In this paper, first we calculate finite-difference coefficients of implicit finite- difference methods （IFDM） for the first and second-order derivatives on normal grids and first- order derivatives on staggered gri...In this paper, first we calculate finite-difference coefficients of implicit finite- difference methods （IFDM） for the first and second-order derivatives on normal grids and first- order derivatives on staggered grids and find that small coefficients of high-order IFDMs exist. Dispersion analysis demonstrates that omitting these small coefficients can retain approximately the same order accuracy but greatly reduce computational costs. Then, we introduce a mirrorimage symmetric boundary condition to improve IFDMs accuracy and stability and adopt the hybrid absorbing boundary condition （ABC） to reduce unwanted reflections from the model boundary. Last, we give elastic wave modeling examples for homogeneous and heterogeneous models to demonstrate the advantages of the proposed scheme.展开更多
In order to simplify the boundary conditions of pavement temperature field,the "Environment-Surface" system which considered the natural environment and pavement surface was established.Based on this system,...In order to simplify the boundary conditions of pavement temperature field,the "Environment-Surface" system which considered the natural environment and pavement surface was established.Based on this system,the partial differential equations of the one-dimensional heat conduction in the pavement were established on the basis of the heat transfer theory.Furthermore,the function forms of the initial and boundary conditions of the equations were created through the field experiments.The general solution of the pavement one-dimensional heat conduction partial differential equations was acquired by using Green's function,and the explicit expression of pavement temperature field under specific constraint conditions was derived.For the purpose of analysis,the pavement temperatures in different seasons were calculated using the explicit expression of pavement temperature field,and the calculation accuracy was analyzed through the comparison between measured and calculated values.Then,the relationship between fitting accuracy and calculation accuracy of pavement temperatures was analyzed.The analysis results show that: the usage of "Environment-Surface" system simplifies the calculation of pavement temperature field; the relative error between calculated and measured values is generally less than 7% and is seldom influenced by seasons; there is a positive correlation between the calculation accuracy and the fitting accuracy of pavement surface temperature; high fitting accuracy would result in less error of pavement temperature prediction.展开更多
A different set of governing equations on the large deflection of plates are derived by the principle of virtual work(PVW), which also leads to a different set of boundary conditions. Boundary conditions play an impor...A different set of governing equations on the large deflection of plates are derived by the principle of virtual work(PVW), which also leads to a different set of boundary conditions. Boundary conditions play an important role in determining the computation accuracy of the large deflection of plates. Our boundary conditions are shown to be more appropriate by analyzing their difference with the previous ones. The accuracy of approximate analytical solutions is important to the bulge/blister tests and the application of various sensors with the plate structure. Different approximate analytical solutions are presented and their accuracies are evaluated by comparing them with the numerical results. The error sources are also analyzed. A new approximate analytical solution is proposed and shown to have a better approximation. The approximate analytical solution offers a much simpler and more direct framework to study the plate-membrane transition behavior of deflection as compared with the previous approaches of complex numerical integration.展开更多
This paper analyzes the stability of milling with variable pitch cutter and tool runout cases characterized by multiple delays,and proposes a new variable-step numerical integration method for efficient and accurate s...This paper analyzes the stability of milling with variable pitch cutter and tool runout cases characterized by multiple delays,and proposes a new variable-step numerical integration method for efficient and accurate stability prediction. The variable-step technique is emphasized here to expand the numerical integration method,especially for the low radial immersion cases with multiple delays. First,the calculation accuracy of the numerical integration method is discussed and the variable-step algorithm is developed for milling stability prediction for single-delay and multiple-delay cases,respectively. The milling stability with variable pitch cutter is analyzed and the result is compared with those predicted with the frequency domain method and the improved full-discretization method. The influence of the runout effect on the stability boundary is investigated by the presented method. The numerical simulation shows that the cutter runout effect increases the stability boundary,and the increasing stability limit is verified by the milling chatter experimental results in the previous research. The numerical and experiment results verify the validity of the proposed method.展开更多
The simulation of wave phenomena in unbounded domains generally requires an artificial boundary to truncate the unbounded exterior and limit the computation to a finite region.At the artificial boundary a boundary con...The simulation of wave phenomena in unbounded domains generally requires an artificial boundary to truncate the unbounded exterior and limit the computation to a finite region.At the artificial boundary a boundary condition is then needed,which allows the propagating waves to exit the computational domain without spurious reflection.In 1977,Engquist and Majda proposed the first hierarchy of absorbing boundary conditions,which allows a systematic reduction of spurious reflection without moving the artificial boundary farther away from the scatterer.Their pioneering work,which initiated an entire research area,is reviewed here from a modern perspective.Recent developments such as high-order local conditions and their extension to multiple scattering are also presented.Finally,the accuracy of high-order local conditions is demonstrated through numerical experiments.展开更多
基金supported by the National Natural Science Foundation of China(NSFC)(Grant No. 41074100)the Program for New Century Excellent Talents in University of Ministry of Education of China(Grant No. NCET-10-0812)
文摘In this paper, first we calculate finite-difference coefficients of implicit finite- difference methods （IFDM） for the first and second-order derivatives on normal grids and first- order derivatives on staggered grids and find that small coefficients of high-order IFDMs exist. Dispersion analysis demonstrates that omitting these small coefficients can retain approximately the same order accuracy but greatly reduce computational costs. Then, we introduce a mirrorimage symmetric boundary condition to improve IFDMs accuracy and stability and adopt the hybrid absorbing boundary condition （ABC） to reduce unwanted reflections from the model boundary. Last, we give elastic wave modeling examples for homogeneous and heterogeneous models to demonstrate the advantages of the proposed scheme.
基金Projects(2012zzts019,2012QNZT048)supported by the Fundamental Research Funds for the Central Universities of Central South University,ChinaProject(201306370121)supported by the State Scholarship Fund of China+3 种基金Project(JT20090898002)supported by Traffic Technology Fund of Hainan Province,ChinaProject(2012M521563)supported by the China Postdoctoral Science FoundationProject(51248006)supported by The National Natural Science Foundation of ChinaProject(511114)supported by the Natural Science Foundation of Hainan Province,China
文摘In order to simplify the boundary conditions of pavement temperature field,the "Environment-Surface" system which considered the natural environment and pavement surface was established.Based on this system,the partial differential equations of the one-dimensional heat conduction in the pavement were established on the basis of the heat transfer theory.Furthermore,the function forms of the initial and boundary conditions of the equations were created through the field experiments.The general solution of the pavement one-dimensional heat conduction partial differential equations was acquired by using Green's function,and the explicit expression of pavement temperature field under specific constraint conditions was derived.For the purpose of analysis,the pavement temperatures in different seasons were calculated using the explicit expression of pavement temperature field,and the calculation accuracy was analyzed through the comparison between measured and calculated values.Then,the relationship between fitting accuracy and calculation accuracy of pavement temperatures was analyzed.The analysis results show that: the usage of "Environment-Surface" system simplifies the calculation of pavement temperature field; the relative error between calculated and measured values is generally less than 7% and is seldom influenced by seasons; there is a positive correlation between the calculation accuracy and the fitting accuracy of pavement surface temperature; high fitting accuracy would result in less error of pavement temperature prediction.
基金the National Natural Science Foundation of China(Grant No.11372321)
文摘A different set of governing equations on the large deflection of plates are derived by the principle of virtual work(PVW), which also leads to a different set of boundary conditions. Boundary conditions play an important role in determining the computation accuracy of the large deflection of plates. Our boundary conditions are shown to be more appropriate by analyzing their difference with the previous ones. The accuracy of approximate analytical solutions is important to the bulge/blister tests and the application of various sensors with the plate structure. Different approximate analytical solutions are presented and their accuracies are evaluated by comparing them with the numerical results. The error sources are also analyzed. A new approximate analytical solution is proposed and shown to have a better approximation. The approximate analytical solution offers a much simpler and more direct framework to study the plate-membrane transition behavior of deflection as compared with the previous approaches of complex numerical integration.
基金supported by the National Key Basic Research Program (Grant No. 2011CB706804)the National Natural Science Foundation of China (Grant No. 50835004)the Ministry of Science and Technology of China (Grant No. 2010ZX04016-012)
文摘This paper analyzes the stability of milling with variable pitch cutter and tool runout cases characterized by multiple delays,and proposes a new variable-step numerical integration method for efficient and accurate stability prediction. The variable-step technique is emphasized here to expand the numerical integration method,especially for the low radial immersion cases with multiple delays. First,the calculation accuracy of the numerical integration method is discussed and the variable-step algorithm is developed for milling stability prediction for single-delay and multiple-delay cases,respectively. The milling stability with variable pitch cutter is analyzed and the result is compared with those predicted with the frequency domain method and the improved full-discretization method. The influence of the runout effect on the stability boundary is investigated by the presented method. The numerical simulation shows that the cutter runout effect increases the stability boundary,and the increasing stability limit is verified by the milling chatter experimental results in the previous research. The numerical and experiment results verify the validity of the proposed method.
文摘The simulation of wave phenomena in unbounded domains generally requires an artificial boundary to truncate the unbounded exterior and limit the computation to a finite region.At the artificial boundary a boundary condition is then needed,which allows the propagating waves to exit the computational domain without spurious reflection.In 1977,Engquist and Majda proposed the first hierarchy of absorbing boundary conditions,which allows a systematic reduction of spurious reflection without moving the artificial boundary farther away from the scatterer.Their pioneering work,which initiated an entire research area,is reviewed here from a modern perspective.Recent developments such as high-order local conditions and their extension to multiple scattering are also presented.Finally,the accuracy of high-order local conditions is demonstrated through numerical experiments.
