally-reinforced composites. Based on the framework developed previously, thermal and moisture effects are incorporated into the LEHT to study the homogenized and localized responses of heterogeneous materials, which are validated using available analytical and numerical techniques. The LEHT programs are then encapsulated as subroutines with Input/Output(I/O) interfaces, to be readily applied in different computational scenarios. In order to illustrate the efficiency of the LEHT, the theory is firstly coupled to the Particle Swarm Optimization(PSO) algorithm in order to minimize the axial thermal expansion mismatch in hexagonal and square fiber arrays by tailoring the fiber volume fraction. The LEHT is then implemented into the lamination theory to study fabrication-induced residual stresses arising during the cool-down process which introduces local laminate stresses owing to thermo-mechanical property mismatch between plies. Both of these applications illustrate the efficiency and accuracy of the LEHT in generating effective properties and local stress distributions, making the theory a golden standard in validating other analytical or numerical techniques as well as a reliable tool in composite design and practice for professionals and non-professionals alike.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11272105 and 11572101)
文摘The dynamic behavior of a rectangular crack in a three-dimensional （3D） orthotropic elastic medium is investigated under a harmonic stress wave based on the non-local theory. The two-dimensional （2D） Fourier transform is applied, and the mixed- boundary value problems are converted into three pairs of dual integral equations with the unknown variables being the displacement jumps across the crack surfaces. The effects of the geometric shape of the rectangular crack, the circular frequency of the incident waves, and the lattice parameter of the orthotropic elastic medium on the dynamic stress field near the crack edges are analyzed. The present solution exhibits no stress singularity at the rectangular crack edges, and the dynamic stress field near the rectangular crack edges is finite.
基金the Post Doctoral Science Foundation of Heilongjiang Provincethe Natural Science Foundation of Heilongjiang Provincethe National Foundation for Excellent Young Investigators.
文摘In this paper, the scattering of harmonic anti-plane shear wavesby a finite crack in infinitely long strip is studied using thenon-local theory. The Fourier transform is applied and a mixedboundary value problem is formulated. Then a set of dual integralequations is solved using the Schmidt method instead of the first orthe second integral equation method. A one-dimensional non-localkernel is used instead of a two-di- mensional one for the anti-planedynamic problem to obtain the stress occurring at the crack tips.Contrary to the classical elasticity solution, it is found that nostress singularity is present at the crack tip. The non-local dynamicelastic solutions yield a finite hoop stress at the crack tip, thusallowing for a fracture criterion based on the maximum dynamic stresshypothesis. The finite hoop stress at the crack tip depends on thecrack length, the width of the strip and the lattice parameters.
文摘The behavior as t→∞ of solutions of the linear system of elastic equations defined on anon-star-tshaped exterior domains in Rn (n≥3) is discussed.It has showed that the local energydecays with arate of t-1+H (0≤H≤1),nonuniformly with respect to the geometrical propertiesof the obstacle.and when n is odd the local energy decays exponentially.For the classical elasticwave,when n=3,the behavior of the solution of the nonhomogeneous system with a right sideterm periodical with respect to time t is discussed.
文摘In this work,we first use momentum density studies to understand strongly correlated electron behavior,which is typically seen in transition metal oxides.We observe that correlated electron behavior as seen in bulk NiO is due to the Fermi break located in the middle of overlapping spectral functions obtained from a GW（G is Green’s function and W is the screened Coulomb interaction） approximation（GWA） calculation while in the case of TiO2 we can see that the origin of the constant momentum distribution in lower momenta is due to a pile up of spectra before the Fermi energy.These observations are then used to compare our calculated Compton profiles with previous experimental studies of Fukamachi and Limandri.Our calculations for NiO are observed to follow the same trend as the experimental profile but it is seen to have a wide difference in the case of TiO2 before the Fermi break.The ground state momentum densities differ significantly from the quasiparticle momentum density,thus stressing the importance of the quasiparticle wave function as the input for the study of charge density and the electron localization function.Finally we perform a calculation of the quasiparticle renormalization function,giving a quantitative description of the discontinuity of the GWA momentum density.
基金the support of a grant from Aeronautical Science Foundation of China(2010ZA53013 and 2011ZA53014)the open funds of Key Laboratory of Advanced Design and Intelligent Computing(Dalian University),Ministry of Education(ADIC2010007)Northwestern Polytechnical University Basic Research Fund(JC201114 andJC20110255)
文摘The wave method is introduced to vibration analysis of the fluid-conveying carbon nanotube. The constitutive relation of carbon nanotube on micro-scale is founded using the non- local elastic theory. The governing equation on micro-scale is obtained. And the first five orders of the natural frequency of the carbon nanotube conveying fluid with various speeds are calculated through the wave method. Besides, the critical flow velocity when the carbon nanotube loses stability is obtained. Meanwhile, a contrast is made between the result obtained through tile wave method and that in previous researches.
文摘The elasticity-based Locally Exact Homogenization Theory(LEHT) is extended to study the mechanical-hygrothermal behaviors of unidirectionally-reinforced composites. Based on the framework developed previously, thermal and moisture effects are incorporated into the LEHT to study the homogenized and localized responses of heterogeneous materials, which are validated using available analytical and numerical techniques. The LEHT programs are then encapsulated as subroutines with Input/Output(I/O) interfaces, to be readily applied in different computational scenarios. In order to illustrate the efficiency of the LEHT, the theory is firstly coupled to the Particle Swarm Optimization(PSO) algorithm in order to minimize the axial thermal expansion mismatch in hexagonal and square fiber arrays by tailoring the fiber volume fraction. The LEHT is then implemented into the lamination theory to study fabrication-induced residual stresses arising during the cool-down process which introduces local laminate stresses owing to thermo-mechanical property mismatch between plies. Both of these applications illustrate the efficiency and accuracy of the LEHT in generating effective properties and local stress distributions, making the theory a golden standard in validating other analytical or numerical techniques as well as a reliable tool in composite design and practice for professionals and non-professionals alike.
