The operator splitting method is used to deal with the Navier-Stokes equation, in which the physical process described by the equation is decomposed into two processes： a diffusion process and a convection process; a...The operator splitting method is used to deal with the Navier-Stokes equation, in which the physical process described by the equation is decomposed into two processes： a diffusion process and a convection process; and the finite element equation is established. The velocity field in the element is described by the shape function of the isoparametric element with nine nodes and the pressure field is described by the interpolation function of the four nodes at the vertex of the isoparametric element with nine nodes. The subroutine of the element and the integrated finite element code are generated by the Finite Element Program Generator （FEPG） successfully. The numerical simulation about the incompressible viscous liquid flowing over a cylinder is carded out. The solution agrees with the experimental results very well.展开更多
In this paper we introduce a new kind of the mixed Hermite--Fejér interpolation with boundary condi- tions and obtain the mean approximation order.Our results include a new theorem of Varma and Prasad.Be- sides,w...In this paper we introduce a new kind of the mixed Hermite--Fejér interpolation with boundary condi- tions and obtain the mean approximation order.Our results include a new theorem of Varma and Prasad.Be- sides,we also get some other results about the mean approximation.展开更多
To explore the influence of meteorological variables on the growth of Korean pine(Pinus koraiensis Sieb.et Zucc.) plantations and provide a scientific reference for the production and management of Korean pine,three a...To explore the influence of meteorological variables on the growth of Korean pine(Pinus koraiensis Sieb.et Zucc.) plantations and provide a scientific reference for the production and management of Korean pine,three approaches to interpolate meteorological variables during the growing season(i.e.,May-September) were compared in Heilongjiang Province,China.Optimized meteorological variable interpolation results were then combined with stand and individual tree variables,based on data from 56 sample plots and 2886 sample trees from Korean pine plantations in two regions of the province to develop an individualtree diameter growth model(Model I) and an individualtree diameter growth model with meteorological variables(Model Ⅱ) using a stepwise regression method.Moreover,an individual-tree diameter growth model with regional effects(Model Ⅲ) was developed using dummy variables in the regression,and the significance of introducing these dummy variables was verified with an F-test statistical analysis.The models were validated using an independent data set,and the predictive performance of the three models was assessed via the adjusted coefficient of determination(R_(a)^(2)) and root mean square error(RMSE).The results suggest that the growth increment in tree diameter of Korean pine plantations was significantly correlated with the natural logarithm of initial diameter(ln D),stand basal area(BAS),logarithmic deformation of the stand density index(ln SDI),ratio of basal area of trees larger than the subject tree to their initial diameter at breast height(DBH)(BAL/D),and the maximum growingseason precipitation(Pgmax).The individual-tree diameter growth models of Korean pine plantations developed in this study will provide a good basis for estimating and predicting growth increments of Korean pine forests over larger areas.展开更多
The main purpose of this paper is to present numerical results of static bending and free vibration of functionally graded porous(FGP) variable-thickness plates by using an edge-based smoothed finite element method(ES...The main purpose of this paper is to present numerical results of static bending and free vibration of functionally graded porous(FGP) variable-thickness plates by using an edge-based smoothed finite element method(ES-FEM) associate with the mixed interpolation of tensorial components technique for the three-node triangular element(MITC3), so-called ES-MITC3. This ES-MITC3 element is performed to eliminate the shear locking problem and to enhance the accuracy of the existing MITC3 element. In the ES-MITC3 element, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains formed by two adjacent MITC3 triangular elements sharing an edge. Materials of the plate are FGP with a power-law index(k) and maximum porosity distributions(U) in the forms of cosine functions. The influences of some geometric parameters, material properties on static bending, and natural frequency of the FGP variable-thickness plates are examined in detail.展开更多
Previously,many studies have illustrated corner blend problem with different parameter curves.Only a few of them take a Pythagorean-hodograph(PH)curve as the transition arc,let alone corresponding real-time interpolat...Previously,many studies have illustrated corner blend problem with different parameter curves.Only a few of them take a Pythagorean-hodograph(PH)curve as the transition arc,let alone corresponding real-time interpolation methods.In this paper,an integrated corner-transition mixing-interpolation-based scheme(ICMS)is proposed,considering transition error and machine tool kinematics.Firstly,the ICMS smooths the sharp corners in a linear path through blending the linear path with G3 continuous PH transition curves.To obtain optimal PH transition curves globally,the problem of corner smoothing is formulated as an optimization problem with constraints.In order to improve optimization efficiency,the transition error constraint is deduced analytically,so is the curvature extreme of each transition curve.After being blended with PH transition curves,a linear path has become a blend curve.Secondly,the ICMS adopts a novel mixed interpolator to process this kind of blend curves by considering machine tool kinematics.The mixed interpolator can not only implement jerk-limited feedrate scheduling with critical points detection,but also realize self-switching of two interpolation modes.Finally,two patterns are machined with a carving platform based on ICMS.Experiment l results show the effectiveness of ICMS.展开更多
The present article considers the free-vibration analysis of plate structures with piezoelectric patches by means of a plate finite element with variable through-the-thickness layer-wise kinematic.The refined models u...The present article considers the free-vibration analysis of plate structures with piezoelectric patches by means of a plate finite element with variable through-the-thickness layer-wise kinematic.The refined models used are derived from Carrera’s Unified Formulation(CUF)and they permit the vibration modes along the thickness to be accurately described.The finite-element method is employed and the plate element implemented has nine nodes,and the mixed interpolation of tensorial component(MITC)method is used to contrast the membrane and shear locking phenomenon.The related governing equations are derived from the principle of virtual displacement,extended to the analysis of electromechanical problems.An isotropic plate with piezoelectric patches is analyzed,with clamped-free boundary conditions and subjected to open-and short-circuit configurations.The results,obtained with different theories,are compared with the higher-order type solutions given in the literature.The conclusion is reached that the plate element based on the CUF is more suitable and efficient compared to the classical models in the study of multilayered structures embedding piezo-patches.展开更多
In this paper, we consider the higher divided difference of a composite function f（g（t）） in which g（t） is an s-dimensional vector. By exploiting some properties from mixed partial divided differences and multiva...In this paper, we consider the higher divided difference of a composite function f（g（t）） in which g（t） is an s-dimensional vector. By exploiting some properties from mixed partial divided differences and multivariate Newton interpolation, we generalize the divided difference form of Faà di Bruno＇s formula with a scalar argument. Moreover, a generalized Faà di Bruno＇s formula with a vector argument is derived.展开更多
文摘The operator splitting method is used to deal with the Navier-Stokes equation, in which the physical process described by the equation is decomposed into two processes： a diffusion process and a convection process; and the finite element equation is established. The velocity field in the element is described by the shape function of the isoparametric element with nine nodes and the pressure field is described by the interpolation function of the four nodes at the vertex of the isoparametric element with nine nodes. The subroutine of the element and the integrated finite element code are generated by the Finite Element Program Generator （FEPG） successfully. The numerical simulation about the incompressible viscous liquid flowing over a cylinder is carded out. The solution agrees with the experimental results very well.
文摘In this paper we introduce a new kind of the mixed Hermite--Fejér interpolation with boundary condi- tions and obtain the mean approximation order.Our results include a new theorem of Varma and Prasad.Be- sides,we also get some other results about the mean approximation.
基金funded partly by the National Key Research and Development Program of China (Project No.2017YFD0600601-01-04)the Fundamental Research Funds for the Central Universities (2572019CP15)。
文摘To explore the influence of meteorological variables on the growth of Korean pine(Pinus koraiensis Sieb.et Zucc.) plantations and provide a scientific reference for the production and management of Korean pine,three approaches to interpolate meteorological variables during the growing season(i.e.,May-September) were compared in Heilongjiang Province,China.Optimized meteorological variable interpolation results were then combined with stand and individual tree variables,based on data from 56 sample plots and 2886 sample trees from Korean pine plantations in two regions of the province to develop an individualtree diameter growth model(Model I) and an individualtree diameter growth model with meteorological variables(Model Ⅱ) using a stepwise regression method.Moreover,an individual-tree diameter growth model with regional effects(Model Ⅲ) was developed using dummy variables in the regression,and the significance of introducing these dummy variables was verified with an F-test statistical analysis.The models were validated using an independent data set,and the predictive performance of the three models was assessed via the adjusted coefficient of determination(R_(a)^(2)) and root mean square error(RMSE).The results suggest that the growth increment in tree diameter of Korean pine plantations was significantly correlated with the natural logarithm of initial diameter(ln D),stand basal area(BAS),logarithmic deformation of the stand density index(ln SDI),ratio of basal area of trees larger than the subject tree to their initial diameter at breast height(DBH)(BAL/D),and the maximum growingseason precipitation(Pgmax).The individual-tree diameter growth models of Korean pine plantations developed in this study will provide a good basis for estimating and predicting growth increments of Korean pine forests over larger areas.
基金funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant number 107.02-2019.330。
文摘The main purpose of this paper is to present numerical results of static bending and free vibration of functionally graded porous(FGP) variable-thickness plates by using an edge-based smoothed finite element method(ES-FEM) associate with the mixed interpolation of tensorial components technique for the three-node triangular element(MITC3), so-called ES-MITC3. This ES-MITC3 element is performed to eliminate the shear locking problem and to enhance the accuracy of the existing MITC3 element. In the ES-MITC3 element, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains formed by two adjacent MITC3 triangular elements sharing an edge. Materials of the plate are FGP with a power-law index(k) and maximum porosity distributions(U) in the forms of cosine functions. The influences of some geometric parameters, material properties on static bending, and natural frequency of the FGP variable-thickness plates are examined in detail.
基金supported by the National Natural Science Foundation of China under Grant No.61573378supports from Henan Province Programs for Science and Technology Development under Grant No.212102210391Anyang Institute of Technology Research and Cultivation Fund under Grant No.YPY2020012。
文摘Previously,many studies have illustrated corner blend problem with different parameter curves.Only a few of them take a Pythagorean-hodograph(PH)curve as the transition arc,let alone corresponding real-time interpolation methods.In this paper,an integrated corner-transition mixing-interpolation-based scheme(ICMS)is proposed,considering transition error and machine tool kinematics.Firstly,the ICMS smooths the sharp corners in a linear path through blending the linear path with G3 continuous PH transition curves.To obtain optimal PH transition curves globally,the problem of corner smoothing is formulated as an optimization problem with constraints.In order to improve optimization efficiency,the transition error constraint is deduced analytically,so is the curvature extreme of each transition curve.After being blended with PH transition curves,a linear path has become a blend curve.Secondly,the ICMS adopts a novel mixed interpolator to process this kind of blend curves by considering machine tool kinematics.The mixed interpolator can not only implement jerk-limited feedrate scheduling with critical points detection,but also realize self-switching of two interpolation modes.Finally,two patterns are machined with a carving platform based on ICMS.Experiment l results show the effectiveness of ICMS.
文摘The present article considers the free-vibration analysis of plate structures with piezoelectric patches by means of a plate finite element with variable through-the-thickness layer-wise kinematic.The refined models used are derived from Carrera’s Unified Formulation(CUF)and they permit the vibration modes along the thickness to be accurately described.The finite-element method is employed and the plate element implemented has nine nodes,and the mixed interpolation of tensorial component(MITC)method is used to contrast the membrane and shear locking phenomenon.The related governing equations are derived from the principle of virtual displacement,extended to the analysis of electromechanical problems.An isotropic plate with piezoelectric patches is analyzed,with clamped-free boundary conditions and subjected to open-and short-circuit configurations.The results,obtained with different theories,are compared with the higher-order type solutions given in the literature.The conclusion is reached that the plate element based on the CUF is more suitable and efficient compared to the classical models in the study of multilayered structures embedding piezo-patches.
基金Acknowledgments. This work was supported by the National Science Foundation of China （Grant Nos. 10471128, 10731060）.
文摘In this paper, we consider the higher divided difference of a composite function f（g（t）） in which g（t） is an s-dimensional vector. By exploiting some properties from mixed partial divided differences and multivariate Newton interpolation, we generalize the divided difference form of Faà di Bruno＇s formula with a scalar argument. Moreover, a generalized Faà di Bruno＇s formula with a vector argument is derived.
