A discontinuous Galerkin finite element method （DG-FEM） is developed for solving the axisymmetric Euler equations based on two-dimensional conservation laws. The method is used to simulate the unsteady-state underex...A discontinuous Galerkin finite element method （DG-FEM） is developed for solving the axisymmetric Euler equations based on two-dimensional conservation laws. The method is used to simulate the unsteady-state underexpanded axisymmetric jet. Several flow property distributions along the jet axis, including density, pres- sure and Mach number are obtained and the qualitative flowfield structures of interest are well captured using the proposed method, including shock waves, slipstreams, traveling vortex ring and multiple Mach disks. Two Mach disk locations agree well with computational and experimental measurement results. It indicates that the method is robust and efficient for solving the unsteady-state underexpanded axisymmetric jet.展开更多
A numerical simulation of the toroidal shock wave focusing in a co-axial cylindrical shock tube is inves- tigated by using discontinuous Galerkin （DG） finite element method to solve the axisymmetric Euler equations....A numerical simulation of the toroidal shock wave focusing in a co-axial cylindrical shock tube is inves- tigated by using discontinuous Galerkin （DG） finite element method to solve the axisymmetric Euler equations. For validating the numerical method, the shock-tube problem with exact solution is computed, and the computed results agree well with the exact cases. Then, several cases with higher incident Mach numbers varying from 2.0 to 5.0 are simulated. Simulation results show that complicated flow-field structures of toroidal shock wave diffraction, reflection, and focusing in a co-axial cylindrical shock tube can be obtained at different incident Mach numbers and the numerical solutions appear steep gradients near the focusing point, which illustrates the DG method has higher accuracy and better resolution near the discontinuous point. Moreover, the focusing peak pres- sure with different grid scales is compared.展开更多
The discrete ordinates(S N)method requires numerous angular unknowns to achieve the desired accu-racy for shielding calculations involving strong anisotropy.Our objective is to develop an angular adaptive algorithm in...The discrete ordinates(S N)method requires numerous angular unknowns to achieve the desired accu-racy for shielding calculations involving strong anisotropy.Our objective is to develop an angular adaptive algorithm in the S N method to automatically optimize the angular distribution and minimize angular discretization errors with lower expenses.The proposed method enables linear dis-continuous finite element quadrature sets over an icosahe-dron to vary their quadrature orders in a one-twentieth sphere so that fine resolutions can be applied to the angular domains that are important.An error estimation that operates in conjunction with the spherical harmonics method is developed to determine the locations where more refinement is required.The adaptive quadrature sets are applied to three duct problems,including the Kobayashi benchmarks and the IRI-TUB research reactor,which emphasize the ability of this method to resolve neutron streaming through ducts with voids.The results indicate that the performance of the adaptive method is more effi-cient than that of uniform quadrature sets for duct transport problems.Our adaptive method offers an appropriate placement of angular unknowns to accurately integrate angular fluxes while reducing the computational costs in terms of unknowns and run times.展开更多
A mixed time discontinuous space-time finite element scheme for secondorder convection diffusion problems is constructed and analyzed. Order of the equation is lowered by the mixed finite element method. The low order...A mixed time discontinuous space-time finite element scheme for secondorder convection diffusion problems is constructed and analyzed. Order of the equation is lowered by the mixed finite element method. The low order equation is discretized with a space-time finite element method, continuous in space but discontinuous in time. Stability, existence, uniqueness and convergence of the approximate solutions are proved. Numerical results are presented to illustrate efficiency of the proposed method.展开更多
In the last decade, three dimensional discontin- uous deformation analyses （3D DDA） has attracted more and more attention of researchers and geotechnical engineers worldwide. The original DDA formulation utilizes a ...In the last decade, three dimensional discontin- uous deformation analyses （3D DDA） has attracted more and more attention of researchers and geotechnical engineers worldwide. The original DDA formulation utilizes a linear displacement function to describe the block movement and deformation, which would cause block expansion under rigid body rotation and thus limit its capability to model block de- formation. In this paper, 3D DDA is coupled with tetrahe- dron finite elements to tackle these two problems. Tetrahe- dron is the simplest in the 3D domain and makes it easy to implement automatic discretization, even for complex topol- ogy shape. Furthermore, element faces will remain planar and element edges will remain straight after deformation for tetrahedron finite elements and polyhedral contact detection schemes can be used directly. The matrices of equilibrium equations for this coupled method are given in detail and an effective contact searching algorithm is suggested. Valida- tion is conducted by comparing the results of the proposed coupled method with that of physical model tests using one of the most common failure modes, i.e., wedge failure. Most of the failure modes predicted by the coupled method agree with the physical model results except for 4 cases out of the total 65 cases. Finally, a complex rockslide example demon- strates the robustness and versatility of the coupled method.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
We consider the mixed discontinuous Galerkin(DG)finite element approximation of the Stokes equation and provide the analysis for the[P_(k)]^d-P_(k-1)element on the tensor product meshes.Comparing to the previous stabi...We consider the mixed discontinuous Galerkin(DG)finite element approximation of the Stokes equation and provide the analysis for the[P_(k)]^d-P_(k-1)element on the tensor product meshes.Comparing to the previous stability proof with[Q_(k)]^(d)-Q_(k-1)discontinuous finite elements in the existing references,our first contribution is to extend the formal proof to the[P_(k)]^d-P_(k-1)discontinuous elements on the tensor product meshes.Numerical infsup tests have been performed to compare Q_(x)and P_(k)types of elements and validate the well-posedness in both settings.Secondly,our contribution is to design the enhanced pressure-robust discretization by only modifying the body source assembling on[P_(k)]^d-P_(k-1)schemes to improve the numerical simulation further.The produced numerical velocity solution via our enhancement shows viscosity and pressure independence and thus outperforms the solution produced by standard discontinuous Galerkin schemes.Robustness analysis and numerical tests have been provided to validate the scheme's robustness.展开更多
Discontinuous deformation problems are common in rock engineering. Numerical analysis methods based on system models of the discrete body can better solve these problems. One of the most effective solutions is discont...Discontinuous deformation problems are common in rock engineering. Numerical analysis methods based on system models of the discrete body can better solve these problems. One of the most effective solutions is discontinuous deformation analysis （DDA） method, but the DDA method brings about rock embedding problems when it uses the strain assumption in elastic deformation and adopts virtual springs to simulate the contact problems. The multi-body finite element method （FEM） proposed in this paper can solve the problems of contact and deformation of blocks very well because it integrates the FEM and multi-body system dynamics theory. It is therefore a complete method for solving discontinuous deformation problems through balance equations of the contact surface and for simulating the displacement of whole blocks. In this study, this method was successfully used for deformation analysis of underground caverns in stratified rock. The simulation results indicate that the multi-body FEM can show contact forces and the stress states on contact surfaces better than DDA, and that the results calculated with the multi-body FEM are more consistent with engineering practice than those calculated with DDA method.展开更多
The complex structure and strong heterogeneity of advanced nuclear reactor systems pose challenges for high-fidelity neutron-shielding calculations. Unstructured meshes exhibit strong geometric adaptability and can ov...The complex structure and strong heterogeneity of advanced nuclear reactor systems pose challenges for high-fidelity neutron-shielding calculations. Unstructured meshes exhibit strong geometric adaptability and can overcome the deficiencies of conventionally structured meshes in complex geometry modeling. A multithreaded parallel upwind sweep algorithm for S_(N) transport was proposed to achieve a more accurate geometric description and improve the computational efficiency. The spatial variables were discretized using the standard discontinuous Galerkin finite-element method. The angular flux transmission between neighboring meshes was handled using an upwind scheme. In addition, a combination of a mesh transport sweep and angular iterations was realized using a multithreaded parallel technique. The algorithm was implemented in the 2D/3D S_(N) transport code ThorSNIPE, and numerical evaluations were conducted using three typical benchmark problems:IAEA, Kobayashi-3i, and VENUS-3. These numerical results indicate that the multithreaded parallel upwind sweep algorithm can achieve high computational efficiency. ThorSNIPE, with a multithreaded parallel upwind sweep algorithm, has good reliability, stability, and high efficiency, making it suitable for complex shielding calculations.展开更多
The present study regards the numerical approximation of solutions of systems of Korteweg-de Vries type,coupled through their nonlinear terms.In our previous work[9],we constructed conservative and dissipative finite ...The present study regards the numerical approximation of solutions of systems of Korteweg-de Vries type,coupled through their nonlinear terms.In our previous work[9],we constructed conservative and dissipative finite element methods for these systems and presented a priori error estimates for the semidiscrete schemes.In this sequel,we present a posteriori error estimates for the semidiscrete and fully discrete approximations introduced in[9].The key tool employed to effect our analysis is the dispersive reconstruction devel-oped by Karakashian and Makridakis[20]for related discontinuous Galerkin methods.We conclude by providing a set of numerical experiments designed to validate the a posteriori theory and explore the effectivity of the resulting error indicators.展开更多
In this paper, a Petrov-Galerkin scheme named the Runge-Kutta control volume （RKCV） discontinuous finite ele- ment method is constructed to solve the one-dimensional compressible Euler equations in the Lagrangian co...In this paper, a Petrov-Galerkin scheme named the Runge-Kutta control volume （RKCV） discontinuous finite ele- ment method is constructed to solve the one-dimensional compressible Euler equations in the Lagrangian coordinate. Its advantages include preservation of the local conservation and a high resolution. Compared with the Runge-Kutta discon- tinuous Galerkin （RKDG） method, the RKCV method is easier to implement. Moreover, the advantages of the RKCV and the Lagrangian methods are combined in the new method. Several numerical examples are given to illustrate the accuracy and the reliability of the algorithm.展开更多
A pressure gradient discontinuous finite element formulation for the compressible Navier-Stokes equations is derived based on local projections. The resulting finite element formulation is stable and uniquely solvable...A pressure gradient discontinuous finite element formulation for the compressible Navier-Stokes equations is derived based on local projections. The resulting finite element formulation is stable and uniquely solvable without requiring a B-B stability condition. An error estimate is Obtained.展开更多
The fatigue damage model based on theory of damage mechanics is capable of predicting the fatigue life under multiaxial loading. Meanwhile, the application of critical plane method in the prediction of multiaxial fati...The fatigue damage model based on theory of damage mechanics is capable of predicting the fatigue life under multiaxial loading. Meanwhile, the application of critical plane method in the prediction of multiaxial fatigue life has made certain progress. According to the law of thermodynamics, a new damage evolution equation is developed in the present study to predict the fatigue life of geometrically discontinuous structure under tension-torsion loading based on damage mechanics and the critical plane method. The essence of this approach is tha t the st rain parame ter of the uniaxial nonlinear fatigue damage model is replaced with the equivalent strain, which consists of the releva nt parame ters of the critical plane. However, it is difficult to calculate the stress-strain status and the critical plane position of geometrically dis? continuous structure by theoretical methods because of the existence of stress concentration and the multiaxial nonproportional characteristics. Therefore, a new numerical simulation method is proposed to determine the critical plane of geometrically discontinuous structure under multiaxial loading by means of the finite element method and MATLAB software. The fatigue life of notched specimens subjected to combined bending and torsion is predicted using the proposed met hod, and the result is compared with t hose from the experimen ts and the Manson-Cfiffin law. The comparisons show that the proposed method is superior to the Manson-Coffin law and is capable of reproducing the experimental results reasonably when the geometry of the structure is complex. It completely meets the needs of engineering practice.展开更多
A discontinuity-capturing scheme of finite element method(FEM)is proposed.The unstructured-grid technique combined with a new type of adaptive mesh approach is developed for both compressible and incompressible unstea...A discontinuity-capturing scheme of finite element method(FEM)is proposed.The unstructured-grid technique combined with a new type of adaptive mesh approach is developed for both compressible and incompressible unsteady flows,which exhibits the capability of capturing the shock waves and/or thin shear layers accurately in an unsteady viscous flow at high Reynolds number. In particular,a new testing variable,i.e.,the disturbed kinetic energy E,is suggested and used in the adaptive mesh computation,which is universally applicable to the capturing of both shock waves and shear layers in the inviscid flow and viscous flow at high Reynolds number.Based on several calculated examples,this approach has been proved to be effective and efficient for the calculations of compressible and incompressible flows.展开更多
A novel conforming discontinuous Galerkin(CDG)finite element method is introduced for the Poisson equation on rectangular meshes.This CDG method with discontinuous P_(k)(k≥1)elements converges to the true solution tw...A novel conforming discontinuous Galerkin(CDG)finite element method is introduced for the Poisson equation on rectangular meshes.This CDG method with discontinuous P_(k)(k≥1)elements converges to the true solution two orders above the continuous finite element counterpart.Superconvergence of order two for the CDG finite element solution is proved in an energy norm and the L^(2)norm.A local post-process is defined which lifts a P_(k)CDG solution to a discontinuous P_(k+2)solution.It is proved that the lifted P_(k+2)solution converges at the optimal order.The numerical tests illustrate the theoretic findings.展开更多
In this paper, we consider the finite element method and discontinuous Galerkin method for the stochastic Helmholtz equation in R^d （d = 2, 3）. Convergence analysis and error estimates are presented for the numerica...In this paper, we consider the finite element method and discontinuous Galerkin method for the stochastic Helmholtz equation in R^d （d = 2, 3）. Convergence analysis and error estimates are presented for the numerical solutions. The effects of the noises on the accuracy of the approximations are illustrated. Numerical experiments are carried out to verify our theoretical results.展开更多
文摘A discontinuous Galerkin finite element method （DG-FEM） is developed for solving the axisymmetric Euler equations based on two-dimensional conservation laws. The method is used to simulate the unsteady-state underexpanded axisymmetric jet. Several flow property distributions along the jet axis, including density, pres- sure and Mach number are obtained and the qualitative flowfield structures of interest are well captured using the proposed method, including shock waves, slipstreams, traveling vortex ring and multiple Mach disks. Two Mach disk locations agree well with computational and experimental measurement results. It indicates that the method is robust and efficient for solving the unsteady-state underexpanded axisymmetric jet.
基金Supported by the National Natural Science Foundation of China(50976072,51106099,10902070)the Leading Academic Discipline Project of Shanghai Municipal Education Commission(J50501)the Science Foundation for the Excellent Youth Scholar of Higher Education of Shanghai(slg09003)~~
文摘A numerical simulation of the toroidal shock wave focusing in a co-axial cylindrical shock tube is inves- tigated by using discontinuous Galerkin （DG） finite element method to solve the axisymmetric Euler equations. For validating the numerical method, the shock-tube problem with exact solution is computed, and the computed results agree well with the exact cases. Then, several cases with higher incident Mach numbers varying from 2.0 to 5.0 are simulated. Simulation results show that complicated flow-field structures of toroidal shock wave diffraction, reflection, and focusing in a co-axial cylindrical shock tube can be obtained at different incident Mach numbers and the numerical solutions appear steep gradients near the focusing point, which illustrates the DG method has higher accuracy and better resolution near the discontinuous point. Moreover, the focusing peak pres- sure with different grid scales is compared.
基金supported by the National Natural Science Foundation of China(No.11975097)the Fundamental Research Funds for the Central Universities(No.2019MS038).
文摘The discrete ordinates(S N)method requires numerous angular unknowns to achieve the desired accu-racy for shielding calculations involving strong anisotropy.Our objective is to develop an angular adaptive algorithm in the S N method to automatically optimize the angular distribution and minimize angular discretization errors with lower expenses.The proposed method enables linear dis-continuous finite element quadrature sets over an icosahe-dron to vary their quadrature orders in a one-twentieth sphere so that fine resolutions can be applied to the angular domains that are important.An error estimation that operates in conjunction with the spherical harmonics method is developed to determine the locations where more refinement is required.The adaptive quadrature sets are applied to three duct problems,including the Kobayashi benchmarks and the IRI-TUB research reactor,which emphasize the ability of this method to resolve neutron streaming through ducts with voids.The results indicate that the performance of the adaptive method is more effi-cient than that of uniform quadrature sets for duct transport problems.Our adaptive method offers an appropriate placement of angular unknowns to accurately integrate angular fluxes while reducing the computational costs in terms of unknowns and run times.
基金supported by the National Natural Science Foundation of China (No. 10601022)NSF ofInner Mongolia Autonomous Region of China (No. 200607010106)513 and Science Fund of InnerMongolia University for Distinguished Young Scholars (No. ND0702)
文摘A mixed time discontinuous space-time finite element scheme for secondorder convection diffusion problems is constructed and analyzed. Order of the equation is lowered by the mixed finite element method. The low order equation is discretized with a space-time finite element method, continuous in space but discontinuous in time. Stability, existence, uniqueness and convergence of the approximate solutions are proved. Numerical results are presented to illustrate efficiency of the proposed method.
基金supported by the Key Project of Chinese National Programs for Fundamental Research and Development(2010CB731502)the National Natural Science Foundation of China(50978745)
文摘In the last decade, three dimensional discontin- uous deformation analyses （3D DDA） has attracted more and more attention of researchers and geotechnical engineers worldwide. The original DDA formulation utilizes a linear displacement function to describe the block movement and deformation, which would cause block expansion under rigid body rotation and thus limit its capability to model block de- formation. In this paper, 3D DDA is coupled with tetrahe- dron finite elements to tackle these two problems. Tetrahe- dron is the simplest in the 3D domain and makes it easy to implement automatic discretization, even for complex topol- ogy shape. Furthermore, element faces will remain planar and element edges will remain straight after deformation for tetrahedron finite elements and polyhedral contact detection schemes can be used directly. The matrices of equilibrium equations for this coupled method are given in detail and an effective contact searching algorithm is suggested. Valida- tion is conducted by comparing the results of the proposed coupled method with that of physical model tests using one of the most common failure modes, i.e., wedge failure. Most of the failure modes predicted by the coupled method agree with the physical model results except for 4 cases out of the total 65 cases. Finally, a complex rockslide example demon- strates the robustness and versatility of the coupled method.
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We consider the mixed discontinuous Galerkin(DG)finite element approximation of the Stokes equation and provide the analysis for the[P_(k)]^d-P_(k-1)element on the tensor product meshes.Comparing to the previous stability proof with[Q_(k)]^(d)-Q_(k-1)discontinuous finite elements in the existing references,our first contribution is to extend the formal proof to the[P_(k)]^d-P_(k-1)discontinuous elements on the tensor product meshes.Numerical infsup tests have been performed to compare Q_(x)and P_(k)types of elements and validate the well-posedness in both settings.Secondly,our contribution is to design the enhanced pressure-robust discretization by only modifying the body source assembling on[P_(k)]^d-P_(k-1)schemes to improve the numerical simulation further.The produced numerical velocity solution via our enhancement shows viscosity and pressure independence and thus outperforms the solution produced by standard discontinuous Galerkin schemes.Robustness analysis and numerical tests have been provided to validate the scheme's robustness.
文摘Discontinuous deformation problems are common in rock engineering. Numerical analysis methods based on system models of the discrete body can better solve these problems. One of the most effective solutions is discontinuous deformation analysis （DDA） method, but the DDA method brings about rock embedding problems when it uses the strain assumption in elastic deformation and adopts virtual springs to simulate the contact problems. The multi-body finite element method （FEM） proposed in this paper can solve the problems of contact and deformation of blocks very well because it integrates the FEM and multi-body system dynamics theory. It is therefore a complete method for solving discontinuous deformation problems through balance equations of the contact surface and for simulating the displacement of whole blocks. In this study, this method was successfully used for deformation analysis of underground caverns in stratified rock. The simulation results indicate that the multi-body FEM can show contact forces and the stress states on contact surfaces better than DDA, and that the results calculated with the multi-body FEM are more consistent with engineering practice than those calculated with DDA method.
文摘The complex structure and strong heterogeneity of advanced nuclear reactor systems pose challenges for high-fidelity neutron-shielding calculations. Unstructured meshes exhibit strong geometric adaptability and can overcome the deficiencies of conventionally structured meshes in complex geometry modeling. A multithreaded parallel upwind sweep algorithm for S_(N) transport was proposed to achieve a more accurate geometric description and improve the computational efficiency. The spatial variables were discretized using the standard discontinuous Galerkin finite-element method. The angular flux transmission between neighboring meshes was handled using an upwind scheme. In addition, a combination of a mesh transport sweep and angular iterations was realized using a multithreaded parallel technique. The algorithm was implemented in the 2D/3D S_(N) transport code ThorSNIPE, and numerical evaluations were conducted using three typical benchmark problems:IAEA, Kobayashi-3i, and VENUS-3. These numerical results indicate that the multithreaded parallel upwind sweep algorithm can achieve high computational efficiency. ThorSNIPE, with a multithreaded parallel upwind sweep algorithm, has good reliability, stability, and high efficiency, making it suitable for complex shielding calculations.
基金This work was supported in part by the National Science Foundation under grant DMS-1620288。
文摘The present study regards the numerical approximation of solutions of systems of Korteweg-de Vries type,coupled through their nonlinear terms.In our previous work[9],we constructed conservative and dissipative finite element methods for these systems and presented a priori error estimates for the semidiscrete schemes.In this sequel,we present a posteriori error estimates for the semidiscrete and fully discrete approximations introduced in[9].The key tool employed to effect our analysis is the dispersive reconstruction devel-oped by Karakashian and Makridakis[20]for related discontinuous Galerkin methods.We conclude by providing a set of numerical experiments designed to validate the a posteriori theory and explore the effectivity of the resulting error indicators.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11261035 and 11171038)the Science Research Foundation of the Institute of Higher Education of Inner Mongolia Autonomous Region, China (Grant No. NJZZ12198)the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant No. 2012MS0102)
文摘In this paper, a Petrov-Galerkin scheme named the Runge-Kutta control volume （RKCV） discontinuous finite ele- ment method is constructed to solve the one-dimensional compressible Euler equations in the Lagrangian coordinate. Its advantages include preservation of the local conservation and a high resolution. Compared with the Runge-Kutta discon- tinuous Galerkin （RKDG） method, the RKCV method is easier to implement. Moreover, the advantages of the RKCV and the Lagrangian methods are combined in the new method. Several numerical examples are given to illustrate the accuracy and the reliability of the algorithm.
基金Project supported by the Science and Technology Foundation of Sichuan Province (No.05GG006- 006-2)the Research Fund for the Introducing Intelligence of University of Electronic Science and Technology of China
文摘A pressure gradient discontinuous finite element formulation for the compressible Navier-Stokes equations is derived based on local projections. The resulting finite element formulation is stable and uniquely solvable without requiring a B-B stability condition. An error estimate is Obtained.
基金the National Natural Science Foundation of China (Grant No. 51605212)the Natural Science Foundation of Gansu Province (Grant No. 17JR5RA122)the Project of Hongliu First-class Disciplines Development Program of Lanzhou University of Technology.
文摘The fatigue damage model based on theory of damage mechanics is capable of predicting the fatigue life under multiaxial loading. Meanwhile, the application of critical plane method in the prediction of multiaxial fatigue life has made certain progress. According to the law of thermodynamics, a new damage evolution equation is developed in the present study to predict the fatigue life of geometrically discontinuous structure under tension-torsion loading based on damage mechanics and the critical plane method. The essence of this approach is tha t the st rain parame ter of the uniaxial nonlinear fatigue damage model is replaced with the equivalent strain, which consists of the releva nt parame ters of the critical plane. However, it is difficult to calculate the stress-strain status and the critical plane position of geometrically dis? continuous structure by theoretical methods because of the existence of stress concentration and the multiaxial nonproportional characteristics. Therefore, a new numerical simulation method is proposed to determine the critical plane of geometrically discontinuous structure under multiaxial loading by means of the finite element method and MATLAB software. The fatigue life of notched specimens subjected to combined bending and torsion is predicted using the proposed met hod, and the result is compared with t hose from the experimen ts and the Manson-Cfiffin law. The comparisons show that the proposed method is superior to the Manson-Coffin law and is capable of reproducing the experimental results reasonably when the geometry of the structure is complex. It completely meets the needs of engineering practice.
基金The project supported by the National Natural Science Foundation of China (10125210),the Hundred-Talent Programme of the Chinese Academy of Sciences and the Innovation Project of the Chinese Academy of Sciences (KJCX-SW-L04,KJCX2-SW-L2)
文摘A discontinuity-capturing scheme of finite element method(FEM)is proposed.The unstructured-grid technique combined with a new type of adaptive mesh approach is developed for both compressible and incompressible unsteady flows,which exhibits the capability of capturing the shock waves and/or thin shear layers accurately in an unsteady viscous flow at high Reynolds number. In particular,a new testing variable,i.e.,the disturbed kinetic energy E,is suggested and used in the adaptive mesh computation,which is universally applicable to the capturing of both shock waves and shear layers in the inviscid flow and viscous flow at high Reynolds number.Based on several calculated examples,this approach has been proved to be effective and efficient for the calculations of compressible and incompressible flows.
文摘A novel conforming discontinuous Galerkin(CDG)finite element method is introduced for the Poisson equation on rectangular meshes.This CDG method with discontinuous P_(k)(k≥1)elements converges to the true solution two orders above the continuous finite element counterpart.Superconvergence of order two for the CDG finite element solution is proved in an energy norm and the L^(2)norm.A local post-process is defined which lifts a P_(k)CDG solution to a discontinuous P_(k+2)solution.It is proved that the lifted P_(k+2)solution converges at the optimal order.The numerical tests illustrate the theoretic findings.
基金NSF under grant number 0609918AFOSR under grant numbers FA9550-06-1-0234 and FA9550-07-1-0154+2 种基金NSFC (10671082,10626026,10471054)NNSF (No.10701039 of China)985 program of Jilin University
文摘In this paper, we consider the finite element method and discontinuous Galerkin method for the stochastic Helmholtz equation in R^d （d = 2, 3）. Convergence analysis and error estimates are presented for the numerical solutions. The effects of the noises on the accuracy of the approximations are illustrated. Numerical experiments are carried out to verify our theoretical results.
