As a highly efficient absorbing boundary condition, Perfectly Matched Layer (PML) has been widely used in Finite Difference Time Domain (FDTD) simulation of Ground Penetrating Radar (GPR) based on the first order elec...As a highly efficient absorbing boundary condition, Perfectly Matched Layer (PML) has been widely used in Finite Difference Time Domain (FDTD) simulation of Ground Penetrating Radar (GPR) based on the first order electromagnetic wave equation. However, the PML boundary condition is difficult to apply in GPR Finite Element Time Domain (FETD) simulation based on the second order electromagnetic wave equation. This paper developed a non-split perfectly matched layer (NPML) boundary condition for GPR FETD simulation based on the second order electromagnetic wave equation. Taking two-dimensional TM wave equation as an example, the second order frequency domain equation of GPR was derived according to the definition of complex extending coordinate transformation. Then it transformed into time domain by means of auxiliary differential equation method, and its FETD equation is derived based on Galerkin method. On this basis, a GPR FETD forward program based on NPML boundary condition is developed. The merits of NPML boundary condition are certified by compared with wave field snapshots, signal and reflection errors of homogeneous medium model with split and non-split PML boundary conditions. The comparison demonstrated that the NPML algorithm can reduce memory occupation and improve calculation efficiency. Furthermore, numerical simulation of a complex model verifies the good absorption effects of the NPML boundary condition in complex structures.展开更多
A direct time integration scheme based on Gauss-Legendre quadrature is proposed to solve problems in linear structural dynamics.The proposed method is a oneparameter non-dissipative scheme.Improved stability,accuracy,...A direct time integration scheme based on Gauss-Legendre quadrature is proposed to solve problems in linear structural dynamics.The proposed method is a oneparameter non-dissipative scheme.Improved stability,accuracy,and dispersion characteristics are achieved using appropriate values of the parameter.The proposed scheme has second-order accuracy with and without physical damping.Moreover,its stability,accuracy,and dispersion are analyzed.In addition,its performance is demonstrated by the two-dimensional scalar wave problem,the single-degree-of-freedom problem,two degrees-of-freedom spring system,and beam with boundary constraints.The wave propagation problem is solved in the high frequency wave regime to demonstrate the advantage of the proposed scheme.When the proposed scheme is applied to solve the wave problem,more accurate solutions than those of other methods are obtained by using the appropriate value of the parameter.For the single-degree-offreedom system,two degrees-of-freedom system,and the time responses of beam,the proposed scheme can be used effectively owing to its high accuracy and lower computational cost.展开更多
Given the complexities of reinforced soil materials’constitutive relationships,this paper compares reinforced soil composite materials to a sliding structure between steel bars and soil and proposes a reinforced soil...Given the complexities of reinforced soil materials’constitutive relationships,this paper compares reinforced soil composite materials to a sliding structure between steel bars and soil and proposes a reinforced soil constitutive model that takes this sliding into account.A finite element dynamic time history calculation software for composite response analysis was created using the Fortran programming language,and time history analysis was performed on reinforced soil retaining walls and gravity retaining walls.The vibration time histories of reinforced soil retaining walls and gravity retaining walls were computed,and the dynamic reactions of the two types of retaining walls to vibration were compared and studied.The dynamic performance of reinforced earth retaining walls was evaluated.展开更多
The superparamagnetic effect arises from the superparamagnetism exhibited by a multitude of nano-sized magnetic mineral particles under an external electric field.This phenomenon manifests in transient electromagnetic...The superparamagnetic effect arises from the superparamagnetism exhibited by a multitude of nano-sized magnetic mineral particles under an external electric field.This phenomenon manifests in transient electromagnetic data primarily as a deceleration in the attenuation rate of late-stage signals,a characteristic difficult to discern directly from airborne transient electromagnetic signals,consequently leading to significant misinterpretations of subterranean electrical structures.This study embarks on 3D forward modeling of airborne electromagnetic responses in the frequency domain,accounting for the superparamagnetic effect,utilizing an unstructured finite element method.Superparamagnetic responses in the time domain were obtained through frequency-time conversion.This investigation explores the influence of various parameters-such as magnetic susceptibility,time constants,and flight altitude-on the superparamagnetic effect by examining the response characteristics of typical targets.Findings indicate that in its late stages,the superparamagnetic effect can induce a relative anomaly of up to 300%.There is a positive correlation between magnetic susceptibility and the strength of the superparamagnetic effect.The influence of the time constant's upper and lower limits on the superparamagnetic effect is minimal;however,the range between these limits significantly affects the effect,showing a negative correlation with its intensity.Higher flight altitudes weaken the superparamagnetic signal.The impact is most pronounced when superparamagnetic minerals are shallowly buried,effectively shielding the underlying geology with the characteristics of a good conductivity anomaly,but this effect diminishes with greater depth.The insights from this study provide a theoretical framework for a deeper understanding of the superparamagnetic effect in transient electromagnetic signals and for more accurate interpretations of subterranean geological and electrical structures.展开更多
This paper presents an investigation of temperature, displacement, stress, and induced magnetic field in a half space perfectly-conductive plate. Finite element equations regarding generalized magneto-thermoelasticity...This paper presents an investigation of temperature, displacement, stress, and induced magnetic field in a half space perfectly-conductive plate. Finite element equations regarding generalized magneto-thermoelasticity problems with two relaxation times （i.e., the G-L theory） are derived using the principle of virtual work. For avoiding numerical complication involved in inverse Laplace and Fourier transformation and low precision thereof, the equations are solved directly in time-domain. As a numerical example, the derived equation is used to investigate the generalized magneto-thermoelastic behavior of a semi-infinite plate under magnetic field and subjecting to a thermal shock loading. The results demonstrate that FEM can faithfully predict the deformation of the plate and the induced magnetic field, and most importantly can reveal the sophisticated second sound effect of heat conduction in two-dimensional generalized thermoelastic solids, which is usually difficult to model by routine transformation methods. A peak can be observed in the distribution of stress and induced front and the magnitude of magnetic field at the heat wave the peak decreases with time, which can not be obtained by transformation methods. The new method can also be used to study generalized piezo-thermoelastic problems.展开更多
A time domain finite element method （FEM） for the analysis of transient elastic response of a very large floating structure （VLFS） subjected to arbitrary time-dependent external loads is presented. This method is ...A time domain finite element method （FEM） for the analysis of transient elastic response of a very large floating structure （VLFS） subjected to arbitrary time-dependent external loads is presented. This method is developed directly in time domain and the hydrodynamic problem is formulated based on linear, inviscid and slightly compressible fluid theory and the structural response is analyzed on the thin plate assumption. The time domain finite element procedure herein is validated by comparing numerical results with available experimental data. Finally, the transient elastic response of a pontoon-type VLFS under the landing of an airplane is computed by the proposed time domain FEM. The time histories of the applied force and the position and velocity of an airplane during landing are modeled with data from a Boeing 747-400 jumbo jet.展开更多
A two-dimensional nonlinear sloshing problem is analyzed by means of the fully nonlinear theory and time domain second order theory of water waves. Liquid sloshing in a rectangular container Subjected to a horizontal ...A two-dimensional nonlinear sloshing problem is analyzed by means of the fully nonlinear theory and time domain second order theory of water waves. Liquid sloshing in a rectangular container Subjected to a horizontal excitation is simulated by the finite element method. Comparisons between the two theories are made based on their numerical results. It is found that good agreement is obtained for the case of small amplitude oscillation and obvious differences occur for large amplitude excitation. Even though, the second order solution can still exhibit typical nonlinear features of nonlinear wave and can be used instead of the fully nonlinear theory.展开更多
In the last 30 years,the scientific community has developed and proposed different models and numerical approaches for the study of vibrations induced by railway traffic.Most of them are formulated in the frequency/wa...In the last 30 years,the scientific community has developed and proposed different models and numerical approaches for the study of vibrations induced by railway traffic.Most of them are formulated in the frequency/wave number domain and with a 2.5D approach.Three-dimensional numerical models formulated in the time/space domain are less frequently used,mainly due to their high computational cost.Notwithstanding,these models present very attractive characteristics,such as the possibility of considering nonlinear behaviors or the modelling of excess pore pressure and non-homogeneous and non-periodic geometries in the longitudinal direction of the track.In this study,two 3D numerical approaches formulated in the time/space domain are compared and experimentally validated.The first one consists of a finite element approach and the second one of a finite difference approach.The experimental validation in an actual case situated in Carregado(Portugal)shows an acceptable fitting between the numerical results and the actual measurements for both models.However,there are some differences among them.This study therefore includes some recommendations for their use in practical soil dynamics and geotechnical engineering.展开更多
A solution scheme is proposed in this paper for an existing RTDHT system to simulate large-scale finite element （FE） numerical substructures. The analysis of the FE numerical substructure is split into response anal...A solution scheme is proposed in this paper for an existing RTDHT system to simulate large-scale finite element （FE） numerical substructures. The analysis of the FE numerical substructure is split into response analysis and signal generation tasks, and executed in two different target computers in real-time. One target computer implements the response analysis task, wherein a large time-step is used to solve the FE substructure, and another target computer implements the signal generation task, wherein an interpolation program is used to generate control signals in a small time-step to meet the input demand of the controller. By using this strategy, the scale of the FE numerical substructure simulation may be increased significantly. The proposed scheme is initially verified by two FE numerical substructure models with 98 and 1240 degrees of freedom （DOFs）. Thereafter, RTDHTs of a single frame-foundation structure are implemented where the foundation, considered as the numerical substructure, is simulated by the FE model with 1240 DOFs. Good agreements between the results of the RTDHT and those from the FE analysis in ABAQUS are obtained.展开更多
A seismic free field input formulation of the coupling procedure of the finite elelnent(FE)and the scaled boundary finite-element(SBFE)is proposed to perform the unbounded soil-structure interaction analysis in time d...A seismic free field input formulation of the coupling procedure of the finite elelnent(FE)and the scaled boundary finite-element(SBFE)is proposed to perform the unbounded soil-structure interaction analysis in time domain. Based on the substructure technique,seismic excitation of the soil-structure system is represented by the free-field motion of an elastic half-space.To reduce the computational effort,the acceleration unit-impulse response function of the unbounded soil is decomposed into two functions:linear and residual.The latter converges to zero and can be truncated as required. With the prescribed tolerance parameter,the balance between accuracy and effMency of the procedure can be controlled. The validity of the model is verified by the scattering analysis of a hemi-spherical canyon subjected to plane harmonic P,SV and SH wave incidence.Numerical results show that the new procedure is very efficient for seismic problems within a nor- real range of frequency.The coupling procedure presented herein can be applied to linear and nonlinear earthquake re- sponse analysis of practical structures which are built on unbounded soil.展开更多
This paper deals with the coupled method of finite and dynamic infinite elements for simulating wave propagation in elastic and viscoelastic solids involving infinite domains.This method can be used to simultaneously ...This paper deals with the coupled method of finite and dynamic infinite elements for simulating wave propagation in elastic and viscoelastic solids involving infinite domains.This method can be used to simultaneously simulate material complexities in the near field and the infinite extent of the far field.Based on the governing equations of wave motion in two-dimensional and three-dimensional elastic/viscoelastic solids,the mass and stiffness matrices of the dynamic infinite element have been derived.The proposed two-dimensional dynamic infinite element can be used to simulate both the P-wave and the SV-wave propagation within the element,while the proposed three-dimensional dynamic infinite element can be used to simultaneously simulate the Rayleigh wave,P-wave and S-wave propagation within the element.The related simulation results have demonstrated that the coupled method of finite and dynamic infinite elements can be accurately used to simulate,both physically and computationally,wave propagation in elastic/viscoelastic solids involving infinite domains.Thus,this method provides an advanced scientific tool for dealing with both scientific and engineering problems involving infinite domains.展开更多
A finite element based numerical method is employed to analyze the wave radiation by multiple or a group of cylinders in the time domain. The nonlinear free surface and body surface boundary conditions are satisfied b...A finite element based numerical method is employed to analyze the wave radiation by multiple or a group of cylinders in the time domain. The nonlinear free surface and body surface boundary conditions are satisfied based on the perturbation method up to the second order. The first- and second-order velocity potential problems at each time step are solved through a Finite Element Method （FEM）. The matrix equation of the FEM is solved through iteration and the initial solution is obtained from the result at the previous time step. The three-dimensional （3-D） mesh required is generated based on a two-dimensional （2-D） hybrid mesh on a horizontal plane and its extension in the vertical direction. The hybrid mesh is generated by combining an unstructured grid away from cylinders and two structured grids near the cylinder and the artificial boundary. The fluid velocity on the free surface and the cylinder surface are calculated by using a differential method. Results for various configurations including the cases of two cylinders and four cylinders and a group of eighteen cylinders are obtained to show the joint influences of cylinders on the first- and second- order waves and forces, including the effects of spacing ratios and wave frequency on the second order waves and the mean force, in particular.展开更多
The paper is discussing problems connected with embedment of the incubation time criterion for brittle fracture into finite element computational schemes. Incubation time fracture criterion is reviewed; practical ques...The paper is discussing problems connected with embedment of the incubation time criterion for brittle fracture into finite element computational schemes. Incubation time fracture criterion is reviewed; practical questions of its numerical implementation are extensively discussed. Several examples of how the incubation time fracture criterion can be used as fracture condition in finite element computations are given. The examples include simulations of dynamic crack propagation and arrest, impact crater formation （i.e. fracture in initially intact media）, spall fracture in plates, propagation of cracks in pipelines. Applicability of the approach to model initiation, development and arrest of dynamic fracture is claimed.展开更多
For a coupled system of multiplayer dynamics of fluids in porous media, the characteristic finite element domain decomposition procedures applicable to parallel arithmetic are put forward. Techniques such as calculus ...For a coupled system of multiplayer dynamics of fluids in porous media, the characteristic finite element domain decomposition procedures applicable to parallel arithmetic are put forward. Techniques such as calculus of variations, domain decomposition, characteristic method, negative norm estimate, energy method and the theory of prior estimates are adopted. Optimal order estimates in L^2 norm are derived for the error in the approximate solution.展开更多
基金Project supported by China Postdoctoral Science Foundation （20100481488）, Key Fund Project of Advanced Research of the Weapon Equipment （9140A33040512JB3401）.
文摘As a highly efficient absorbing boundary condition, Perfectly Matched Layer (PML) has been widely used in Finite Difference Time Domain (FDTD) simulation of Ground Penetrating Radar (GPR) based on the first order electromagnetic wave equation. However, the PML boundary condition is difficult to apply in GPR Finite Element Time Domain (FETD) simulation based on the second order electromagnetic wave equation. This paper developed a non-split perfectly matched layer (NPML) boundary condition for GPR FETD simulation based on the second order electromagnetic wave equation. Taking two-dimensional TM wave equation as an example, the second order frequency domain equation of GPR was derived according to the definition of complex extending coordinate transformation. Then it transformed into time domain by means of auxiliary differential equation method, and its FETD equation is derived based on Galerkin method. On this basis, a GPR FETD forward program based on NPML boundary condition is developed. The merits of NPML boundary condition are certified by compared with wave field snapshots, signal and reflection errors of homogeneous medium model with split and non-split PML boundary conditions. The comparison demonstrated that the NPML algorithm can reduce memory occupation and improve calculation efficiency. Furthermore, numerical simulation of a complex model verifies the good absorption effects of the NPML boundary condition in complex structures.
文摘A direct time integration scheme based on Gauss-Legendre quadrature is proposed to solve problems in linear structural dynamics.The proposed method is a oneparameter non-dissipative scheme.Improved stability,accuracy,and dispersion characteristics are achieved using appropriate values of the parameter.The proposed scheme has second-order accuracy with and without physical damping.Moreover,its stability,accuracy,and dispersion are analyzed.In addition,its performance is demonstrated by the two-dimensional scalar wave problem,the single-degree-of-freedom problem,two degrees-of-freedom spring system,and beam with boundary constraints.The wave propagation problem is solved in the high frequency wave regime to demonstrate the advantage of the proposed scheme.When the proposed scheme is applied to solve the wave problem,more accurate solutions than those of other methods are obtained by using the appropriate value of the parameter.For the single-degree-offreedom system,two degrees-of-freedom system,and the time responses of beam,the proposed scheme can be used effectively owing to its high accuracy and lower computational cost.
基金supported in part by the Chongqing Social Science Planning Project(2021BS064)Chongqing Construction Science and Technology Plan Project(Grant 2023-0187)+1 种基金Special Foundation of Chongqing Postdoctoral Research(2021XM2052)Scientific and Technological Research Program of Chongqing Municipal Education Commission(Grant KJQN202304703).
文摘Given the complexities of reinforced soil materials’constitutive relationships,this paper compares reinforced soil composite materials to a sliding structure between steel bars and soil and proposes a reinforced soil constitutive model that takes this sliding into account.A finite element dynamic time history calculation software for composite response analysis was created using the Fortran programming language,and time history analysis was performed on reinforced soil retaining walls and gravity retaining walls.The vibration time histories of reinforced soil retaining walls and gravity retaining walls were computed,and the dynamic reactions of the two types of retaining walls to vibration were compared and studied.The dynamic performance of reinforced earth retaining walls was evaluated.
文摘The superparamagnetic effect arises from the superparamagnetism exhibited by a multitude of nano-sized magnetic mineral particles under an external electric field.This phenomenon manifests in transient electromagnetic data primarily as a deceleration in the attenuation rate of late-stage signals,a characteristic difficult to discern directly from airborne transient electromagnetic signals,consequently leading to significant misinterpretations of subterranean electrical structures.This study embarks on 3D forward modeling of airborne electromagnetic responses in the frequency domain,accounting for the superparamagnetic effect,utilizing an unstructured finite element method.Superparamagnetic responses in the time domain were obtained through frequency-time conversion.This investigation explores the influence of various parameters-such as magnetic susceptibility,time constants,and flight altitude-on the superparamagnetic effect by examining the response characteristics of typical targets.Findings indicate that in its late stages,the superparamagnetic effect can induce a relative anomaly of up to 300%.There is a positive correlation between magnetic susceptibility and the strength of the superparamagnetic effect.The influence of the time constant's upper and lower limits on the superparamagnetic effect is minimal;however,the range between these limits significantly affects the effect,showing a negative correlation with its intensity.Higher flight altitudes weaken the superparamagnetic signal.The impact is most pronounced when superparamagnetic minerals are shallowly buried,effectively shielding the underlying geology with the characteristics of a good conductivity anomaly,but this effect diminishes with greater depth.The insights from this study provide a theoretical framework for a deeper understanding of the superparamagnetic effect in transient electromagnetic signals and for more accurate interpretations of subterranean geological and electrical structures.
基金The project supported by the National Natural Science Foundation of China(10132010 and 10472089)
文摘This paper presents an investigation of temperature, displacement, stress, and induced magnetic field in a half space perfectly-conductive plate. Finite element equations regarding generalized magneto-thermoelasticity problems with two relaxation times （i.e., the G-L theory） are derived using the principle of virtual work. For avoiding numerical complication involved in inverse Laplace and Fourier transformation and low precision thereof, the equations are solved directly in time-domain. As a numerical example, the derived equation is used to investigate the generalized magneto-thermoelastic behavior of a semi-infinite plate under magnetic field and subjecting to a thermal shock loading. The results demonstrate that FEM can faithfully predict the deformation of the plate and the induced magnetic field, and most importantly can reveal the sophisticated second sound effect of heat conduction in two-dimensional generalized thermoelastic solids, which is usually difficult to model by routine transformation methods. A peak can be observed in the distribution of stress and induced front and the magnitude of magnetic field at the heat wave the peak decreases with time, which can not be obtained by transformation methods. The new method can also be used to study generalized piezo-thermoelastic problems.
文摘A time domain finite element method （FEM） for the analysis of transient elastic response of a very large floating structure （VLFS） subjected to arbitrary time-dependent external loads is presented. This method is developed directly in time domain and the hydrodynamic problem is formulated based on linear, inviscid and slightly compressible fluid theory and the structural response is analyzed on the thin plate assumption. The time domain finite element procedure herein is validated by comparing numerical results with available experimental data. Finally, the transient elastic response of a pontoon-type VLFS under the landing of an airplane is computed by the proposed time domain FEM. The time histories of the applied force and the position and velocity of an airplane during landing are modeled with data from a Boeing 747-400 jumbo jet.
文摘A two-dimensional nonlinear sloshing problem is analyzed by means of the fully nonlinear theory and time domain second order theory of water waves. Liquid sloshing in a rectangular container Subjected to a horizontal excitation is simulated by the finite element method. Comparisons between the two theories are made based on their numerical results. It is found that good agreement is obtained for the case of small amplitude oscillation and obvious differences occur for large amplitude excitation. Even though, the second order solution can still exhibit typical nonlinear features of nonlinear wave and can be used instead of the fully nonlinear theory.
文摘In the last 30 years,the scientific community has developed and proposed different models and numerical approaches for the study of vibrations induced by railway traffic.Most of them are formulated in the frequency/wave number domain and with a 2.5D approach.Three-dimensional numerical models formulated in the time/space domain are less frequently used,mainly due to their high computational cost.Notwithstanding,these models present very attractive characteristics,such as the possibility of considering nonlinear behaviors or the modelling of excess pore pressure and non-homogeneous and non-periodic geometries in the longitudinal direction of the track.In this study,two 3D numerical approaches formulated in the time/space domain are compared and experimentally validated.The first one consists of a finite element approach and the second one of a finite difference approach.The experimental validation in an actual case situated in Carregado(Portugal)shows an acceptable fitting between the numerical results and the actual measurements for both models.However,there are some differences among them.This study therefore includes some recommendations for their use in practical soil dynamics and geotechnical engineering.
基金National Natural Science Foundation under Grant Nos.51179093,91215301 and 41274106the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20130002110032Tsinghua University Initiative Scientific Research Program under Grant No.20131089285
文摘A solution scheme is proposed in this paper for an existing RTDHT system to simulate large-scale finite element （FE） numerical substructures. The analysis of the FE numerical substructure is split into response analysis and signal generation tasks, and executed in two different target computers in real-time. One target computer implements the response analysis task, wherein a large time-step is used to solve the FE substructure, and another target computer implements the signal generation task, wherein an interpolation program is used to generate control signals in a small time-step to meet the input demand of the controller. By using this strategy, the scale of the FE numerical substructure simulation may be increased significantly. The proposed scheme is initially verified by two FE numerical substructure models with 98 and 1240 degrees of freedom （DOFs）. Thereafter, RTDHTs of a single frame-foundation structure are implemented where the foundation, considered as the numerical substructure, is simulated by the FE model with 1240 DOFs. Good agreements between the results of the RTDHT and those from the FE analysis in ABAQUS are obtained.
基金the National Key Basic Research and Development Program under Grant No.2002CB412709
文摘A seismic free field input formulation of the coupling procedure of the finite elelnent(FE)and the scaled boundary finite-element(SBFE)is proposed to perform the unbounded soil-structure interaction analysis in time domain. Based on the substructure technique,seismic excitation of the soil-structure system is represented by the free-field motion of an elastic half-space.To reduce the computational effort,the acceleration unit-impulse response function of the unbounded soil is decomposed into two functions:linear and residual.The latter converges to zero and can be truncated as required. With the prescribed tolerance parameter,the balance between accuracy and effMency of the procedure can be controlled. The validity of the model is verified by the scattering analysis of a hemi-spherical canyon subjected to plane harmonic P,SV and SH wave incidence.Numerical results show that the new procedure is very efficient for seismic problems within a nor- real range of frequency.The coupling procedure presented herein can be applied to linear and nonlinear earthquake re- sponse analysis of practical structures which are built on unbounded soil.
文摘This paper deals with the coupled method of finite and dynamic infinite elements for simulating wave propagation in elastic and viscoelastic solids involving infinite domains.This method can be used to simultaneously simulate material complexities in the near field and the infinite extent of the far field.Based on the governing equations of wave motion in two-dimensional and three-dimensional elastic/viscoelastic solids,the mass and stiffness matrices of the dynamic infinite element have been derived.The proposed two-dimensional dynamic infinite element can be used to simulate both the P-wave and the SV-wave propagation within the element,while the proposed three-dimensional dynamic infinite element can be used to simultaneously simulate the Rayleigh wave,P-wave and S-wave propagation within the element.The related simulation results have demonstrated that the coupled method of finite and dynamic infinite elements can be accurately used to simulate,both physically and computationally,wave propagation in elastic/viscoelastic solids involving infinite domains.Thus,this method provides an advanced scientific tool for dealing with both scientific and engineering problems involving infinite domains.
基金supported by the Fundamental Research Funds for the Central Universities and NPRP 08-691-2-289 grantfrom Qatar National Research Fund (QNRF)
文摘A finite element based numerical method is employed to analyze the wave radiation by multiple or a group of cylinders in the time domain. The nonlinear free surface and body surface boundary conditions are satisfied based on the perturbation method up to the second order. The first- and second-order velocity potential problems at each time step are solved through a Finite Element Method （FEM）. The matrix equation of the FEM is solved through iteration and the initial solution is obtained from the result at the previous time step. The three-dimensional （3-D） mesh required is generated based on a two-dimensional （2-D） hybrid mesh on a horizontal plane and its extension in the vertical direction. The hybrid mesh is generated by combining an unstructured grid away from cylinders and two structured grids near the cylinder and the artificial boundary. The fluid velocity on the free surface and the cylinder surface are calculated by using a differential method. Results for various configurations including the cases of two cylinders and four cylinders and a group of eighteen cylinders are obtained to show the joint influences of cylinders on the first- and second- order waves and forces, including the effects of spacing ratios and wave frequency on the second order waves and the mean force, in particular.
基金supported by RFBR research (10-01-00810-a,11-01-00491-a,10-01-91154-GFEN a),Russian Federation State contracts and academic programs of the Russian Academy of Sciences
文摘The paper is discussing problems connected with embedment of the incubation time criterion for brittle fracture into finite element computational schemes. Incubation time fracture criterion is reviewed; practical questions of its numerical implementation are extensively discussed. Several examples of how the incubation time fracture criterion can be used as fracture condition in finite element computations are given. The examples include simulations of dynamic crack propagation and arrest, impact crater formation （i.e. fracture in initially intact media）, spall fracture in plates, propagation of cracks in pipelines. Applicability of the approach to model initiation, development and arrest of dynamic fracture is claimed.
基金Supported by the Major State Basic Research Program of China (No. 1999032803)the National Tackling Key Problems Program (No. 2002020094)+1 种基金the National Natural Scicnccs Foundation of China (Nos.19972039,10271066)the Doctorate Foundation of the Ministry of Education of China (No.2003042047)
文摘For a coupled system of multiplayer dynamics of fluids in porous media, the characteristic finite element domain decomposition procedures applicable to parallel arithmetic are put forward. Techniques such as calculus of variations, domain decomposition, characteristic method, negative norm estimate, energy method and the theory of prior estimates are adopted. Optimal order estimates in L^2 norm are derived for the error in the approximate solution.
