This paper discusses electromagnetic boundary conditions on crack faces in magneto- electroelastic materials, where piezoelectric, piezomagnetic and magnetoelectric effects are coupled. A notch of finite thickness in ...This paper discusses electromagnetic boundary conditions on crack faces in magneto- electroelastic materials, where piezoelectric, piezomagnetic and magnetoelectric effects are coupled. A notch of finite thickness in these materials is also addressed. Four idealized electromagnetic boundary conditions assumed for the crack-faces are separately investigated, i.e. (a) electrically and magnetically impermeable (crack-face), (b) electrically impermeable and magnetically permeable, (c) electrically permeable and magnetically impermeable, and (d) electrically and magnetically permeable. The influence of the notch thickness on important parameters, such as the field intensity factors, the energy release rate at the notch tips and the electromagnetic fields inside the notch, are studied and the results are obtained in closed-form. Results under different idealized electromagnetic boundary conditions on the crack-face are compared, and the applicability of these idealized assumptions is discussed.展开更多
Describing matrix–fracture interaction is one of the most important factors for modeling natural fractured reservoirs.A common approach for simulation of naturally fractured reservoirs is dual-porosity modeling where...Describing matrix–fracture interaction is one of the most important factors for modeling natural fractured reservoirs.A common approach for simulation of naturally fractured reservoirs is dual-porosity modeling where the degree of communication between the low-permeability medium(matrix)and high-permeability medium(fracture)is usually determined by a transfer function.Most of the proposed matrix–fracture functions depend on the geometry of the matrix and fractures that are lumped to a factor called shape factor.Unfortunately,there is no unique solution for calculating the shape factor even for symmetric cases.Conducting fine-scale modeling is a tool for calculating the shape factor and validating the current solutions in the literature.In this study,the shape factor is calculated based on the numerical simulation of fine-grid simulations for single-phase flow using finite element method.To the best of the author’s knowledge,this is the first study to calculate the shape factors for multidimensional irregular bodies in a systematic approach.Several models were used,and shape factors were calculated for both transient and pseudo-steady-state(PSS)cases,although in some cases they were not clarified and assumptions were not clear.The boundary condition dependency of the shape factor was also investigated,and the obtained results were compared with the results of other studies.Results show that some of the most popular formulas cannot capture the exact physics of matrix–fracture interaction.The obtained results also show that both PSS and transient approaches for describing matrix–fracture transfer lead to constant shape factors that are not unique and depend on the fracture pressure(boundary condition)and how it changes with time.展开更多
Axially moving beams are often discussed with several classic boundary conditions, such as simply-supported ends, fixed ends, and free ends. Here, axially moving beams with generalized boundary conditions are discusse...Axially moving beams are often discussed with several classic boundary conditions, such as simply-supported ends, fixed ends, and free ends. Here, axially moving beams with generalized boundary conditions are discussed for the first time. The beam is supported by torsional springs and vertical springs at both ends. By modifying the stiffness of the springs, generalized boundaries can replace those classical boundaries. Dynamic stiffness matrices are, respectively, established for axially moving Timoshenko beams and Euler-Bernoulli (EB) beams with generalized boundaries. In order to verify the applicability of the EB model, the natural frequencies of the axially moving Timoshenko beam and EB beam are compared. Furthermore, the effects of constrained spring stiffness on the vibration frequencies of the axially moving beam are studied. Interestingly, it can be found that the critical speed of the axially moving beam does not change with the vertical spring stiffness. In addition, both the moving speed and elastic boundaries make the Timoshenko beam theory more needed. The validity of the dynamic stiffness method is demonstrated by using numerical simulation.展开更多
The electrical boundary conditions on the crack faces and their applicability in piezoelectric materials are discussed. A slit crack and a notch of ?nite thickness in piezoelectric materials subjected to combined me...The electrical boundary conditions on the crack faces and their applicability in piezoelectric materials are discussed. A slit crack and a notch of ?nite thickness in piezoelectric materials subjected to combined mechanical and electrical loads is considered. Here, a crack is de?ned as a notch without thickness, which is ?lled with air or vacuum. The crack or notch is perpendicular to the poling direction of the medium. The ideal crack face electrical boundary conditions, i.e., the electrically permeable crack and the electrically impermeable crack, are in- vestigated ?rst. Then dependence of the ?eld intensity factors on notch thickness at the notch tips is analyzed to obtain a closed-form. The results are compared with the ideal crack solutions. Some useful results are found.展开更多
In the light of a growing need for fracture control of rapid crack propagation (RCP) in gas pipelines, a program PFRAC(Pipeline FRacture Analysis Code) has been developed((1)) to analyse the various events. In this pa...In the light of a growing need for fracture control of rapid crack propagation (RCP) in gas pipelines, a program PFRAC(Pipeline FRacture Analysis Code) has been developed((1)) to analyse the various events. In this paper, by using PFRAC for the simulation of axial crack propagation in gas pipelines, a number of dynamic analysis issues relating to boundary effects for uncracked and cracked pipes are investigated. This indicates that the boundary conditions along the length of the pipe play an important role for fracture analysis in the pipe. In contrast, the boundary conditions at the ends of a long pipeline have little effect on the dynamic fracture events.展开更多
A split-step second-order predictor-corrector method for space-fractional reaction-diffusion equations with nonhomogeneous boundary conditions is presented and analyzed for the stability and convergence.The matrix tra...A split-step second-order predictor-corrector method for space-fractional reaction-diffusion equations with nonhomogeneous boundary conditions is presented and analyzed for the stability and convergence.The matrix transfer technique is used for spatial discretization of the problem.The method is shown to be unconditionally stable and second-order convergent.Numerical experiments are performed to confirm the stability and secondorder convergence of the method.The split-step predictor-corrector method is also compared with an IMEX predictor-corrector method which is found to incur oscillatory behavior for some time steps.Our method is seen to produce reliable and oscillatioresults for any time step when implemented on numerical examples with nonsmooth initial data.We also present a priori reliability constraint for the IMEX predictor-corrector method to avoid unwanted oscillations and show its validity numerically.展开更多
We consider a profound problem of two-point resistance in the resistor network with a null resistor edge and an arbitrary boundary,which has not been solved before because the Green's function technique and the Lapla...We consider a profound problem of two-point resistance in the resistor network with a null resistor edge and an arbitrary boundary,which has not been solved before because the Green's function technique and the Laplacian matrix approach are invalid in this case.Looking for the exact solutions of resistance is important but difficult in the case of the arbitrary boundary since the boundary is a wall or trap which affects the behavior of a finite network.In this paper,we give a general resistance formula that is composed of a single summation by using the recursion-transform method.Meanwhile,several interesting results are derived by the general formula.Further,the current distribution is given explicitly as a byproduct of the method.展开更多
在对地质构造及构造应力场数值模拟分析过程中,关键问题是在地质建模时如何确定模型边界条件的应力量值大小。以塔里木盆地塔中 I#断裂带构造数值模拟的建模过程为例,应用岩石 Kaiser 效应与方解石晶体晶格位错的测试结果,结合构造特征...在对地质构造及构造应力场数值模拟分析过程中,关键问题是在地质建模时如何确定模型边界条件的应力量值大小。以塔里木盆地塔中 I#断裂带构造数值模拟的建模过程为例,应用岩石 Kaiser 效应与方解石晶体晶格位错的测试结果,结合构造特征和构造演化的解析进行综合分析,确定了研究区域目的层位在不同构造运动时期古构造应力场应力量值的大小,并成功地建立了研究区域构造地质模型。展开更多
基金The project supported by the National Natural Science Foundation of China (10102004) The English text was polished by Yunming Chen
文摘This paper discusses electromagnetic boundary conditions on crack faces in magneto- electroelastic materials, where piezoelectric, piezomagnetic and magnetoelectric effects are coupled. A notch of finite thickness in these materials is also addressed. Four idealized electromagnetic boundary conditions assumed for the crack-faces are separately investigated, i.e. (a) electrically and magnetically impermeable (crack-face), (b) electrically impermeable and magnetically permeable, (c) electrically permeable and magnetically impermeable, and (d) electrically and magnetically permeable. The influence of the notch thickness on important parameters, such as the field intensity factors, the energy release rate at the notch tips and the electromagnetic fields inside the notch, are studied and the results are obtained in closed-form. Results under different idealized electromagnetic boundary conditions on the crack-face are compared, and the applicability of these idealized assumptions is discussed.
文摘Describing matrix–fracture interaction is one of the most important factors for modeling natural fractured reservoirs.A common approach for simulation of naturally fractured reservoirs is dual-porosity modeling where the degree of communication between the low-permeability medium(matrix)and high-permeability medium(fracture)is usually determined by a transfer function.Most of the proposed matrix–fracture functions depend on the geometry of the matrix and fractures that are lumped to a factor called shape factor.Unfortunately,there is no unique solution for calculating the shape factor even for symmetric cases.Conducting fine-scale modeling is a tool for calculating the shape factor and validating the current solutions in the literature.In this study,the shape factor is calculated based on the numerical simulation of fine-grid simulations for single-phase flow using finite element method.To the best of the author’s knowledge,this is the first study to calculate the shape factors for multidimensional irregular bodies in a systematic approach.Several models were used,and shape factors were calculated for both transient and pseudo-steady-state(PSS)cases,although in some cases they were not clarified and assumptions were not clear.The boundary condition dependency of the shape factor was also investigated,and the obtained results were compared with the results of other studies.Results show that some of the most popular formulas cannot capture the exact physics of matrix–fracture interaction.The obtained results also show that both PSS and transient approaches for describing matrix–fracture transfer lead to constant shape factors that are not unique and depend on the fracture pressure(boundary condition)and how it changes with time.
基金Project supported by the National Natural Science Foundation of China(Nos.11772181 and11422214)the “Dawn” Program of Shanghai Education Commission(Nos.17SG38 and 2019-01-07-00-09-E00018)the Key Research Project of Shanghai Science and Technology Commission(No.18010500100)
文摘Axially moving beams are often discussed with several classic boundary conditions, such as simply-supported ends, fixed ends, and free ends. Here, axially moving beams with generalized boundary conditions are discussed for the first time. The beam is supported by torsional springs and vertical springs at both ends. By modifying the stiffness of the springs, generalized boundaries can replace those classical boundaries. Dynamic stiffness matrices are, respectively, established for axially moving Timoshenko beams and Euler-Bernoulli (EB) beams with generalized boundaries. In order to verify the applicability of the EB model, the natural frequencies of the axially moving Timoshenko beam and EB beam are compared. Furthermore, the effects of constrained spring stiffness on the vibration frequencies of the axially moving beam are studied. Interestingly, it can be found that the critical speed of the axially moving beam does not change with the vertical spring stiffness. In addition, both the moving speed and elastic boundaries make the Timoshenko beam theory more needed. The validity of the dynamic stiffness method is demonstrated by using numerical simulation.
基金Project supported by the National Natural Science Foundation of China (No. 10102004) and the Australian Research Council (DP0346037).
文摘The electrical boundary conditions on the crack faces and their applicability in piezoelectric materials are discussed. A slit crack and a notch of ?nite thickness in piezoelectric materials subjected to combined mechanical and electrical loads is considered. Here, a crack is de?ned as a notch without thickness, which is ?lled with air or vacuum. The crack or notch is perpendicular to the poling direction of the medium. The ideal crack face electrical boundary conditions, i.e., the electrically permeable crack and the electrically impermeable crack, are in- vestigated ?rst. Then dependence of the ?eld intensity factors on notch thickness at the notch tips is analyzed to obtain a closed-form. The results are compared with the ideal crack solutions. Some useful results are found.
文摘In the light of a growing need for fracture control of rapid crack propagation (RCP) in gas pipelines, a program PFRAC(Pipeline FRacture Analysis Code) has been developed((1)) to analyse the various events. In this paper, by using PFRAC for the simulation of axial crack propagation in gas pipelines, a number of dynamic analysis issues relating to boundary effects for uncracked and cracked pipes are investigated. This indicates that the boundary conditions along the length of the pipe play an important role for fracture analysis in the pipe. In contrast, the boundary conditions at the ends of a long pipeline have little effect on the dynamic fracture events.
文摘A split-step second-order predictor-corrector method for space-fractional reaction-diffusion equations with nonhomogeneous boundary conditions is presented and analyzed for the stability and convergence.The matrix transfer technique is used for spatial discretization of the problem.The method is shown to be unconditionally stable and second-order convergent.Numerical experiments are performed to confirm the stability and secondorder convergence of the method.The split-step predictor-corrector method is also compared with an IMEX predictor-corrector method which is found to incur oscillatory behavior for some time steps.Our method is seen to produce reliable and oscillatioresults for any time step when implemented on numerical examples with nonsmooth initial data.We also present a priori reliability constraint for the IMEX predictor-corrector method to avoid unwanted oscillations and show its validity numerically.
文摘We consider a profound problem of two-point resistance in the resistor network with a null resistor edge and an arbitrary boundary,which has not been solved before because the Green's function technique and the Laplacian matrix approach are invalid in this case.Looking for the exact solutions of resistance is important but difficult in the case of the arbitrary boundary since the boundary is a wall or trap which affects the behavior of a finite network.In this paper,we give a general resistance formula that is composed of a single summation by using the recursion-transform method.Meanwhile,several interesting results are derived by the general formula.Further,the current distribution is given explicitly as a byproduct of the method.
文摘在对地质构造及构造应力场数值模拟分析过程中,关键问题是在地质建模时如何确定模型边界条件的应力量值大小。以塔里木盆地塔中 I#断裂带构造数值模拟的建模过程为例,应用岩石 Kaiser 效应与方解石晶体晶格位错的测试结果,结合构造特征和构造演化的解析进行综合分析,确定了研究区域目的层位在不同构造运动时期古构造应力场应力量值的大小,并成功地建立了研究区域构造地质模型。