The anisotropic Perfectly Matched Layer(PML) absorbing boundary condition is implemented in a 2-D finite element formulation to solve dielectric waveguide discontinuity problems. The choice of parameters of anisotropi...The anisotropic Perfectly Matched Layer(PML) absorbing boundary condition is implemented in a 2-D finite element formulation to solve dielectric waveguide discontinuity problems. The choice of parameters of anisotropic PML has been investigated. Using the boundary truncating technique, the solution process of Finite-Element Method (FEM) has been greatly simplified compared with other hybrid methods. The required computational resources have also significantly declined since the anisotropic PML interface can be placed much closer to the scatterer compared to other well known artificial boundary.展开更多
A novel high-order three-dimensional （3-D） discontinuous Galerkin time domain （DGTD） method based on a normalized formulation of Maxwell＇s equations is developed for modeling and simulating silicon-on-insulator ...A novel high-order three-dimensional （3-D） discontinuous Galerkin time domain （DGTD） method based on a normalized formulation of Maxwell＇s equations is developed for modeling and simulating silicon-on-insulator （SOD thin-ridge waveguide. The DGTD method employs unstructured meshes and piecewise high-order polynomials for spatial discretization, and Runge-Kutta methods for time integration. It is found that the numerical results of the leakage loss of SOI thin-ridge waveguide agree well with those of analytical solutions, which proves that the proposed method is an ideal tool for the quantitative analysis for SOI thin-ridge waveguide.展开更多
The estimation of shear strength of rock mass discontinuity is always a focal, but difficult, problem in the field of geotechnical engineering. Considering the disadvantages and limitation of exist- ing estimation met...The estimation of shear strength of rock mass discontinuity is always a focal, but difficult, problem in the field of geotechnical engineering. Considering the disadvantages and limitation of exist- ing estimation methods, a new approach based on the shadow area percentage （SAP） that can be used to quantify surface roughness is proposed in this article. Firstly, by the help of laser scanning technique, the three-dimensional model of the surface of rock discontinuity was established. Secondly, a light source was simulated, and there would be some shadows produced on the model surface. Thirdly, to obtain the value of SAP of each specimen, the shadow detection technique was introduced for use. Fourthly, compared with the result from direct shear testing and based on statistics, an empirical for- mula was found among SAP, normal stress, and shear strength. Data of Yujian （~ River were used as an example, and the following conclusions have been made. （1） In the case of equal normal stress, the peak shear stress is positively proportional to the SAP. （2） The formula for estimating was derived, and the predictions of peak-shear strength made with this equation well agreed with the experimental re- suits obtained in laboratory tests.展开更多
An extended displacement discontinuity method(EDDM)is proposed to analyze the stress wave propagation in jointed viscoelastic rock mass(VRM).The discontinuities in a rock mass are divided into two groups.The primary g...An extended displacement discontinuity method(EDDM)is proposed to analyze the stress wave propagation in jointed viscoelastic rock mass(VRM).The discontinuities in a rock mass are divided into two groups.The primary group with an average geometrical size larger than or in the same order of magnitude of wavelength of a concerned stress wave is defined as'macro-joints',while the secondary group with a high density and relatively small geometrical size compared to the wavelength is known as'micro-defects'.The rock mass with micro-defects is modeled as an equivalent viscoelastic medium while the macro-joints in the rock mass are modeled explicitly as physical discontinuities.Viscoelastic properties of a micro-defected sedimentary rock are obtained by longitudinally impacting a cored long sedimentary rod with a pendulum.Wave propagation coefficient and dynamic viscoelastic modulus are measured.The EDDM is then successfully employed to analyze the wave propagation across macro-joint in VRM.The effect of the rock viscosity on the stress wave propagation is evaluated by comparing the results of VRM from the presented EDDM with those of an elastic rock mass(ERM)from the conventional displacement discontinuity method(CDDM).The CDDM is a special case of the EDDM under the condition that the rock viscosity is ignored.Comparison of the reflected and transmitted waves shows that the essential rock viscosity has a significant effect on stress wave attenuation.When a short propagation distance of a stress wave is considered,the results obtained from the CDDM approximate to the EDDM solutions,however,when the propagation distance is sufficiently long relative to the wavelength,the effect of rock viscosity on the stress wave propagation cannot be ignored.展开更多
A revised displacement discontinuity method(DDM) program is developed for the simulation of rock joint propagation and dilatancy analysis. The non-linear joint model used in the program adopts Barton-Bandis normal def...A revised displacement discontinuity method(DDM) program is developed for the simulation of rock joint propagation and dilatancy analysis. The non-linear joint model used in the program adopts Barton-Bandis normal deformation model, Kulhaway shear deformation model and Mohr-Coulomb criterion. The joint propagation criterion is based on the equivalent stress intensity factor which can be obtained by regression analysis. The simulated rock joint propagation accords well with the existing knowledge. The closure and opening of joint is investigated by DDM, and it is shown that if the opening volume of propagated joint is larger than closure volume of the old joint, the joint dilatancy occurs. The dilatancy condition is mainly controlled by the normal stiffness of the rock joint. When the normal stiffness is larger than the critical value, joint dilatancy occurs. The critical normal stiffness of rock joint changes with the joint-load angle, and joint dilatancy is most possible to occur at 30°.展开更多
In this paper,a new strategy for a sub-element-based shock capturing for discontinuous Galerkin(DG)approximations is presented.The idea is to interpret a DG element as a col-lection of data and construct a hierarchy o...In this paper,a new strategy for a sub-element-based shock capturing for discontinuous Galerkin(DG)approximations is presented.The idea is to interpret a DG element as a col-lection of data and construct a hierarchy of low-to-high-order discretizations on this set of data,including a first-order finite volume scheme up to the full-order DG scheme.The dif-ferent DG discretizations are then blended according to sub-element troubled cell indicators,resulting in a final discretization that adaptively blends from low to high order within a single DG element.The goal is to retain as much high-order accuracy as possible,even in simula-tions with very strong shocks,as,e.g.,presented in the Sedov test.The framework retains the locality of the standard DG scheme and is hence well suited for a combination with adaptive mesh refinement and parallel computing.The numerical tests demonstrate the sub-element adaptive behavior of the new shock capturing approach and its high accuracy.展开更多
The multimodal admittance method and its improvement are presented to deal with various aspects in underwater acoustics,mostly for the sound propagation in inhomogeneous waveguides with sound-speed profiles,arbitrary-...The multimodal admittance method and its improvement are presented to deal with various aspects in underwater acoustics,mostly for the sound propagation in inhomogeneous waveguides with sound-speed profiles,arbitrary-shaped liquid-like scatterers,and range-dependent environments.In all cases,the propagation problem governed by the Helmholtz equation is transformed into initial value problems of two coupled first-order evolution equations with respect to the modal components of field quantities(sound pressure and its derivative),by projecting the Helmholtz equation on a constructed orthogonal and complete local basis.The admittance matrix,which is the modal representation of Direchlet-to-Neumann operator,is introduced to compute the first-order evolution equations with no numerical instability caused by evanescent modes.The fourth-order Magnus scheme is used for the numerical integration of differential equations in the numerical implementation.The numerical experiments of sound field in underwater inhomogeneous waveguides generated by point sources are performed.Besides,the numerical results computed by simulation software COMSOL Multiphysics are given to validate the correction of the multimodal admittance method.It is shown that the multimodal admittance method is an efficient and stable numerical method to solve the wave propagation problem in inhomogeneous underwater waveguides with sound-speed profiles,liquid-like scatterers,and range-dependent environments.The extension of the method to more complicated waveguides such as horizontally stratified waveguides is available.展开更多
The displacement discontinuity method(DDM) is a kind of boundary element method aiming at modeling two-dimensional linear elastic crack problems. The singularity around the crack tip prevents the DDM from optimally co...The displacement discontinuity method(DDM) is a kind of boundary element method aiming at modeling two-dimensional linear elastic crack problems. The singularity around the crack tip prevents the DDM from optimally converging when the basis functions are polynomials of first order or higher. To overcome this issue,enlightened by the mapped finite element method(FEM) proposed in Ref. [13], we present an optimally convergent mapped DDM in this work, called the mapped DDM(MDDM). It is essentially based on approximating a much smoother function obtained by reformulating the problem with an appropriate auxiliary map. Two numerical examples of crack problems are presented in comparison with the conventional DDM. The results show that the proposed method improves the accuracy of the DDM; moreover, it yields an optimal convergence rate for quadratic interpolating polynomials.展开更多
In this paper, we consider the inverse scattering problem of reconstructing a bounded obstacle in a three-dimensional planar waveguide from the scattered near-field data measured on a finite cylindrical surface contai...In this paper, we consider the inverse scattering problem of reconstructing a bounded obstacle in a three-dimensional planar waveguide from the scattered near-field data measured on a finite cylindrical surface containing the obstacle and corresponding to infinitely many incident point sources also placed on the measurement surface. The obstacle is allowed to be an impenetrable scatterer or a penetrable scatterer. We establish the validity of the factorization method with the nearfield data to characterize the obstacle in the planar waveguide by constructing an outgoing-to-incoming operator which is an integral operator defined on the measurement surface with the kernel given in terms of an infinite series.展开更多
The higher order displacement discontinuity method(HODDM) utilizing special crack tip elements has been used in the solution of linear elastic fracture mechanics(LEFM) problems. The paper has selected several example ...The higher order displacement discontinuity method(HODDM) utilizing special crack tip elements has been used in the solution of linear elastic fracture mechanics(LEFM) problems. The paper has selected several example problems from the fracture mechanics literature(with available analytical solutions) including center slant crack in an infinite and finite body, single and double edge cracks, cracks emanating from a circular hole. The numerical values of Mode Ⅰ and Mode Ⅱ SIFs for these problems using HODDM are in excellent agreement with analytical results(reaching up to 0.001% deviation from their analytical results). The HODDM is also compared with the XFEM and a modified XFEM results. The results show that the HODDM needs a considerably lower computational effort(with less than 400 nodes) than the XFEM and the modified XFEM(which needs more than 10000 nodes) to reach a much higher accuracy. The proposed HODDM offers higher accuracy and lower computation effort for a wide range of problems in LEFM.展开更多
A 3D displacement discontinuity method is applied to solve the fracture mechanics problems of the mixed mode crack under compression.Friction between the surface of the closed crack is considered by establishing a sim...A 3D displacement discontinuity method is applied to solve the fracture mechanics problems of the mixed mode crack under compression.Friction between the surface of the closed crack is considered by establishing a simple and efficient iterative algorithm based on method of contact resistance mitigation.On the surfaces of the closed crack,the Mohr-coulomb rule is satisfied by iteration when the crack is in condition of sliding.The stress intensity factors are obtained using displacement fitting method.It is shown that the numerical results agree with the experimental results well and that friction plays an important role in resisting crack propagation.展开更多
A hyperbolic conservation equation can easily generate strong discontinuous solutions such as shock waves and contact discontinuity.By introducing the arc-length parameter,the pseudo arc-length method(PALM)smoothens t...A hyperbolic conservation equation can easily generate strong discontinuous solutions such as shock waves and contact discontinuity.By introducing the arc-length parameter,the pseudo arc-length method(PALM)smoothens the discontinuous solution in the arc-length space.This in turn weakens the singularity of the equation.To avoid constructing a high-order scheme directly in the deformed physical space,the entire calculation process is conducted in a uniform orthogonal arc-length space.Furthermore,to ensure the stability of the equation,the time step is reduced by limiting the moving speed of the mesh.Given that the calculation does not involve the interpolation process of physical quantities after the mesh moves,it maintains a high computational efficiency.The numerical examples show that the algorithm can effectively reduce numerical oscillations while maintaining excellent characteristics such as high precision and high resolution.展开更多
In this paper,a fully discrete stability analysis is carried out for the direct discontinuous Galerkin(DDG)methods coupled with Runge-Kutta-type implicit-explicit time marching,for solving one-dimensional linear conve...In this paper,a fully discrete stability analysis is carried out for the direct discontinuous Galerkin(DDG)methods coupled with Runge-Kutta-type implicit-explicit time marching,for solving one-dimensional linear convection-diffusion problems.In the spatial discretization,both the original DDG methods and the refined DDG methods with interface corrections are considered.In the time discretization,the convection term is treated explicitly and the diffusion term implicitly.By the energy method,we show that the corresponding fully discrete schemes are unconditionally stable,in the sense that the time-stepis only required to be upper bounded by a constant which is independent of the mesh size h.Opti-mal error estimate is also obtained by the aid of a special global projection.Numerical experiments are given to verify the stability and accuracy of the proposed schemes.展开更多
In this paper, an absorbing Fictitious Boundary Condition (FBC) is presented to generate an iterative Domain Decomposition Method (DDM) for analyzing waveguide problems.The relaxed algorithm is introduced to improve t...In this paper, an absorbing Fictitious Boundary Condition (FBC) is presented to generate an iterative Domain Decomposition Method (DDM) for analyzing waveguide problems.The relaxed algorithm is introduced to improve the iterative convergence. And the matrix equations are solved using the multifrontal algorithm. The resulting CPU time is greatly reduced.Finally, a number of numerical examples are given to illustrate its accuracy and efficiency.展开更多
A technique for modelling of three-dimensional(3D)quasi-statically propagating cracks in elastic bodies by the displacement discontinuity method(DDM)was described.When the crack is closed,the Mohr-coulomb rule on the ...A technique for modelling of three-dimensional(3D)quasi-statically propagating cracks in elastic bodies by the displacement discontinuity method(DDM)was described.When the crack is closed,the Mohr-coulomb rule on the two contacted surfaces of the crack must be satisfied.A simple iterative method was adopted in order to consider three different states of cracks.Under the assumption that the advance of the point on the crack front would occur only in the normal plane which is through this edge point,the maximum energy release rate criterion is modified to be used as the criterion for the crack growth.With discretization,the process of crack propagation can be seen as the advance of the vertices of the crack front.The program MCP3D was developed based on these theories to simulate the 3D quasi-static crack propagation.A numerical example of a penny-shaped crack subject to tension and compression in an infinite elastic media was analyzed with MCP3D,and the results in comparison with others' show that the present method for 3D crack propagation is effective.展开更多
Discontinuous deformation analysis(DDA)has been widely applied for the simulation of block systems that have many discontinuous surfaces.The penalty method is utilized to ensure that there are no penetrations between ...Discontinuous deformation analysis(DDA)has been widely applied for the simulation of block systems that have many discontinuous surfaces.The penalty method is utilized to ensure that there are no penetrations between blocks.A linear polynomial function for displacement leads to a constant stress for a block,which cannot precisely describe the stress field within the block.Therefore,a high-order polynomial displacement function and a flue mesh are always used to improve the precision of the stress field.However,these means are not practical for simulating block systems that have many contacts.In this paper,the contact-stress-based stress recovery methods are proposed for DDA.High-precision solutions for the contact stresses on the boundaries of the blocks are utilized.The first-order Gaussian point of a block is the block's centroid,where the constant stress obtained via DDA is of higher precision.The high-precision solutions for the stresses are utilized in the least squares method to recover a single block's inner stress field.The proposed methods enhance the resolution of the stress field inside a single block without increasing the computational effort in the main iterative process for displacement in DDA.Numerical examples are simulated using both the finite element method(FEM)with a fine mesh and the proposed DDA program.The recovered DDA results can accurately describe the distribution of the stresses in a single block and,in some areas,have the same precision as the FEM results.Moreover,the precision of the proposed methods improves as the gradient of the contact stress on the boundary decreases.展开更多
The present research is focused on the numerical crack coalescence analysis of the micro-cracks and cracks produced during the cutting action of TBM disc cutters. The linear elastic fracture mechanics(LEFM) concepts a...The present research is focused on the numerical crack coalescence analysis of the micro-cracks and cracks produced during the cutting action of TBM disc cutters. The linear elastic fracture mechanics(LEFM) concepts and the maximum tangential stress criterion are used to investigate the micro crack propagation and its direction underneath the excavating discs. A higher order displacement discontinuity method with quadratic displacement discontinuity elements is used to estimate the stress intensity factors near the crack tips. Rock cutting mechanisms under single and double type discs are simulated by the proposed numerical method.The main purposes of the present modeling are to simulate the chip formation process of indented rocks by single and double discs.The effects of specific disc parameters(except speed) on the thrust force Ft, the rolling force Fr, and the specific energy ES are investigated. It has been shown that the specific energy(energy required to cut through a unit volume of rock) of the double disc is less than that of the single disc. Crack propagation in rocks under disc cutters is numerically modeled and the optimum ratio of disc spacing S to penetration depth Pd(i.e. S/Pd ratio) of about 10 is obtained, which is in good agreement with the theoretical and experimental results cited in the literature.展开更多
The back analysis of initial stress is usually based on measured stress values, but the measuring of initial stress demands substantial investment. Therefore, amounts of underground engineering have no measured initia...The back analysis of initial stress is usually based on measured stress values, but the measuring of initial stress demands substantial investment. Therefore, amounts of underground engineering have no measured initial stress data, such as tunneling engineering. Focusing on this problem, a new back analysis method which does not need measured initial stress data is developed. The fault is assumed to be caused by initial load, the displacement discontinuity method (DDM) which considered non-linear fault is adopted to establish a numerical model of the engineering site, and the multivariable regression analysis of the initial stress field around the faults is carried out based on the fault throw. The result shows that the initial stress field around the faults is disturbed significantly, stress concentration appears in the tip zone, the regressive fault throw matches the measured values well, and the regressive initial stress field is reliable.展开更多
In this paper,we study the superconvergence properties of the energy-conserving discontinuous Galerkin(DG)method in[18]for one-dimensional linear hyperbolic equations.We prove the approximate solution superconverges t...In this paper,we study the superconvergence properties of the energy-conserving discontinuous Galerkin(DG)method in[18]for one-dimensional linear hyperbolic equations.We prove the approximate solution superconverges to a particular projection of the exact solution.The order of this superconvergence is proved to be k+2 when piecewise Pk polynomials with K≥1 are used.The proof is valid for arbitrary non-uniform regular meshes and for piecewise polynomials with arbitrary K≥1.Furthermore,we find that the derivative and function value approxi?mations of the DG solution are superconvergent at a class of special points,with an order of k+1 and R+2,respectively.We also prove,under suitable choice of initial discretization,a(2k+l)-th order superconvergence rate of the DG solution for the numerical fluxes and the cell averages.Numerical experiments are given to demonstrate these theoretical results.展开更多
<div style="text-align:justify;"> In this paper, we study the error estimates for direct discontinuous Galerkin methods based on the upwind-biased fluxes. We use a newly global projection to obtain the...<div style="text-align:justify;"> In this paper, we study the error estimates for direct discontinuous Galerkin methods based on the upwind-biased fluxes. We use a newly global projection to obtain the optimal error estimates. The numerical experiments imply that <em>L</em><sup>2 </sup>norms error estimates can reach to order <em>k</em> + 1 by using time discretization methods. </div>展开更多
文摘The anisotropic Perfectly Matched Layer(PML) absorbing boundary condition is implemented in a 2-D finite element formulation to solve dielectric waveguide discontinuity problems. The choice of parameters of anisotropic PML has been investigated. Using the boundary truncating technique, the solution process of Finite-Element Method (FEM) has been greatly simplified compared with other hybrid methods. The required computational resources have also significantly declined since the anisotropic PML interface can be placed much closer to the scatterer compared to other well known artificial boundary.
基金Supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘A novel high-order three-dimensional （3-D） discontinuous Galerkin time domain （DGTD） method based on a normalized formulation of Maxwell＇s equations is developed for modeling and simulating silicon-on-insulator （SOD thin-ridge waveguide. The DGTD method employs unstructured meshes and piecewise high-order polynomials for spatial discretization, and Runge-Kutta methods for time integration. It is found that the numerical results of the leakage loss of SOI thin-ridge waveguide agree well with those of analytical solutions, which proves that the proposed method is an ideal tool for the quantitative analysis for SOI thin-ridge waveguide.
基金supported by the China Geological Survey (No.1212011014030)the Major State Basic Research Development Program of China (973 Program) (No.2011CB710600)
文摘The estimation of shear strength of rock mass discontinuity is always a focal, but difficult, problem in the field of geotechnical engineering. Considering the disadvantages and limitation of exist- ing estimation methods, a new approach based on the shadow area percentage （SAP） that can be used to quantify surface roughness is proposed in this article. Firstly, by the help of laser scanning technique, the three-dimensional model of the surface of rock discontinuity was established. Secondly, a light source was simulated, and there would be some shadows produced on the model surface. Thirdly, to obtain the value of SAP of each specimen, the shadow detection technique was introduced for use. Fourthly, compared with the result from direct shear testing and based on statistics, an empirical for- mula was found among SAP, normal stress, and shear strength. Data of Yujian （~ River were used as an example, and the following conclusions have been made. （1） In the case of equal normal stress, the peak shear stress is positively proportional to the SAP. （2） The formula for estimating was derived, and the predictions of peak-shear strength made with this equation well agreed with the experimental re- suits obtained in laboratory tests.
文摘An extended displacement discontinuity method(EDDM)is proposed to analyze the stress wave propagation in jointed viscoelastic rock mass(VRM).The discontinuities in a rock mass are divided into two groups.The primary group with an average geometrical size larger than or in the same order of magnitude of wavelength of a concerned stress wave is defined as'macro-joints',while the secondary group with a high density and relatively small geometrical size compared to the wavelength is known as'micro-defects'.The rock mass with micro-defects is modeled as an equivalent viscoelastic medium while the macro-joints in the rock mass are modeled explicitly as physical discontinuities.Viscoelastic properties of a micro-defected sedimentary rock are obtained by longitudinally impacting a cored long sedimentary rod with a pendulum.Wave propagation coefficient and dynamic viscoelastic modulus are measured.The EDDM is then successfully employed to analyze the wave propagation across macro-joint in VRM.The effect of the rock viscosity on the stress wave propagation is evaluated by comparing the results of VRM from the presented EDDM with those of an elastic rock mass(ERM)from the conventional displacement discontinuity method(CDDM).The CDDM is a special case of the EDDM under the condition that the rock viscosity is ignored.Comparison of the reflected and transmitted waves shows that the essential rock viscosity has a significant effect on stress wave attenuation.When a short propagation distance of a stress wave is considered,the results obtained from the CDDM approximate to the EDDM solutions,however,when the propagation distance is sufficiently long relative to the wavelength,the effect of rock viscosity on the stress wave propagation cannot be ignored.
基金Project(2009318000046) supported by the Western Transport Technical Program of the Ministry of Transport,China
文摘A revised displacement discontinuity method(DDM) program is developed for the simulation of rock joint propagation and dilatancy analysis. The non-linear joint model used in the program adopts Barton-Bandis normal deformation model, Kulhaway shear deformation model and Mohr-Coulomb criterion. The joint propagation criterion is based on the equivalent stress intensity factor which can be obtained by regression analysis. The simulated rock joint propagation accords well with the existing knowledge. The closure and opening of joint is investigated by DDM, and it is shown that if the opening volume of propagated joint is larger than closure volume of the old joint, the joint dilatancy occurs. The dilatancy condition is mainly controlled by the normal stiffness of the rock joint. When the normal stiffness is larger than the critical value, joint dilatancy occurs. The critical normal stiffness of rock joint changes with the joint-load angle, and joint dilatancy is most possible to occur at 30°.
文摘In this paper,a new strategy for a sub-element-based shock capturing for discontinuous Galerkin(DG)approximations is presented.The idea is to interpret a DG element as a col-lection of data and construct a hierarchy of low-to-high-order discretizations on this set of data,including a first-order finite volume scheme up to the full-order DG scheme.The dif-ferent DG discretizations are then blended according to sub-element troubled cell indicators,resulting in a final discretization that adaptively blends from low to high order within a single DG element.The goal is to retain as much high-order accuracy as possible,even in simula-tions with very strong shocks,as,e.g.,presented in the Sedov test.The framework retains the locality of the standard DG scheme and is hence well suited for a combination with adaptive mesh refinement and parallel computing.The numerical tests demonstrate the sub-element adaptive behavior of the new shock capturing approach and its high accuracy.
文摘The multimodal admittance method and its improvement are presented to deal with various aspects in underwater acoustics,mostly for the sound propagation in inhomogeneous waveguides with sound-speed profiles,arbitrary-shaped liquid-like scatterers,and range-dependent environments.In all cases,the propagation problem governed by the Helmholtz equation is transformed into initial value problems of two coupled first-order evolution equations with respect to the modal components of field quantities(sound pressure and its derivative),by projecting the Helmholtz equation on a constructed orthogonal and complete local basis.The admittance matrix,which is the modal representation of Direchlet-to-Neumann operator,is introduced to compute the first-order evolution equations with no numerical instability caused by evanescent modes.The fourth-order Magnus scheme is used for the numerical integration of differential equations in the numerical implementation.The numerical experiments of sound field in underwater inhomogeneous waveguides generated by point sources are performed.Besides,the numerical results computed by simulation software COMSOL Multiphysics are given to validate the correction of the multimodal admittance method.It is shown that the multimodal admittance method is an efficient and stable numerical method to solve the wave propagation problem in inhomogeneous underwater waveguides with sound-speed profiles,liquid-like scatterers,and range-dependent environments.The extension of the method to more complicated waveguides such as horizontally stratified waveguides is available.
基金the National Natural Science Foundation of China(No.11402146)the Young 1000 Talent Program of China
文摘The displacement discontinuity method(DDM) is a kind of boundary element method aiming at modeling two-dimensional linear elastic crack problems. The singularity around the crack tip prevents the DDM from optimally converging when the basis functions are polynomials of first order or higher. To overcome this issue,enlightened by the mapped finite element method(FEM) proposed in Ref. [13], we present an optimally convergent mapped DDM in this work, called the mapped DDM(MDDM). It is essentially based on approximating a much smoother function obtained by reformulating the problem with an appropriate auxiliary map. Two numerical examples of crack problems are presented in comparison with the conventional DDM. The results show that the proposed method improves the accuracy of the DDM; moreover, it yields an optimal convergence rate for quadratic interpolating polynomials.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61421062 and 61520106004)the Microsoft Research Fund of Asia
文摘In this paper, we consider the inverse scattering problem of reconstructing a bounded obstacle in a three-dimensional planar waveguide from the scattered near-field data measured on a finite cylindrical surface containing the obstacle and corresponding to infinitely many incident point sources also placed on the measurement surface. The obstacle is allowed to be an impenetrable scatterer or a penetrable scatterer. We establish the validity of the factorization method with the nearfield data to characterize the obstacle in the planar waveguide by constructing an outgoing-to-incoming operator which is an integral operator defined on the measurement surface with the kernel given in terms of an infinite series.
文摘The higher order displacement discontinuity method(HODDM) utilizing special crack tip elements has been used in the solution of linear elastic fracture mechanics(LEFM) problems. The paper has selected several example problems from the fracture mechanics literature(with available analytical solutions) including center slant crack in an infinite and finite body, single and double edge cracks, cracks emanating from a circular hole. The numerical values of Mode Ⅰ and Mode Ⅱ SIFs for these problems using HODDM are in excellent agreement with analytical results(reaching up to 0.001% deviation from their analytical results). The HODDM is also compared with the XFEM and a modified XFEM results. The results show that the HODDM needs a considerably lower computational effort(with less than 400 nodes) than the XFEM and the modified XFEM(which needs more than 10000 nodes) to reach a much higher accuracy. The proposed HODDM offers higher accuracy and lower computation effort for a wide range of problems in LEFM.
文摘A 3D displacement discontinuity method is applied to solve the fracture mechanics problems of the mixed mode crack under compression.Friction between the surface of the closed crack is considered by establishing a simple and efficient iterative algorithm based on method of contact resistance mitigation.On the surfaces of the closed crack,the Mohr-coulomb rule is satisfied by iteration when the crack is in condition of sliding.The stress intensity factors are obtained using displacement fitting method.It is shown that the numerical results agree with the experimental results well and that friction plays an important role in resisting crack propagation.
基金Project supported by the National Natural Science Foundation of China(Nos.11822203 and 12032006)
文摘A hyperbolic conservation equation can easily generate strong discontinuous solutions such as shock waves and contact discontinuity.By introducing the arc-length parameter,the pseudo arc-length method(PALM)smoothens the discontinuous solution in the arc-length space.This in turn weakens the singularity of the equation.To avoid constructing a high-order scheme directly in the deformed physical space,the entire calculation process is conducted in a uniform orthogonal arc-length space.Furthermore,to ensure the stability of the equation,the time step is reduced by limiting the moving speed of the mesh.Given that the calculation does not involve the interpolation process of physical quantities after the mesh moves,it maintains a high computational efficiency.The numerical examples show that the algorithm can effectively reduce numerical oscillations while maintaining excellent characteristics such as high precision and high resolution.
基金the NSFC grant 11871428the Nature Science Research Program for Colleges and Universities of Jiangsu Province grant 20KJB110011Qiang Zhang:Research supported by the NSFC grant 11671199。
文摘In this paper,a fully discrete stability analysis is carried out for the direct discontinuous Galerkin(DDG)methods coupled with Runge-Kutta-type implicit-explicit time marching,for solving one-dimensional linear convection-diffusion problems.In the spatial discretization,both the original DDG methods and the refined DDG methods with interface corrections are considered.In the time discretization,the convection term is treated explicitly and the diffusion term implicitly.By the energy method,we show that the corresponding fully discrete schemes are unconditionally stable,in the sense that the time-stepis only required to be upper bounded by a constant which is independent of the mesh size h.Opti-mal error estimate is also obtained by the aid of a special global projection.Numerical experiments are given to verify the stability and accuracy of the proposed schemes.
文摘In this paper, an absorbing Fictitious Boundary Condition (FBC) is presented to generate an iterative Domain Decomposition Method (DDM) for analyzing waveguide problems.The relaxed algorithm is introduced to improve the iterative convergence. And the matrix equations are solved using the multifrontal algorithm. The resulting CPU time is greatly reduced.Finally, a number of numerical examples are given to illustrate its accuracy and efficiency.
文摘A technique for modelling of three-dimensional(3D)quasi-statically propagating cracks in elastic bodies by the displacement discontinuity method(DDM)was described.When the crack is closed,the Mohr-coulomb rule on the two contacted surfaces of the crack must be satisfied.A simple iterative method was adopted in order to consider three different states of cracks.Under the assumption that the advance of the point on the crack front would occur only in the normal plane which is through this edge point,the maximum energy release rate criterion is modified to be used as the criterion for the crack growth.With discretization,the process of crack propagation can be seen as the advance of the vertices of the crack front.The program MCP3D was developed based on these theories to simulate the 3D quasi-static crack propagation.A numerical example of a penny-shaped crack subject to tension and compression in an infinite elastic media was analyzed with MCP3D,and the results in comparison with others' show that the present method for 3D crack propagation is effective.
文摘Discontinuous deformation analysis(DDA)has been widely applied for the simulation of block systems that have many discontinuous surfaces.The penalty method is utilized to ensure that there are no penetrations between blocks.A linear polynomial function for displacement leads to a constant stress for a block,which cannot precisely describe the stress field within the block.Therefore,a high-order polynomial displacement function and a flue mesh are always used to improve the precision of the stress field.However,these means are not practical for simulating block systems that have many contacts.In this paper,the contact-stress-based stress recovery methods are proposed for DDA.High-precision solutions for the contact stresses on the boundaries of the blocks are utilized.The first-order Gaussian point of a block is the block's centroid,where the constant stress obtained via DDA is of higher precision.The high-precision solutions for the stresses are utilized in the least squares method to recover a single block's inner stress field.The proposed methods enhance the resolution of the stress field inside a single block without increasing the computational effort in the main iterative process for displacement in DDA.Numerical examples are simulated using both the finite element method(FEM)with a fine mesh and the proposed DDA program.The recovered DDA results can accurately describe the distribution of the stresses in a single block and,in some areas,have the same precision as the FEM results.Moreover,the precision of the proposed methods improves as the gradient of the contact stress on the boundary decreases.
文摘The present research is focused on the numerical crack coalescence analysis of the micro-cracks and cracks produced during the cutting action of TBM disc cutters. The linear elastic fracture mechanics(LEFM) concepts and the maximum tangential stress criterion are used to investigate the micro crack propagation and its direction underneath the excavating discs. A higher order displacement discontinuity method with quadratic displacement discontinuity elements is used to estimate the stress intensity factors near the crack tips. Rock cutting mechanisms under single and double type discs are simulated by the proposed numerical method.The main purposes of the present modeling are to simulate the chip formation process of indented rocks by single and double discs.The effects of specific disc parameters(except speed) on the thrust force Ft, the rolling force Fr, and the specific energy ES are investigated. It has been shown that the specific energy(energy required to cut through a unit volume of rock) of the double disc is less than that of the single disc. Crack propagation in rocks under disc cutters is numerically modeled and the optimum ratio of disc spacing S to penetration depth Pd(i.e. S/Pd ratio) of about 10 is obtained, which is in good agreement with the theoretical and experimental results cited in the literature.
基金the Western Transport Construction Science and Technology Project of the Ministry of Transport of the People's Republic of China(No.2009318000046)
文摘The back analysis of initial stress is usually based on measured stress values, but the measuring of initial stress demands substantial investment. Therefore, amounts of underground engineering have no measured initial stress data, such as tunneling engineering. Focusing on this problem, a new back analysis method which does not need measured initial stress data is developed. The fault is assumed to be caused by initial load, the displacement discontinuity method (DDM) which considered non-linear fault is adopted to establish a numerical model of the engineering site, and the multivariable regression analysis of the initial stress field around the faults is carried out based on the fault throw. The result shows that the initial stress field around the faults is disturbed significantly, stress concentration appears in the tip zone, the regressive fault throw matches the measured values well, and the regressive initial stress field is reliable.
文摘In this paper,we study the superconvergence properties of the energy-conserving discontinuous Galerkin(DG)method in[18]for one-dimensional linear hyperbolic equations.We prove the approximate solution superconverges to a particular projection of the exact solution.The order of this superconvergence is proved to be k+2 when piecewise Pk polynomials with K≥1 are used.The proof is valid for arbitrary non-uniform regular meshes and for piecewise polynomials with arbitrary K≥1.Furthermore,we find that the derivative and function value approxi?mations of the DG solution are superconvergent at a class of special points,with an order of k+1 and R+2,respectively.We also prove,under suitable choice of initial discretization,a(2k+l)-th order superconvergence rate of the DG solution for the numerical fluxes and the cell averages.Numerical experiments are given to demonstrate these theoretical results.
文摘<div style="text-align:justify;"> In this paper, we study the error estimates for direct discontinuous Galerkin methods based on the upwind-biased fluxes. We use a newly global projection to obtain the optimal error estimates. The numerical experiments imply that <em>L</em><sup>2 </sup>norms error estimates can reach to order <em>k</em> + 1 by using time discretization methods. </div>
