The wave propagation behavior in an elastic wedge-shaped medium with an arbitrary shaped cylindrical canyon at its vertex has been studied.Numerical computation of the wave displacement field is carried out on and nea...The wave propagation behavior in an elastic wedge-shaped medium with an arbitrary shaped cylindrical canyon at its vertex has been studied.Numerical computation of the wave displacement field is carried out on and near the canyon surfaces using weighted-residuals(moment method).The wave displacement fields are computed by the residual method for the cases of elliptic,circular,rounded-rectangular and flat-elliptic canyons,The analysis demonstrates that the resulting surface displacement depends,as in similar previous analyses,on several factors including,but not limited,to the angle of the wedge,the geometry of the vertex,the frequencies of the incident waves,the angles of incidence,and the material properties of the media.The analysis provides intriguing results that help to explain geophysical observations regarding the amplification of seismic energy as a function of site conditions.展开更多
In numerical simulation of wave scattering under oblique incident body waves using the finite element method, the free field motion at the incident lateral boundary induced by the background layered half-space complic...In numerical simulation of wave scattering under oblique incident body waves using the finite element method, the free field motion at the incident lateral boundary induced by the background layered half-space complicates the computational area. In order to replace the complex frequency domain method, a time-domain method to calculate the free field motion of a layered half-space subjected to oblique incident body waves is developed in this paper. The new method decouples the equations of motion used in the finite element method and offers an interpolation formula of the free field motion. This formula is based on the fact that the apparent horizontal velocity of the free field motion is constant and can be calculated exactly. Both the theoretical analysis and numerical results demonstrate that the proposed method offers a high degree of accuracy.展开更多
This paper presents a novel wideband fast multipole boundary element approach to 3D half-space/planesymmetric acoustic wave problems.The half-space fundamental solution is employed in the boundary integral equations s...This paper presents a novel wideband fast multipole boundary element approach to 3D half-space/planesymmetric acoustic wave problems.The half-space fundamental solution is employed in the boundary integral equations so that the tree structure required in the fast multipole algorithm is constructed for the boundary elements in the real domain only.Moreover,a set of symmetric relations between the multipole expansion coefficients of the real and image domains are derived,and the half-space fundamental solution is modified for the purpose of applying such relations to avoid calculating,translating and saving the multipole/local expansion coefficients of the image domain.The wideband adaptive multilevel fast multipole algorithm associated with the iterative solver GMRES is employed so that the present method is accurate and efficient for both lowand high-frequency acoustic wave problems.As for exterior acoustic problems,the Burton-Miller method is adopted to tackle the fictitious eigenfrequency problem involved in the conventional boundary integral equation method.Details on the implementation of the present method are described,and numerical examples are given to demonstrate its accuracy and efficiency.展开更多
Natural soil generally exhibits significant transverse isotropy(TI)due to weathering and sedimentation,meaning that horizontal moduli differ from their vertical counterpart.The TI mechanical model is more appropriate ...Natural soil generally exhibits significant transverse isotropy(TI)due to weathering and sedimentation,meaning that horizontal moduli differ from their vertical counterpart.The TI mechanical model is more appropriate for actual situations.Although soil exhibits material nonlinearity under earthquake excitation,existing research on the TI medium is limited to soil linearity and neglects the nonlinear response of TI sites.A 2D equivalent linear model for a layered TI half-space subjected to seismic waves is derived in the transformed wave number domain using the exact dynamic stiffness matrix of the TI medium.This study introduces a method for determining the effective shear strain of TI sites under oblique wave incidence,and further describes a systematic study on the effects of TI parameters and soil nonlinearity on site responses.Numerical results indicate that seismic responses of the TI medium significantly differ from those of isotropic sites and that the responses are highly dependent on TI parameters,particularly in nonlinear cases,while also being sensitive to incident angle and excitation intensity.Moreover,the differences in peak acceleration and waveform for various TI materials may also be amplified due to the strong nonlinearity.The study provides valuable insights for improving the accuracy of seismic response analysis in engineering applications.展开更多
The Laguerre polynomial method has been successfully used to investigate the dynamic responses of a half-space.However,it fails to obtain the correct stress at the interfaces in a layered half-space,especially when th...The Laguerre polynomial method has been successfully used to investigate the dynamic responses of a half-space.However,it fails to obtain the correct stress at the interfaces in a layered half-space,especially when there are significant differences in material properties.Therefore,a coupled Legendre-Laguerre polynomial method with analytical integration is proposed.The Rayleigh waves in a one-dimensional(1D)hexagonal quasicrystal(QC)layered half-space with an imperfect interface are investigated.The correctness is validated by comparison with available results.Its computation efficiency is analyzed.The dispersion curves of the phase velocity,displacement distributions,and stress distributions are illustrated.The effects of the phonon-phason coupling and imperfect interface coefficients on the wave characteristics are investigated.Some novel findings reveal that the proposed method is highly efficient for addressing the Rayleigh waves in a QC layered half-space.It can save over 99%of the computation time.This method can be expanded to investigate waves in various layered half-spaces,including earth-layered media and surface acoustic wave(SAW)devices.展开更多
This paper presents a 2.5D scattering of incident plane SV waves by a canyon in a layered half-space by using the indirect boundary element method （IBEM）. A free field response analysis is performed to provide the d...This paper presents a 2.5D scattering of incident plane SV waves by a canyon in a layered half-space by using the indirect boundary element method （IBEM）. A free field response analysis is performed to provide the displacements and stresses on the boundary of the canyon where fictitious uniform moving loads are applied to calculate the Green＇s fi.mctions for the displacements and stresses. The amplitudes of the loads are determined by the boundary conditions. The free field displacements are added to the fictitious uniform moving loads induced displacements and the total response is obtained. Numerical calculations are performed for a canyon with homogenous and in one layer over bedrock. The effects of the thickness and stiffness of the layer on the amplification are studied and discussed.展开更多
The dynamic soil-tunnel interaction is studied by indirect boundary element method （IBEM）, using the model of a rigid tunnel in layered half-space, which is simplified to a single soil layer on elastic bedrock, subj...The dynamic soil-tunnel interaction is studied by indirect boundary element method （IBEM）, using the model of a rigid tunnel in layered half-space, which is simplified to a single soil layer on elastic bedrock, subjected to incident plane SH waves. The accuracy of the results is verified through comparison with the analytical solution. It is shown that soil-tunnel interaction in layered half-space is larger than that in homogeneous half-space and this interaction mechanism is essentially different from that of soil-foundation-superstructure interaction.展开更多
In the past two decades numerous studies were made to develop and improve the theory and practical computation techniques of synthesizing theoretical seismograms for the model of multi-layered half-space. Today, synth...In the past two decades numerous studies were made to develop and improve the theory and practical computation techniques of synthesizing theoretical seismograms for the model of multi-layered half-space. Today, synthesizing theoretical seismograms in multi-layered half-space is an important tool for understanding the structure of the Earth’s interior as well as the seismic source process from well-recorded seismograms data. As part of a review of the state-of-the-art, in this article I shall present a systematic and self-contained theory of elastic waves in multi-layered half-space media based on the developments in the past two decades.展开更多
The dynamic stiffness method combined with the Fourier transform is utilized to derive the in-plane Green’s functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic（TI）half-s...The dynamic stiffness method combined with the Fourier transform is utilized to derive the in-plane Green’s functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic（TI）half-space.The loaded layer is fixed to obtain solutions restricted in it and the corresponding reactions forces,which are then applied to the total system with the opposite sign.By adding solutions restricted in the loaded layer to solutions from the reaction forces,the global solutions in the wavenumber domain are obtained,and the dynamic Green’s functions in the space domain are recovered by the inverse Fourier transform.The presented formulations can be reduced to the isotropic case developed by Wolf（1985）,and are further verified by comparisons with existing solutions in a uniform isotropic as well as a layered TI halfspace subjected to horizontally distributed loads which are special cases of the more general problem addressed.The deduced Green’s functions,in conjunction with boundary element methods,will lead to significant advances in the investigation of a variety of wave scattering,wave radiation and soil-structure interaction problems in a layered TI site.Selected numerical results are given to investigate the influence of material anisotropy,frequency of excitation,inclination angle and layered on the responses of displacement and stress,and some conclusions are drawn.展开更多
Diffraction of plane P waves around an alluvial valley of arbitrary shape in poroelastic half-space is investigated by using an indirect boundary integral equation method. Based on the Green＇s fimctions of line sourc...Diffraction of plane P waves around an alluvial valley of arbitrary shape in poroelastic half-space is investigated by using an indirect boundary integral equation method. Based on the Green＇s fimctions of line source in poroelastic half-space, the scattered waves are constructed using the fictitious wave sources close to the interface of the valley and the density of ficti- tious wave sources are determined by boundary conditions. The precision of the method is verified by the satisfaction extent of boundary conditions, and the comparison between the degenerated solutions and available results in single-phase case. Finally, the nature of diffraction of plane P waves around an alluvial valley in poroelastic half-space is investigated in detail through nu- merical examples.展开更多
The dynamic soil-tunnel interaction is studied by the model of a rigid tunnel embedded in layered half-space, which is simplified as a single soil layer on elastic bedrock to the excitation of P- and SV-waves. The ind...The dynamic soil-tunnel interaction is studied by the model of a rigid tunnel embedded in layered half-space, which is simplified as a single soil layer on elastic bedrock to the excitation of P- and SV-waves. The indirect boundary element method is used, combined with the Green＇ s function of distributed loads acting on inclined lines. It is shown that the dynamic characteristics of soil-tunnel interaction in layered half-space are different much from that in homoge- neous half-space, and that the mechanism of soil-tunnel interaction is also different much from that of soil-founda- tion-superstructure interaction. For oblique incidence, the tunnel response for in-plane incident SV-waves is com- pletely different from that for incident SH-waves, while the tunnel response for vertically incident SV-wave is very similar to that of vertically incident SH-wave.展开更多
The indirect boundary element method (IBEM) is used to study the surface motion of an alluvial valley in layered half-space for incident plane P-waves based on Wolf’s theory. Firstly, the free field response can be s...The indirect boundary element method (IBEM) is used to study the surface motion of an alluvial valley in layered half-space for incident plane P-waves based on Wolf’s theory. Firstly, the free field response can be solved by the direct stiffness method, and the scattering wave response is calculated by Green’s functions of distributed loads acting on inclined lines in a layered half-space. The method is verified by comparing its results with literature and numerical analyses are performed by taking the amplification of incident plane P-waves by an alluvial valley in one soil layer resting on bedrock as an example. The results show that there exist distinct differences between the wave amplification by an alluvial valley embedded in layered half-space and that in homogeneous half-space and there is interaction between the valley and the soil layer. The amplitudes are relatively large when incident frequencies are close to the soil layer’s resonant frequencies.展开更多
A cylindrical system of vector functions, the stiffness matrix method and the corresponding recursive algorithm are proposed to investigate the static response of transversely isotropic,layered magneto-electro-elastic...A cylindrical system of vector functions, the stiffness matrix method and the corresponding recursive algorithm are proposed to investigate the static response of transversely isotropic,layered magneto-electro-elastic（MEE） structures over a homogeneous half-space substrate subjected to circular surface loading. In terms of the system of vector functions, we expand the extended displacements and stresses, and deduce two sets of ordinary differential equations, which are related to the expansion coeficients. The solution to one of the two sets of these ordinary differential equations can be evaluated by using the stiffness matrix method and the corresponding recursive algorithm. These expansion coeficients are then integrated by adaptive Gaussian quadrature to obtain the displacements and stresses in the physical domain. Two types of surface loads, mechanical pressure and electric loading,are considered in the numerical examples. The calculated results show that the proposed technique is stable and effective in analyzing the layered half-space MEE structures under surface loading.展开更多
This work has a two-fold purpose.On the one hand,the theoretical formulation of a three-dimensional(3D)acoustic propagation model for shallow waters with a constant sound speed is presented,based on the boundary eleme...This work has a two-fold purpose.On the one hand,the theoretical formulation of a three-dimensional(3D)acoustic propagation model for shallow waters with a constant sound speed is presented,based on the boundary element method(BEM),which uses a half-space Green function instead of the more conventional free-space Green function.On the other hand,a numerical implementation is illustrated to explore the formulation in simple idealized cases,controlled by a few parameters,which provides necessary tests for the accuracy and performance of the model.The half-space Green's function,which has been previously used in scattering and diffraction,adds terms to the usual expressions of the integral operators without altering their continuity properties.Verifications against the wavenumber integration solution of the Pekeris waveguide suggest that the model allows an adequate prediction for the acoustic field.Likewise,numerical experiments in relation to the necessary mesh size for the description of the water-marine sediment interface lead to the conclusion that a transmission loss prediction with acceptable accuracy can be obtained with the use of a limited mesh around the desired evaluation region.展开更多
Gibali[J.Nonlinear Anal.Optim.,2015,6(1):41‒51]presented a self-adaptive subgradient extragradient projection method for solving variational inequalities without Lipschitz continuity,where its next iterative point was...Gibali[J.Nonlinear Anal.Optim.,2015,6(1):41‒51]presented a self-adaptive subgradient extragradient projection method for solving variational inequalities without Lipschitz continuity,where its next iterative point was obtained by projecting a vector onto a specific half-space.In this paper,we present new kinds of self-adaptive subgradient extragradient projection methods by using a new descent direction.With the help of the techniques in the method of He and Liao[J.Optim.Theory Appl,2002,112(1):111‒128],we get a longer step-size for these kinds of algorithms,which proves the global convergence of the generated sequence.Numerical results show that these kinds of extragradient subgradient projection methods are less dependent on the choice of the initial point,the dimension of the variational inequalities,and the tolerance of accuracy than the known methods.Moreover,the new methods proposed in this paper outperform(with respect to the number of iterations and cpu-time)the method presented by Gibali.展开更多
In the numerical study of rough surfaces in contact problem, the flexible body beneath the roughness is commonly assumed as a half-space or a half-plane. The surface displacement on the boundary, the displacement comp...In the numerical study of rough surfaces in contact problem, the flexible body beneath the roughness is commonly assumed as a half-space or a half-plane. The surface displacement on the boundary, the displacement components and state of stress inside the half-space can be determined through the convolution of the traction and the corresponding influence function in a closed-form. The influence function is often represented by the Boussinesq-Cerruti solution and the Flamant solution for three-dimensional elasticity and plane strain/stress, respectively. In this study, we rigorously show that any numerical model using the above mentioned half-space solution is a special form of the boundary element method(BEM). The boundary integral equations(BIEs) in the BEM is simplified to the Flamant solution when the domain is strictly a half-plane for the plane strain/stress condition. Similarly, the BIE is degraded to the Boussinesq-Cerruti solution if the domain is strictly a half-space. Therefore, the numerical models utilizing these closed-form influence functions are the special BEM where the domain is a half-space(or a half-plane). This analytical work sheds some light on how to accurately simulate the non-half-space contact problem using the BEM.展开更多
文摘The wave propagation behavior in an elastic wedge-shaped medium with an arbitrary shaped cylindrical canyon at its vertex has been studied.Numerical computation of the wave displacement field is carried out on and near the canyon surfaces using weighted-residuals(moment method).The wave displacement fields are computed by the residual method for the cases of elliptic,circular,rounded-rectangular and flat-elliptic canyons,The analysis demonstrates that the resulting surface displacement depends,as in similar previous analyses,on several factors including,but not limited,to the angle of the wedge,the geometry of the vertex,the frequencies of the incident waves,the angles of incidence,and the material properties of the media.The analysis provides intriguing results that help to explain geophysical observations regarding the amplification of seismic energy as a function of site conditions.
基金National Natural Science Foundation of China Under Grant No. 50178065
文摘In numerical simulation of wave scattering under oblique incident body waves using the finite element method, the free field motion at the incident lateral boundary induced by the background layered half-space complicates the computational area. In order to replace the complex frequency domain method, a time-domain method to calculate the free field motion of a layered half-space subjected to oblique incident body waves is developed in this paper. The new method decouples the equations of motion used in the finite element method and offers an interpolation formula of the free field motion. This formula is based on the fact that the apparent horizontal velocity of the free field motion is constant and can be calculated exactly. Both the theoretical analysis and numerical results demonstrate that the proposed method offers a high degree of accuracy.
基金supported by the National Natural Science Foundation of China (11172291)the National Science Foundation for Post-doctoral Scientists of China (2012M510162)the Fundamental Research Funds for the Central Universities (KB2090050024)
文摘This paper presents a novel wideband fast multipole boundary element approach to 3D half-space/planesymmetric acoustic wave problems.The half-space fundamental solution is employed in the boundary integral equations so that the tree structure required in the fast multipole algorithm is constructed for the boundary elements in the real domain only.Moreover,a set of symmetric relations between the multipole expansion coefficients of the real and image domains are derived,and the half-space fundamental solution is modified for the purpose of applying such relations to avoid calculating,translating and saving the multipole/local expansion coefficients of the image domain.The wideband adaptive multilevel fast multipole algorithm associated with the iterative solver GMRES is employed so that the present method is accurate and efficient for both lowand high-frequency acoustic wave problems.As for exterior acoustic problems,the Burton-Miller method is adopted to tackle the fictitious eigenfrequency problem involved in the conventional boundary integral equation method.Details on the implementation of the present method are described,and numerical examples are given to demonstrate its accuracy and efficiency.
基金National Natural Science Foundation of China under Grant No.U2139208。
文摘Natural soil generally exhibits significant transverse isotropy(TI)due to weathering and sedimentation,meaning that horizontal moduli differ from their vertical counterpart.The TI mechanical model is more appropriate for actual situations.Although soil exhibits material nonlinearity under earthquake excitation,existing research on the TI medium is limited to soil linearity and neglects the nonlinear response of TI sites.A 2D equivalent linear model for a layered TI half-space subjected to seismic waves is derived in the transformed wave number domain using the exact dynamic stiffness matrix of the TI medium.This study introduces a method for determining the effective shear strain of TI sites under oblique wave incidence,and further describes a systematic study on the effects of TI parameters and soil nonlinearity on site responses.Numerical results indicate that seismic responses of the TI medium significantly differ from those of isotropic sites and that the responses are highly dependent on TI parameters,particularly in nonlinear cases,while also being sensitive to incident angle and excitation intensity.Moreover,the differences in peak acceleration and waveform for various TI materials may also be amplified due to the strong nonlinearity.The study provides valuable insights for improving the accuracy of seismic response analysis in engineering applications.
基金Project supported by the National Natural Science Foundation of China(No.12102131)the Natural Science Foundation of Henan Province of China(No.242300420248)the International Science and Technology Cooperation Project of Henan Province of China(No.242102521010)。
文摘The Laguerre polynomial method has been successfully used to investigate the dynamic responses of a half-space.However,it fails to obtain the correct stress at the interfaces in a layered half-space,especially when there are significant differences in material properties.Therefore,a coupled Legendre-Laguerre polynomial method with analytical integration is proposed.The Rayleigh waves in a one-dimensional(1D)hexagonal quasicrystal(QC)layered half-space with an imperfect interface are investigated.The correctness is validated by comparison with available results.Its computation efficiency is analyzed.The dispersion curves of the phase velocity,displacement distributions,and stress distributions are illustrated.The effects of the phonon-phason coupling and imperfect interface coefficients on the wave characteristics are investigated.Some novel findings reveal that the proposed method is highly efficient for addressing the Rayleigh waves in a QC layered half-space.It can save over 99%of the computation time.This method can be expanded to investigate waves in various layered half-spaces,including earth-layered media and surface acoustic wave(SAW)devices.
基金National Natural Science Foundation of China Under Grant No.50908156 and 50978183Tianjin Natural Science Foundation Under Grant No. 07JCZDJC10100
文摘This paper presents a 2.5D scattering of incident plane SV waves by a canyon in a layered half-space by using the indirect boundary element method （IBEM）. A free field response analysis is performed to provide the displacements and stresses on the boundary of the canyon where fictitious uniform moving loads are applied to calculate the Green＇s fi.mctions for the displacements and stresses. The amplitudes of the loads are determined by the boundary conditions. The free field displacements are added to the fictitious uniform moving loads induced displacements and the total response is obtained. Numerical calculations are performed for a canyon with homogenous and in one layer over bedrock. The effects of the thickness and stiffness of the layer on the amplification are studied and discussed.
基金National Natural Science Foundation of China under Grant 51378384Key Project of Natural Science Foundation of Tianjin Municipality under Grant 12JCZDJC29000
文摘The dynamic soil-tunnel interaction is studied by indirect boundary element method （IBEM）, using the model of a rigid tunnel in layered half-space, which is simplified to a single soil layer on elastic bedrock, subjected to incident plane SH waves. The accuracy of the results is verified through comparison with the analytical solution. It is shown that soil-tunnel interaction in layered half-space is larger than that in homogeneous half-space and this interaction mechanism is essentially different from that of soil-foundation-superstructure interaction.
文摘In the past two decades numerous studies were made to develop and improve the theory and practical computation techniques of synthesizing theoretical seismograms for the model of multi-layered half-space. Today, synthesizing theoretical seismograms in multi-layered half-space is an important tool for understanding the structure of the Earth’s interior as well as the seismic source process from well-recorded seismograms data. As part of a review of the state-of-the-art, in this article I shall present a systematic and self-contained theory of elastic waves in multi-layered half-space media based on the developments in the past two decades.
基金National Natural Science Foundation of China under grant No.51578373 and 51578372the Natural Science Foundation of Tianjin Municipality under Grant No.16JCYBJC21600
文摘The dynamic stiffness method combined with the Fourier transform is utilized to derive the in-plane Green’s functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic（TI）half-space.The loaded layer is fixed to obtain solutions restricted in it and the corresponding reactions forces,which are then applied to the total system with the opposite sign.By adding solutions restricted in the loaded layer to solutions from the reaction forces,the global solutions in the wavenumber domain are obtained,and the dynamic Green’s functions in the space domain are recovered by the inverse Fourier transform.The presented formulations can be reduced to the isotropic case developed by Wolf（1985）,and are further verified by comparisons with existing solutions in a uniform isotropic as well as a layered TI halfspace subjected to horizontally distributed loads which are special cases of the more general problem addressed.The deduced Green’s functions,in conjunction with boundary element methods,will lead to significant advances in the investigation of a variety of wave scattering,wave radiation and soil-structure interaction problems in a layered TI site.Selected numerical results are given to investigate the influence of material anisotropy,frequency of excitation,inclination angle and layered on the responses of displacement and stress,and some conclusions are drawn.
基金supported by National Natural Science Foundation of China (50978183)
文摘Diffraction of plane P waves around an alluvial valley of arbitrary shape in poroelastic half-space is investigated by using an indirect boundary integral equation method. Based on the Green＇s fimctions of line source in poroelastic half-space, the scattered waves are constructed using the fictitious wave sources close to the interface of the valley and the density of ficti- tious wave sources are determined by boundary conditions. The precision of the method is verified by the satisfaction extent of boundary conditions, and the comparison between the degenerated solutions and available results in single-phase case. Finally, the nature of diffraction of plane P waves around an alluvial valley in poroelastic half-space is investigated in detail through nu- merical examples.
基金supported by the National Natural Science Foundation of China(No.51378384)the Key Project of Natural Science Foundation of Tianjin Municipality(No. 12JCZDJC29000)
文摘The dynamic soil-tunnel interaction is studied by the model of a rigid tunnel embedded in layered half-space, which is simplified as a single soil layer on elastic bedrock to the excitation of P- and SV-waves. The indirect boundary element method is used, combined with the Green＇ s function of distributed loads acting on inclined lines. It is shown that the dynamic characteristics of soil-tunnel interaction in layered half-space are different much from that in homoge- neous half-space, and that the mechanism of soil-tunnel interaction is also different much from that of soil-founda- tion-superstructure interaction. For oblique incidence, the tunnel response for in-plane incident SV-waves is com- pletely different from that for incident SH-waves, while the tunnel response for vertically incident SV-wave is very similar to that of vertically incident SH-wave.
基金Supported by National Natural Science Foundation of China (No. 50978156 and No. 50908183)
文摘The indirect boundary element method (IBEM) is used to study the surface motion of an alluvial valley in layered half-space for incident plane P-waves based on Wolf’s theory. Firstly, the free field response can be solved by the direct stiffness method, and the scattering wave response is calculated by Green’s functions of distributed loads acting on inclined lines in a layered half-space. The method is verified by comparing its results with literature and numerical analyses are performed by taking the amplification of incident plane P-waves by an alluvial valley in one soil layer resting on bedrock as an example. The results show that there exist distinct differences between the wave amplification by an alluvial valley embedded in layered half-space and that in homogeneous half-space and there is interaction between the valley and the soil layer. The amplitudes are relatively large when incident frequencies are close to the soil layer’s resonant frequencies.
基金supported by National Natural Science Foundation of China (Nos. U1333201, 11502123 and 11262012 )
文摘A cylindrical system of vector functions, the stiffness matrix method and the corresponding recursive algorithm are proposed to investigate the static response of transversely isotropic,layered magneto-electro-elastic（MEE） structures over a homogeneous half-space substrate subjected to circular surface loading. In terms of the system of vector functions, we expand the extended displacements and stresses, and deduce two sets of ordinary differential equations, which are related to the expansion coeficients. The solution to one of the two sets of these ordinary differential equations can be evaluated by using the stiffness matrix method and the corresponding recursive algorithm. These expansion coeficients are then integrated by adaptive Gaussian quadrature to obtain the displacements and stresses in the physical domain. Two types of surface loads, mechanical pressure and electric loading,are considered in the numerical examples. The calculated results show that the proposed technique is stable and effective in analyzing the layered half-space MEE structures under surface loading.
文摘This work has a two-fold purpose.On the one hand,the theoretical formulation of a three-dimensional(3D)acoustic propagation model for shallow waters with a constant sound speed is presented,based on the boundary element method(BEM),which uses a half-space Green function instead of the more conventional free-space Green function.On the other hand,a numerical implementation is illustrated to explore the formulation in simple idealized cases,controlled by a few parameters,which provides necessary tests for the accuracy and performance of the model.The half-space Green's function,which has been previously used in scattering and diffraction,adds terms to the usual expressions of the integral operators without altering their continuity properties.Verifications against the wavenumber integration solution of the Pekeris waveguide suggest that the model allows an adequate prediction for the acoustic field.Likewise,numerical experiments in relation to the necessary mesh size for the description of the water-marine sediment interface lead to the conclusion that a transmission loss prediction with acceptable accuracy can be obtained with the use of a limited mesh around the desired evaluation region.
文摘Gibali[J.Nonlinear Anal.Optim.,2015,6(1):41‒51]presented a self-adaptive subgradient extragradient projection method for solving variational inequalities without Lipschitz continuity,where its next iterative point was obtained by projecting a vector onto a specific half-space.In this paper,we present new kinds of self-adaptive subgradient extragradient projection methods by using a new descent direction.With the help of the techniques in the method of He and Liao[J.Optim.Theory Appl,2002,112(1):111‒128],we get a longer step-size for these kinds of algorithms,which proves the global convergence of the generated sequence.Numerical results show that these kinds of extragradient subgradient projection methods are less dependent on the choice of the initial point,the dimension of the variational inequalities,and the tolerance of accuracy than the known methods.Moreover,the new methods proposed in this paper outperform(with respect to the number of iterations and cpu-time)the method presented by Gibali.
文摘In the numerical study of rough surfaces in contact problem, the flexible body beneath the roughness is commonly assumed as a half-space or a half-plane. The surface displacement on the boundary, the displacement components and state of stress inside the half-space can be determined through the convolution of the traction and the corresponding influence function in a closed-form. The influence function is often represented by the Boussinesq-Cerruti solution and the Flamant solution for three-dimensional elasticity and plane strain/stress, respectively. In this study, we rigorously show that any numerical model using the above mentioned half-space solution is a special form of the boundary element method(BEM). The boundary integral equations(BIEs) in the BEM is simplified to the Flamant solution when the domain is strictly a half-plane for the plane strain/stress condition. Similarly, the BIE is degraded to the Boussinesq-Cerruti solution if the domain is strictly a half-space. Therefore, the numerical models utilizing these closed-form influence functions are the special BEM where the domain is a half-space(or a half-plane). This analytical work sheds some light on how to accurately simulate the non-half-space contact problem using the BEM.
