The finite element artificial transmitting boundary method is employed here to treat the near field scattering of a cylindrical wave from an irregular cylinder. A comparison is made between this method and the analy...The finite element artificial transmitting boundary method is employed here to treat the near field scattering of a cylindrical wave from an irregular cylinder. A comparison is made between this method and the analytical one. And then examples are given to demonstrate the solution of several problems of the irregular object scattering. The method can not only produce clear physical pictures, but can efficiently handle many complicated scattering problems.展开更多
After a brief review of studies on artificial boundaries in dynamic soil-structure interaction, a three-dimensional viscous-spring artificial boundary （VSAB） in the time domain is developed in this paper. First, the...After a brief review of studies on artificial boundaries in dynamic soil-structure interaction, a three-dimensional viscous-spring artificial boundary （VSAB） in the time domain is developed in this paper. First, the 3D VSAB equations in the normal and tangential directions are derived based on the elastic wave motion theory. Secondly, a numerical simulation technique of wave motion equations along with the VSAB condition in the time domain is studied. Finally, numerical examples of some classical elastic wave motion problems are presented and the results are compared with the associated theoretical solutions, demonstrating that high precision and adequate stability can be achieved by using the proposed 3D VSAB. The proposed 3D VSAB can be conveniently incorporated in the general finite element program, which is commonly used to study dynamic soil-structure interaction problems.展开更多
An improved version of the regular boundary element method, the artificial boundary node approach, is derived. A simple contact algorithm is designed and implemented into the direct boundary element, regular boundary ...An improved version of the regular boundary element method, the artificial boundary node approach, is derived. A simple contact algorithm is designed and implemented into the direct boundary element, regular boundary element and artificial boundary node approaches. The exisiting and derived approaches are tested using some case studies. The results of the artificial boundary node approach are compared with those of the existing boundary element program, the regular element approach, ANSYS and analytical solution whenever possible. The results show the effectiveness of the artificial boundary node approach for a wider range of boundary offsets.展开更多
Anew artificial boundary model based on multi-directional transmitting and viscous-spring artificial boundary theories is proposed to absorb stress waves in a saturated soil foundation in dynamic analysis. Since shear...Anew artificial boundary model based on multi-directional transmitting and viscous-spring artificial boundary theories is proposed to absorb stress waves in a saturated soil foundation in dynamic analysis. Since shear waves （S-waves） are the same in a saturated soil foundation and a single-phase medium foundation, a tangential visco-elastic boundary condition for a single-phase medium foundation can also be used for saturated soil foundations. Thus, the purpose of the artificial boundary proposed in this paper is primarily to absorb two types of P-waves in a saturated soil foundation. The main idea is that the stress of the P-waves in the saturated soil foundation is decomposed into two types. The first type of stress, δra＇ is absorbed by the first artificial boundary. The second type of stress, δrb, is balanced by the stress generated by the second artificial boundary. Ultimately, both types of P-waves （fast-P-waves and slow-P-waves） are absorbed by the artificial boundary model proposed in this paper. In particular, note that the fast-P-waves and slow-P-waves are absorbed at the position of the first boundary. Thus, the artificial boundary model proposed herein can simultaneously absorb P-fast waves, P-slow waves and shear waves. Finally, a numerical example is given to examine the proposed artificial boundary model, and the results show that it is very accurate.展开更多
Numerical simulation technology is nowadays an important means for groundwater issues because of its efficiency and economical advantages. But in case of natural hydrogeological boundaries are not within the interest ...Numerical simulation technology is nowadays an important means for groundwater issues because of its efficiency and economical advantages. But in case of natural hydrogeological boundaries are not within the interest area, it may be a big trouble to set boundary conditions of the model artificially without enough field investigation information. This paper introduced a method for solving such problem applying field pumping test and recovery test. The method was applied to build an in-situ leaching of uranium model. Results showed that the model boundary conditions can be set satisfactorily, and also the calculated heads matched the observed data well in both two models.展开更多
When conducting dynamic tests of underground structure by a rigid container, reasonable boundary conditions are one of the essential factors related to the accuracy of test results, especially the artificial boundary ...When conducting dynamic tests of underground structure by a rigid container, reasonable boundary conditions are one of the essential factors related to the accuracy of test results, especially the artificial boundary perpendicular to the excitation direction. On the basis of numerous studies, shaking table tests with four different typical boundaries are performed in this study. The tests consider the seismic intensity and seismic wave types. Then, the simulation effects of the four boundary conditions are evaluated from four aspects as follows: the differential rate of peak acceleration, acceleration curve, similarity of Fourier frequency spectra, and uneven soil settlement in rigid containers. Results show that the simulation effects of the boundary conditions are not only affected by the nature of the boundary material but also related to the seismic intensity, types of seismic waves, and filter characteristic of the filling medium in containers. In comparison with the other three types of boundary condition, foamed polyethylene shows the best simulation effect and its effect decreases gradually with the increase in earthquake intensity. Finally, on the basis of existing studies, the evaluation criteria of boundary effect, the principle for the selection of boundary material type and the thickness of boundary material are discussed and summarized, and the corresponding design methods and suggestions are then provided.展开更多
In a semi-discretized Euler-Bernoulli beam equa- tion, the non-nearest neighboring interaction and large span of temporal scales for wave propagations pose challenges to the effectiveness and stability for artificial ...In a semi-discretized Euler-Bernoulli beam equa- tion, the non-nearest neighboring interaction and large span of temporal scales for wave propagations pose challenges to the effectiveness and stability for artificial boundary treat- ments. With the discrete equation regarded as an atomic lattice with a three-atom potential, two accurate artificial boundary conditions are first derived here. Reflection co- efficient and numerical tests illustrate the capability of the proposed methods. In particular, the time history treatment gives an exact boundary condition, yet with sensitivity to nu- merical implementations. The ALEX （almost EXact） bound- ary condition is numerically more effective.展开更多
The method of inputting the seismic wave determines the accuracy of the simulation of soil-structure dynamic interaction. The wave method is a commonly used approach for seismic wave input, which converts the incident...The method of inputting the seismic wave determines the accuracy of the simulation of soil-structure dynamic interaction. The wave method is a commonly used approach for seismic wave input, which converts the incident wave into equivalent loads on the cutoff boundaries. The wave method has high precision, but the implementation is complicated, especially for three-dimensional models. By deducing another form of equivalent input seismic loads in the fi nite element model, a new seismic wave input method is proposed. In the new method, by imposing the displacements of the free wave fi eld on the nodes of the substructure composed of elements that contain artifi cial boundaries, the equivalent input seismic loads are obtained through dynamic analysis of the substructure. Subsequently, the equivalent input seismic loads are imposed on the artifi cial boundary nodes to complete the seismic wave input and perform seismic analysis of the soil-structure dynamic interaction model. Compared with the wave method, the new method is simplifi ed by avoiding the complex processes of calculating the equivalent input seismic loads. The validity of the new method is verifi ed by the dynamic analysis numerical examples of the homogeneous and layered half space under vertical and oblique incident seismic waves.展开更多
The theory of perfectly matched layer （PML） artificial boundary condition （ABC）, which is characterized by absorption any wave motions with arbitrary frequency and arbitrarily incident angle, is introduced. The co...The theory of perfectly matched layer （PML） artificial boundary condition （ABC）, which is characterized by absorption any wave motions with arbitrary frequency and arbitrarily incident angle, is introduced. The construction process of PML boundary based on elastodynamic partial differential equation （PDE） system is developed. Combining with velocity-stress hybrid finite element formulation, the applicability of PML boundary is investigated and the numerical reflection of PML boundary is estimated. The reflectivity of PML and multi-transmitting formula （MTF） boundary is then compared based on body wave and surface wave simulations. The results show that although PML boundary yields some reflection, its absorption performance is superior to MTF boundary in the numerical simulations of near-fault wave propagation, especially in comer and large angle grazing incidence situations. The PML boundary does not arise any unstable phenomenon and the stability of PML boundary is better than MTF boundary in hybrid finite element method. For a specified problem and analysis tolerance, the computational efficiency of PML boundary is only a little lower than MTF boundary.展开更多
An innovative local artificial boundary condition is proposed to numerically solve the Cauchy problem of the Klein-Gordon equation in an unbounded domain.Initially,the equation is considered as the axial wave prop-aga...An innovative local artificial boundary condition is proposed to numerically solve the Cauchy problem of the Klein-Gordon equation in an unbounded domain.Initially,the equation is considered as the axial wave prop-agation in a bar supported on a spring foundation.The numerical model is then truncated by replacing the half-infinitely long bar with an equivalent mechanical structure.The effective frequency-dependent stiffness of the half-infinitely long bar is expressed as the sum of rational terms using Pade approximation.For each term,a corresponding substructure composed of dampers and masses is constructed.Finally,the equivalent mechan-ical structure is obtained by parallelly connecting these substructures.The proposed approach can be easily implemented within a standard finite element framework by incorporating additional mass points and damper elements.Numerical examples show that with just a few extra degrees of freedom,the proposed approach effec-tively suppresses artificial reflections at the truncation boundary and exhibits first-order convergence.展开更多
Viscoelastic artificial boundaries are widely adopted in numerical simulations of wave propagation problems.When explicit time-domain integration algorithms are used,the stability condition of the boundary domain is s...Viscoelastic artificial boundaries are widely adopted in numerical simulations of wave propagation problems.When explicit time-domain integration algorithms are used,the stability condition of the boundary domain is stricter than that of the internal region due to the influence of the damping and stiffness of an viscoelastic artificial boundary.The lack of a clear and practical stability criterion for this problem,however,affects the reasonable selection of an integral time step when using viscoelastic artificial boundaries.In this study,we investigate the stability conditions of explicit integration algorithms when using three-dimensional(3D)viscoelastic artificial boundaries through an analysis method based on a local subsystem.Several boundary subsystems that can represent localized characteristics of a complete numerical model are established,and their analytical stability conditions are derived from and further compared to one another.The stability of the complete model is controlled by the corner regions,and thus,the global stability criterion for the numerical model with viscoelastic artificial boundaries is obtained.Next,by analyzing the impact of different factors on stability conditions,we recommend a stability coefficient for practically estimating the maximum stable integral time step in the dynamic analysis when using 3D viscoelastic artificial boundaries.展开更多
Artificial neural networks (ANN) are employed using different combinations among the surface friction velocity u*, surface buoyancy flux Bs, free-flow stability N, Coriolis parameter f, and surface roughness length z0...Artificial neural networks (ANN) are employed using different combinations among the surface friction velocity u*, surface buoyancy flux Bs, free-flow stability N, Coriolis parameter f, and surface roughness length z0 from large-eddy simulation data as inputs to investigate which variables are essential in determining the stable boundary layer(SBL) height h. In addition, the performances of several conventional linear SBL height parameterizations are evaluated. ANN results indicate that the surface friction velocity u* is the most predominant variable in the estimation of SBL height h. When u* is absent, the secondly important variable is the surface buoyancy flux Bs. The relevance of N, f, and z0 to h is also discussed;f affects more than N does, and z0 shows to be the most insensitive variable to h.展开更多
An approximate artificial boundary condition based on a boundary integral equa- tion is designed for the vortex movements. Point vortex and cloud in cell methods are used in numerical simulation of vortex motions. The...An approximate artificial boundary condition based on a boundary integral equa- tion is designed for the vortex movements. Point vortex and cloud in cell methods are used in numerical simulation of vortex motions. The numerical experiments show that the ap- proximate artificial boundary condition is useful and su?ciently accurate in hydrodynamics.展开更多
We apply the newly proposed double absorbing boundary condition（DABC）（Hagstrom et al., 2014） to solve the boundary reflection problem in seismic finite-difference（FD） modeling. In the DABC scheme, the local high...We apply the newly proposed double absorbing boundary condition（DABC）（Hagstrom et al., 2014） to solve the boundary reflection problem in seismic finite-difference（FD） modeling. In the DABC scheme, the local high-order absorbing boundary condition is used on two parallel artificial boundaries, and thus double absorption is achieved. Using the general 2D acoustic wave propagation equations as an example, we use the DABC in seismic FD modeling, and discuss the derivation and implementation steps in detail. Compared with the perfectly matched layer（PML）, the complexity decreases, and the stability and fl exibility improve. A homogeneous model and the SEG salt model are selected for numerical experiments. The results show that absorption using the DABC is considerably improved relative to the Clayton–Engquist boundary condition and nearly the same as that in the PML.展开更多
The boundary between the near and far fields is generally defined as the distance from the vibration source beyond which ground vibrations are mainly dominated by Rayleigh waves. It is closely related to the type of v...The boundary between the near and far fields is generally defined as the distance from the vibration source beyond which ground vibrations are mainly dominated by Rayleigh waves. It is closely related to the type of vibration source and the soil properties. Based on the solutions of the Lamb＇s problem, the boundary at the surface between the near and far fields of ground vibration was investigated for a harmonic vertical concentrated load and an infinite line load at the surface of a visco-elastic half-space. Particularly, the variation of the boundary with the material damping was investigated for both cases. The results indicate that the material damping slightly contributes to the attenuation of vibrations in the near-source region, but significantly reduces the vibrations in the region that is at some distance away from the source. When taking the material damping into consideration, the boundary between the near and far fields tends to move towards the vibration source. Compared with the vibrations caused by a concentrated load, the vibrations induced by an infinite line load can affect a larger range of the surrounding environment, and they attenuate more slowly. This means the boundary between the near field and far field should move fitrther away from the source. Finally, the boundaries are defined in terms of R-wave length （2R） and Poisson ratio of the ground （o）. For the case of a point load, the boundary is located at the distance of （5.0-6.0）2R for v≤0.30 and at the distance of （2.0--3.0）2R for v≥0.35. For the case of an infinite line load, the boundary is located at the distance （5.5-6.5）2rt for v≤0.30 and at the distance （2.5--3.5）2R for v≥0.35.展开更多
After reviewing the studies on the lateral artificial boundaries in dynamic soil-structure interactions,the free field boundary was theoretically analyzed in asymmetric-and symmetric-matrix forms.First,the lumped mass...After reviewing the studies on the lateral artificial boundaries in dynamic soil-structure interactions,the free field boundary was theoretically analyzed in asymmetric-and symmetric-matrix forms.First,the lumped mass system was combined with viscous or viscoelastic elements to obtain a lumped mass-free field boundary.Second,typical examples were implemented using the finite element software ABAQUS.The incident shear wave was taken to be perpendicular to the bottom to verify the effectiveness of the lumped mass-free field under various sites:underground structures,uniform sites,and layered sites.Finally,the accuracy of the lumped mass-free field boundary was compared with those of the viscoelastic and roller boundaries on different calculation scales,soil damping ratios,structure sizes,and ground motion characteristics.Subsequently,the engineering design values for different damping ratios are given.The results show that the precision of the lumped mass-free field boundary was reasonable,and the operation was simple within the same engineering application.展开更多
The present paper focuses on the wave radiation by an oscillating body with six degrees of freedom by using the DtN artifi-cial boundary condition.The artificial boundary is usually selected as a circle or spherical s...The present paper focuses on the wave radiation by an oscillating body with six degrees of freedom by using the DtN artifi-cial boundary condition.The artificial boundary is usually selected as a circle or spherical surface to solve various types of fields,such as sound waves or electromagnetic waves,provided that the considered domain is infinite or unbounded in all directions.However,the substantial wave motion is considered in water of finite depth,that is,the fluid domain is bounded vertically but unbounded horizon-tally.Thus,the DtN boundary condition is given on an artificial cylindrical surface,which divides the water domain into an interior and exterior region.The boundary integral equation is adopted to implement the present model.In the case of a floating cylinder,the results of hydrodynamic coefficients of a chamfer box are discussed.展开更多
文摘The finite element artificial transmitting boundary method is employed here to treat the near field scattering of a cylindrical wave from an irregular cylinder. A comparison is made between this method and the analytical one. And then examples are given to demonstrate the solution of several problems of the irregular object scattering. The method can not only produce clear physical pictures, but can efficiently handle many complicated scattering problems.
基金National Natural Science Foundation of ChinaUnder Grant No.50478014Special Funds for Major State Basic Research Project Under Grant No.2002CB412706Research Funds from National Civil Defense Oficce of Chinafor the Tenth Five-year Plan。
文摘After a brief review of studies on artificial boundaries in dynamic soil-structure interaction, a three-dimensional viscous-spring artificial boundary （VSAB） in the time domain is developed in this paper. First, the 3D VSAB equations in the normal and tangential directions are derived based on the elastic wave motion theory. Secondly, a numerical simulation technique of wave motion equations along with the VSAB condition in the time domain is studied. Finally, numerical examples of some classical elastic wave motion problems are presented and the results are compared with the associated theoretical solutions, demonstrating that high precision and adequate stability can be achieved by using the proposed 3D VSAB. The proposed 3D VSAB can be conveniently incorporated in the general finite element program, which is commonly used to study dynamic soil-structure interaction problems.
文摘An improved version of the regular boundary element method, the artificial boundary node approach, is derived. A simple contact algorithm is designed and implemented into the direct boundary element, regular boundary element and artificial boundary node approaches. The exisiting and derived approaches are tested using some case studies. The results of the artificial boundary node approach are compared with those of the existing boundary element program, the regular element approach, ANSYS and analytical solution whenever possible. The results show the effectiveness of the artificial boundary node approach for a wider range of boundary offsets.
基金National Natural Science Foundation of China Under Grant Nos.51109029,51178081,51138001,51009020China Postdoctoral Science Foundation Under Grant No. 20110491535
文摘Anew artificial boundary model based on multi-directional transmitting and viscous-spring artificial boundary theories is proposed to absorb stress waves in a saturated soil foundation in dynamic analysis. Since shear waves （S-waves） are the same in a saturated soil foundation and a single-phase medium foundation, a tangential visco-elastic boundary condition for a single-phase medium foundation can also be used for saturated soil foundations. Thus, the purpose of the artificial boundary proposed in this paper is primarily to absorb two types of P-waves in a saturated soil foundation. The main idea is that the stress of the P-waves in the saturated soil foundation is decomposed into two types. The first type of stress, δra＇ is absorbed by the first artificial boundary. The second type of stress, δrb, is balanced by the stress generated by the second artificial boundary. Ultimately, both types of P-waves （fast-P-waves and slow-P-waves） are absorbed by the artificial boundary model proposed in this paper. In particular, note that the fast-P-waves and slow-P-waves are absorbed at the position of the first boundary. Thus, the artificial boundary model proposed herein can simultaneously absorb P-fast waves, P-slow waves and shear waves. Finally, a numerical example is given to examine the proposed artificial boundary model, and the results show that it is very accurate.
文摘Numerical simulation technology is nowadays an important means for groundwater issues because of its efficiency and economical advantages. But in case of natural hydrogeological boundaries are not within the interest area, it may be a big trouble to set boundary conditions of the model artificially without enough field investigation information. This paper introduced a method for solving such problem applying field pumping test and recovery test. The method was applied to build an in-situ leaching of uranium model. Results showed that the model boundary conditions can be set satisfactorily, and also the calculated heads matched the observed data well in both two models.
基金Projects(51978669,U1734208)supported by the National Natural Science Foundation of ChinaProject(2018JJ3657)supported by the Natural Science Foundation of Hunan Province,China
文摘When conducting dynamic tests of underground structure by a rigid container, reasonable boundary conditions are one of the essential factors related to the accuracy of test results, especially the artificial boundary perpendicular to the excitation direction. On the basis of numerous studies, shaking table tests with four different typical boundaries are performed in this study. The tests consider the seismic intensity and seismic wave types. Then, the simulation effects of the four boundary conditions are evaluated from four aspects as follows: the differential rate of peak acceleration, acceleration curve, similarity of Fourier frequency spectra, and uneven soil settlement in rigid containers. Results show that the simulation effects of the boundary conditions are not only affected by the nature of the boundary material but also related to the seismic intensity, types of seismic waves, and filter characteristic of the filling medium in containers. In comparison with the other three types of boundary condition, foamed polyethylene shows the best simulation effect and its effect decreases gradually with the increase in earthquake intensity. Finally, on the basis of existing studies, the evaluation criteria of boundary effect, the principle for the selection of boundary material type and the thickness of boundary material are discussed and summarized, and the corresponding design methods and suggestions are then provided.
基金supported by the National Natural Science Foundation of China(11272009)National Basic Research Program of China(2010CB731503)U.S. National Science Foundation(0900498)
文摘In a semi-discretized Euler-Bernoulli beam equa- tion, the non-nearest neighboring interaction and large span of temporal scales for wave propagations pose challenges to the effectiveness and stability for artificial boundary treat- ments. With the discrete equation regarded as an atomic lattice with a three-atom potential, two accurate artificial boundary conditions are first derived here. Reflection co- efficient and numerical tests illustrate the capability of the proposed methods. In particular, the time history treatment gives an exact boundary condition, yet with sensitivity to nu- merical implementations. The ALEX （almost EXact） bound- ary condition is numerically more effective.
基金National Natural Science Foundation of China under Grant No.51478247National Key Research and Development Program of China under Grant No.2016YFC1402800
文摘The method of inputting the seismic wave determines the accuracy of the simulation of soil-structure dynamic interaction. The wave method is a commonly used approach for seismic wave input, which converts the incident wave into equivalent loads on the cutoff boundaries. The wave method has high precision, but the implementation is complicated, especially for three-dimensional models. By deducing another form of equivalent input seismic loads in the fi nite element model, a new seismic wave input method is proposed. In the new method, by imposing the displacements of the free wave fi eld on the nodes of the substructure composed of elements that contain artifi cial boundaries, the equivalent input seismic loads are obtained through dynamic analysis of the substructure. Subsequently, the equivalent input seismic loads are imposed on the artifi cial boundary nodes to complete the seismic wave input and perform seismic analysis of the soil-structure dynamic interaction model. Compared with the wave method, the new method is simplifi ed by avoiding the complex processes of calculating the equivalent input seismic loads. The validity of the new method is verifi ed by the dynamic analysis numerical examples of the homogeneous and layered half space under vertical and oblique incident seismic waves.
基金National Natural Science Foundation of China (50608024 and 50538050).
文摘The theory of perfectly matched layer （PML） artificial boundary condition （ABC）, which is characterized by absorption any wave motions with arbitrary frequency and arbitrarily incident angle, is introduced. The construction process of PML boundary based on elastodynamic partial differential equation （PDE） system is developed. Combining with velocity-stress hybrid finite element formulation, the applicability of PML boundary is investigated and the numerical reflection of PML boundary is estimated. The reflectivity of PML and multi-transmitting formula （MTF） boundary is then compared based on body wave and surface wave simulations. The results show that although PML boundary yields some reflection, its absorption performance is superior to MTF boundary in the numerical simulations of near-fault wave propagation, especially in comer and large angle grazing incidence situations. The PML boundary does not arise any unstable phenomenon and the stability of PML boundary is better than MTF boundary in hybrid finite element method. For a specified problem and analysis tolerance, the computational efficiency of PML boundary is only a little lower than MTF boundary.
基金supported by the National Natural Science Foundation of China(Grant Nos.11832001 and 11702046).
文摘An innovative local artificial boundary condition is proposed to numerically solve the Cauchy problem of the Klein-Gordon equation in an unbounded domain.Initially,the equation is considered as the axial wave prop-agation in a bar supported on a spring foundation.The numerical model is then truncated by replacing the half-infinitely long bar with an equivalent mechanical structure.The effective frequency-dependent stiffness of the half-infinitely long bar is expressed as the sum of rational terms using Pade approximation.For each term,a corresponding substructure composed of dampers and masses is constructed.Finally,the equivalent mechan-ical structure is obtained by parallelly connecting these substructures.The proposed approach can be easily implemented within a standard finite element framework by incorporating additional mass points and damper elements.Numerical examples show that with just a few extra degrees of freedom,the proposed approach effec-tively suppresses artificial reflections at the truncation boundary and exhibits first-order convergence.
基金National Natural Science Foundation of China under Grant Nos.52108458 and U1839201China National Postdoctoral Program of Innovative Talents under Grant No.BX20200192+1 种基金Shuimu Tsinghua Scholar Program under Grant No.2020SM005National Key Research and Development Program of China under Grant No.2018YFC1504305。
文摘Viscoelastic artificial boundaries are widely adopted in numerical simulations of wave propagation problems.When explicit time-domain integration algorithms are used,the stability condition of the boundary domain is stricter than that of the internal region due to the influence of the damping and stiffness of an viscoelastic artificial boundary.The lack of a clear and practical stability criterion for this problem,however,affects the reasonable selection of an integral time step when using viscoelastic artificial boundaries.In this study,we investigate the stability conditions of explicit integration algorithms when using three-dimensional(3D)viscoelastic artificial boundaries through an analysis method based on a local subsystem.Several boundary subsystems that can represent localized characteristics of a complete numerical model are established,and their analytical stability conditions are derived from and further compared to one another.The stability of the complete model is controlled by the corner regions,and thus,the global stability criterion for the numerical model with viscoelastic artificial boundaries is obtained.Next,by analyzing the impact of different factors on stability conditions,we recommend a stability coefficient for practically estimating the maximum stable integral time step in the dynamic analysis when using 3D viscoelastic artificial boundaries.
文摘Artificial neural networks (ANN) are employed using different combinations among the surface friction velocity u*, surface buoyancy flux Bs, free-flow stability N, Coriolis parameter f, and surface roughness length z0 from large-eddy simulation data as inputs to investigate which variables are essential in determining the stable boundary layer(SBL) height h. In addition, the performances of several conventional linear SBL height parameterizations are evaluated. ANN results indicate that the surface friction velocity u* is the most predominant variable in the estimation of SBL height h. When u* is absent, the secondly important variable is the surface buoyancy flux Bs. The relevance of N, f, and z0 to h is also discussed;f affects more than N does, and z0 shows to be the most insensitive variable to h.
文摘An approximate artificial boundary condition based on a boundary integral equa- tion is designed for the vortex movements. Point vortex and cloud in cell methods are used in numerical simulation of vortex motions. The numerical experiments show that the ap- proximate artificial boundary condition is useful and su?ciently accurate in hydrodynamics.
基金supported by the National Nature Science Foundation of China(Grant No.U1262208)the Important National Science & Technology Specific Projects(Grant No.2011ZX05019-008)
文摘We apply the newly proposed double absorbing boundary condition（DABC）（Hagstrom et al., 2014） to solve the boundary reflection problem in seismic finite-difference（FD） modeling. In the DABC scheme, the local high-order absorbing boundary condition is used on two parallel artificial boundaries, and thus double absorption is achieved. Using the general 2D acoustic wave propagation equations as an example, we use the DABC in seismic FD modeling, and discuss the derivation and implementation steps in detail. Compared with the perfectly matched layer（PML）, the complexity decreases, and the stability and fl exibility improve. A homogeneous model and the SEG salt model are selected for numerical experiments. The results show that absorption using the DABC is considerably improved relative to the Clayton–Engquist boundary condition and nearly the same as that in the PML.
基金Project(51178342)supported by the National Natural Science Foundation of ChinaProject(KLE-TJGE-C1301)supported by the Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education(Tongji University)under the International Cooperation and Exchange Program,China
文摘The boundary between the near and far fields is generally defined as the distance from the vibration source beyond which ground vibrations are mainly dominated by Rayleigh waves. It is closely related to the type of vibration source and the soil properties. Based on the solutions of the Lamb＇s problem, the boundary at the surface between the near and far fields of ground vibration was investigated for a harmonic vertical concentrated load and an infinite line load at the surface of a visco-elastic half-space. Particularly, the variation of the boundary with the material damping was investigated for both cases. The results indicate that the material damping slightly contributes to the attenuation of vibrations in the near-source region, but significantly reduces the vibrations in the region that is at some distance away from the source. When taking the material damping into consideration, the boundary between the near and far fields tends to move towards the vibration source. Compared with the vibrations caused by a concentrated load, the vibrations induced by an infinite line load can affect a larger range of the surrounding environment, and they attenuate more slowly. This means the boundary between the near field and far field should move fitrther away from the source. Finally, the boundaries are defined in terms of R-wave length （2R） and Poisson ratio of the ground （o）. For the case of a point load, the boundary is located at the distance of （5.0-6.0）2R for v≤0.30 and at the distance of （2.0--3.0）2R for v≥0.35. For the case of an infinite line load, the boundary is located at the distance （5.5-6.5）2rt for v≤0.30 and at the distance （2.5--3.5）2R for v≥0.35.
基金Natural Science Foundation of Henan Province under Grant No.222300420415。
文摘After reviewing the studies on the lateral artificial boundaries in dynamic soil-structure interactions,the free field boundary was theoretically analyzed in asymmetric-and symmetric-matrix forms.First,the lumped mass system was combined with viscous or viscoelastic elements to obtain a lumped mass-free field boundary.Second,typical examples were implemented using the finite element software ABAQUS.The incident shear wave was taken to be perpendicular to the bottom to verify the effectiveness of the lumped mass-free field under various sites:underground structures,uniform sites,and layered sites.Finally,the accuracy of the lumped mass-free field boundary was compared with those of the viscoelastic and roller boundaries on different calculation scales,soil damping ratios,structure sizes,and ground motion characteristics.Subsequently,the engineering design values for different damping ratios are given.The results show that the precision of the lumped mass-free field boundary was reasonable,and the operation was simple within the same engineering application.
文摘The present paper focuses on the wave radiation by an oscillating body with six degrees of freedom by using the DtN artifi-cial boundary condition.The artificial boundary is usually selected as a circle or spherical surface to solve various types of fields,such as sound waves or electromagnetic waves,provided that the considered domain is infinite or unbounded in all directions.However,the substantial wave motion is considered in water of finite depth,that is,the fluid domain is bounded vertically but unbounded horizon-tally.Thus,the DtN boundary condition is given on an artificial cylindrical surface,which divides the water domain into an interior and exterior region.The boundary integral equation is adopted to implement the present model.In the case of a floating cylinder,the results of hydrodynamic coefficients of a chamfer box are discussed.
