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Green's functions of two-dimensional piezoelectric quasicrystal in half-space and bimaterials

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Applied Mathematics and Mechanics(English Edition) 2023年第2期44卷 237-254页

作者： Xiaoyu FU Xiang MU Jinming ZHANG Liangliang ZHANG Yang GAO College of Science China Agricultural UniversityBeijing 100083China College of Engineering China Agricultural UniversityBeijing 100083China

In this paper,we obtain Green’s functions of two-dimensional(2D)piezoelectric quasicrystal(PQC)in half-space and bimaterials.Based on the elastic theory of QCs,the Stroh formalism is used to derive the general solutions of displacements and stresses.Then,we obtain the analytical solutions of half-space and bimaterial Green’s functions.Besides,the interfacial Green’s function for bimaterials is also obtained in the analytical form.Before numerical studies,a comparative study is carried out to validate the present solutions.Typical numerical examples are performed to investigate the effects of multi-physics loadings such as the line force,the line dislocation,the line charge,and the phason line force.As a result,the coupling effect among the phonon field,the phason field,and the electric field is prominent,and the butterfly-shaped contours are characteristic in 2D PQCs.In addition,the changes of material parameters cause variations in physical quantities to a certain degree.

关键词： Green’s function two-dimensional(2D)piezoelectric quasicrystal(PQC) Stroh formalism half-space bimaterial

Local weak solutions of the isentropic compressible Navier-Stokes equations in a half-space

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Science China Mathematics 2022年第5期65卷 993-1002页

作者： Qin Duan Xiangdi Huang College of Mathematics and Statistics Shenzhen UniversityShenzhen 518060China Institute of Mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China Hua Loo-Keng Center for Mathematical Sciences Chinese Academy of SciencesBeijing 100190China

In this paper, we establish the local existence of weak solutions with higher regularity of the threedimensional half-space compressible isentropic Navier-Stokes equations with the adiabatic exponent γ > 1 in the pre... 详细信息

关键词： Navier-Stokes equation half-space local weak solution vacuum

THE ELASTIC FIELD INDUCED BY A HEMISPHERICAL INCLUSION IN THE half—space

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Acta Mechanica Sinica 2003年第3期19卷 253-262页

作者：吴林志 SchoolofAstronautics HarbinInstituteofTechnologyHarbin150001China

The elastic field induced by a hemispherical inclusion with uniform eigenstrains in a semi-infinite elastic medium is solved by using the Green's function method and series expansion technique.The exact solutions are presented for the displacement and stress fields which can be expressed by complete elliptic integrals of the first,second,and third kinds and hypergeometric functions.The present method can be used to determine the corresponding elastic fields when the shape of the inclusion is a spherical crown or a spherical segment.Finally,numerical results are given for the displacement and stress fields along the axis of symmetry (x3-axis).

关键词： hemispherical inclusion elastic field Green's function eigenstrain half-space

Solution of a Green's function for a saturated porous medium in a half-space subjected to a torsional force

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Earthquake Engineering and Engineering Vibration 2012年第1期11卷 133-138页

作者： Ding Boyang Chen Jun Ouyang Ming College of Civil Engineering and Architecture Zhejiang University of TechnologyHangzhou 310014China

Based on the solutions of the Green＇s function for a saturated porous medium obtained by the authors, and using transformation of axisymmetric coordinates, Sommerfeld integrals and superposition of the influence field on a free surface, the authors have obtained displacement solutions of a saturated porous medium subjected to a torsional force in a half-space. The relationship curves of the displacement solutions and various parameters （permeability, frequency, etc.） under action of a unit of torque are also given in this paper. The results are consistent with previous Reissner＇s solutions, where a two-phase medium decays to a single-phase medium. The solution is useful in solving relevant dynamic problems of a two- phase saturated medium in engineering.

关键词： torsional force saturated porous medium Green＇s function half-space Sommerfeld integrals

STRESS IN TRANSVERSELY ISOTROPIC half-space WITH TYPICAL LOADS ACTING ON ITS SURFACE

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Applied Mathematics and Mechanics(English Edition) 2000年第8期21卷 901-908页

作者：吴世明梁剑胡亚元 Department of Geotechnical Engineering Tongji University P R China Department of Mechanics Zhejiang University Hangzhou P R China Department of Civil Engineering Zhejiang University Hangzhou P R China

Based on the results of Hu and Lekhnitskii, the united solution of additional vertical stress coefficient for both transversely isotropic and isotropic half-space was obtained. Five typical load cases, namely, vertical circular uniform load, rectangular uniform load, linearly distributed rectangular load, uniform linear and strip loads are studied in detail. The final solutions are expressed in terms of elementary functions. Numerical results show that there are anisotropic effects on the variation of additional vertical stress coefficients.

关键词： transversely isotropy half-space additional stress coefficients

EFFECT OF SURFACE ENERGY ON DISLOCATION-INDUCED FIELD IN half-space WITH APPLICATION TO THIN FILM-SUBSTRATE SYSTEMS

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Acta Mechanica Solida Sinica 2009年第5期22卷 436-442页

作者： Ganyun Huang Bob Svendsen Zhixing Lu Institute of Mechanics Dortmund University of Technology 44221 Dortmund Germany Sehool of Mechanical Engineering Tianjin University Tianjin 300072 China Department of Mechanical Engineering University of Colorado at Boulder Colorado USA

In this work the elastic field of an edge dislocation in a half-space with the effect of surface energy has been obtained. The elastic field is then used to study the image force on the dislocation, the critical thickness for dislocation generation in epitaxial thin films with strain mismatch and the yielding strength of thin films on substrates. The results show that the image forces on the dislocation deviate from the conventional solutions when the distance of the dislocation from the free surface is smaller than several times of the characteristic length. Also due to the effect of surface energy, the critical thickness for dislocation generation is smaller than that predicted by the conventional elastic solutions and the extent of the deviation depends on the magnitude of mismatch strain. In contrast, the effect of surface energy on the yielding strength for many practical thin films can be neglected except for some soft ones where the characteristic length is comparable to the thickness.

关键词： thin film surface energy effect dislocation half-space critical thickness yielding strength

STEADY-STATE RESPONSE OF A TIMOSHENKO BEAM ON AN ELASTIC half-space UNDER A MOVING LOAD

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Acta Mechanica Solida Sinica 2006年第1期19卷 26-39页

作者： Chen Vunmin Wang Changjing Department of Civil Engineering Zhejiang University Hangzhou 310027 China City College Zhejiang University Hangzhou 310015 China

By introducing the equivalent stiffness of an elastic half-space interacting with a Timoshenko beam, the displacement solution of the beam resting on an elastic half-space subjected to a moving load is presented. Based on the relative relation of wave velocities of the half-space and the beam, four cases with the combination of different parameters of the half-space and the beam, the system of soft beam and hard half-space, the system of sub-soft beam and hard half- space, the system of sub-hard beam and soft half-space, and the system of hard beam and soft half-space are considered. The critical velocities of the moving load are studied using dispersion curves. It is found that critical velocities of the moving load on the Timoshenko beam depend on the relative relation of wave velocities of the half-space and the beam. The Rayleigh wave velocity in the half-space is always a critical velocity and the response of the system will be infinite when the load velocity reaches it. For the system of soft beam and hard half-space, wave velocities of the beam are also critical velocities. Besides the shear wave velocity of the beam, there is an additional minimum critical velocity for the system of sub-soft beam and hard half-space. While for systems of （sub-） hard beams and soft half-space, wave velocities of the beam are no longer critical ones. Comparison with the Euler-Bernoulli beam shows that the critical velocities and response of the two types of beams are much different for the system of （sub-） soft beam and hard half-space but are similar to each other for the system of （sub-） hard beam and soft half space. The largest displacement of the beam is almost at the location of the load and the displacement along the beam is almost symmetrical if the load velocity is smaller than the minimum critical velocity （the shear wave velocity of the beam for the system of soft beam and hard half-space）. The largest displacement of the beam shifts behind the load and the asymmetry of the displacement along the beam increases w

关键词： critical velocities equivalent stiffness Timoshenko beam half-space moving load,dispersion curve

Long Time L^1-behavior for the Incompressible Magneto-hydrodynamic Equations in a half-space

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Acta Mathematicae Applicatae Sinica 2016年第4期32卷 933-944页

作者： Zhao-xia LIU Xing-jiang YU Department of information and Computational Science School of SciencesMinzu University of China College of Mathematics Science Liaocheng University

The large time Ll-behavior of the strong solution （including the first and second order spacial derivatives） to the incompressible magneto-hydrodynamic （MHD） equations is given in a half-space. The main tool employed in this article is a new weighted estimate for the Stokes flow in L1（Rn＋）, such a study is of independent interest.

关键词： MHD equation strong solution asymptotic behavior half-space

Dynamic Stress and Pore Pressure Around Circular Cavity in Saturated Porous Elastic half-space Under Harmonic Plane Dilatational Waves

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Journal of Shanghai Jiaotong university(Science) 2006年第4期11卷 506-511页

作者：姜领发王建华周香莲 School of Naval Architecture Ocean & Civil Eng. Shanghai Jiaotong Univ.

Dynamic stress concentration and pore pressure concentration around an infinitely long cylindrical cavity of circular cross-section subjected to harmonic plane dilatational waves in fluid-saturated porous elastic half-space were obtained by a complex function method based on potential function and multi-polar coordinate. The steady state Biot’s dynamic field equations of porous elastic solid with a viscous liquid were uncoupled into Helmholtz equations via given potential functions. A circular cavity with large radius is used to replace the straight boundary of the saturated porous elastic half-space. The stresses and pore pressures were obtained by using complex functions in multi-polar coordinates with certain boundary conditions of the solid matrix and the fluid matrix. The approximate solutions were compared to existing numerical solutions. Then the variations of the coefficients of dynamic stress concentration and the pore pressures concentration on boundaries of the cavity were discussed with different parameter conditions. The results of the given numerical example indicate that the method used is useful and efficient to the scattering and dynamic stress concentration of plane dilatational waves in saturated porous elastic half-space.

关键词： multi-polar coordinate saturated porous elastic half-space viscous complex function cavity