In this paper, we give the definition of weak WT2-class of differential forms, and then obtain its weak reverse Holder inequality. As an application, we give an alternative proof of the higher integrability result of ...In this paper, we give the definition of weak WT2-class of differential forms, and then obtain its weak reverse Holder inequality. As an application, we give an alternative proof of the higher integrability result of weakly A-harmonic tensors due to B. Stroffolini.展开更多
Flexural and eigen-buckling analyses for rectangular steel-concrete partially composite plates(PCPs)with interlayer slip under simply supported and clamped boundary conditions are conducted using the weak form quadrat...Flexural and eigen-buckling analyses for rectangular steel-concrete partially composite plates(PCPs)with interlayer slip under simply supported and clamped boundary conditions are conducted using the weak form quadrature element method(QEM).Both of the derivatives and integrals in the variational description of a problem to be solved are directly evaluated by the aid of identical numerical interpolation points in the weak form QEM.The effectiveness of the presented numerical model is validated by comparing numerical results of the weak form QEM with those from FEM or analytic solution.It can be observed that only one quadrature element is fully competent for flexural and eigen-buckling analysis of a rectangular partially composite plate with shear connection stiffness commonly used.The numerical integration order of quadrature element can be adjusted neatly to meet the convergence requirement.The quadrature element model presented here is an effective and promising tool for further analysis of steel-concrete PCPs under more general circumstances.Parametric studies on the shear connection stiffness and length-width ratio of the plate are also presented.It is shown that the flexural deflections and the critical buckling loads of PCPs are significantly affected by the shear connection stiffness when its value is within a certain range.展开更多
This paper presents a weak form quadrature element formulation in the analysis of nonlinear bifurcation and post-buckling of cylindrical composite stiffened laminates subjected to transverse loads.A total Lagrangian u...This paper presents a weak form quadrature element formulation in the analysis of nonlinear bifurcation and post-buckling of cylindrical composite stiffened laminates subjected to transverse loads.A total Lagrangian updating scheme is used in combination with arc-length method,and the branch-switching method is adopted to identify the whole post-buckling procedure of the laminates.The formulation of the shell model and beam model are based on the basic concept of Ahmad.The coincidence of discrete nodes and integration points in quadrature element endows it with compactness and conciseness in the nonlinear buckling analysis of the cylindrical stiffened laminates.Several numerical examples are firstly presented to verify the effectiveness and accuracy of present formulation.Parametric studies on the effects of the height-to-breadth ratio,lamination schemes,positions,distribution,number of the stiffeners on the bifurcation and post-buckling behavior are performed.展开更多
This paper investigates the empirical validity of the Weak Form Efficient Market Hypothesis for American, European and Asian stock markets. Random Walk Hypothesis is used to prove weak form efficiency in American, Eur...This paper investigates the empirical validity of the Weak Form Efficient Market Hypothesis for American, European and Asian stock markets. Random Walk Hypothesis is used to prove weak form efficiency in American, European and Asian stock indices. ADF and PP Unit Root Tests have been used to test unit root in time series of daily data of American, European and Asian stock indices. Results show that sample of stock markets are weak-form efficient in terms of the Random Walk Hypothesis.展开更多
A planar nonlinear weak form quadrature beam element of arbitrary number of axial nodes is proposed on the basis of the absolute nodal coordinate formulation (ANCF). Elastic forces of the element are established throu...A planar nonlinear weak form quadrature beam element of arbitrary number of axial nodes is proposed on the basis of the absolute nodal coordinate formulation (ANCF). Elastic forces of the element are established through geometrically exact beam theory, resulting in good consistency with classical beam theory. Two examples with strong geometrical nonlinearity are presented to verify the effec-tiveness of the formulation.展开更多
The meshless local Petrov_Galerkin (MLPG) method for solving the bending problem of the thin plate were presented and discussed. The method used the moving least_squares approximation to interpolate the solution varia...The meshless local Petrov_Galerkin (MLPG) method for solving the bending problem of the thin plate were presented and discussed. The method used the moving least_squares approximation to interpolate the solution variables, and employed a local symmetric weak form. The present method was a truly meshless one as it did not need a finite element or boundary element mesh, either for purpose of interpolation of the solution, or for the integration of the energy. All integrals could be easily evaluated over regularly shaped domains (in general, spheres in three_dimensional problems) and their boundaries. The essential boundary conditions were enforced by the penalty method. Several numerical examples were presented to illustrate the implementation and performance of the present method. The numerical examples presented show that high accuracy can be achieved for arbitrary grid geometries for clamped and simply_supported edge conditions. No post processing procedure is required to computer the strain and stress, since the original solution from the present method, using the moving least squares approximation, is already smooth enough.展开更多
The main aim of this paper is to analyze the numerical method based upon the spectral element technique for the numerical solution of the fractional advection-diffusion equa-tion.The time variable has been discretized...The main aim of this paper is to analyze the numerical method based upon the spectral element technique for the numerical solution of the fractional advection-diffusion equa-tion.The time variable has been discretized by a second-order finite difference procedure.The stability and the convergence of the semi-discrete formula have been proven.Then,the spatial variable of the main PDEs is approximated by the spectral element method.The convergence order of the fully discrete scheme is studied.The basis functions of the spectral element method are based upon a class of Legendre polynomials.The numerical experiments confirm the theoretical results.展开更多
In this paper,we considered the improved element-free Galerkin(IEFG)method for solving 2D anisotropic steadystate heat conduction problems.The improved moving least-squares(IMLS)approximation is used to establish the ...In this paper,we considered the improved element-free Galerkin(IEFG)method for solving 2D anisotropic steadystate heat conduction problems.The improved moving least-squares(IMLS)approximation is used to establish the trial function,and the penalty method is applied to enforce the boundary conditions,thus the final discretized equations of the IEFG method for anisotropic steady-state heat conduction problems can be obtained by combining with the corresponding Galerkin weak form.The influences of node distribution,weight functions,scale parameters and penalty factors on the computational accuracy of the IEFG method are analyzed respectively,and these numerical solutions show that less computational resources are spent when using the IEFG method.展开更多
The recently proposed weak form quadrature element method （QEM） is applied to flexural and vibrational analysis of thin plates The integrals involved in the variational description of a thin plate are evaluated by a...The recently proposed weak form quadrature element method （QEM） is applied to flexural and vibrational analysis of thin plates The integrals involved in the variational description of a thin plate are evaluated by an efficient numerical scheme and the par- tial derivatives at the integration sampling points are then approximated using differential quadrature analogs. Neither the grid pattern nor the number of nodes is fixed, being adjustable according to convergence need. The C~ continuity conditions char- acterizing the thin plate theory are discussed and the robustness of the weak form quadrature element for thin plates against shape distortion is examined. Examples are presented and comparisons with analytical solutions and the results of the finite element method are made to demonstrate the convergence and computational efficiency of the weak form quadrature element method. It is shown that the present formulation is applicable to thin plates with varying thickness as well as uniform plates.展开更多
This paper presents a novel stochastic collocation method based on the equivalent weak form of multivariate function integral to quantify and manage uncertainties in complex mechanical systems. The proposed method, wh...This paper presents a novel stochastic collocation method based on the equivalent weak form of multivariate function integral to quantify and manage uncertainties in complex mechanical systems. The proposed method, which combines the advantages of the response surface method and the traditional stochastic collocation method, only sets integral points at the guide lines of the response surface. The statistics, in an engineering problem with many uncertain parameters, are then transformed into a linear combination of simple functions' statistics. Furthermore, the issue of determining a simple method to solve the weight-factor sets is discussed in detail. The weight-factor sets of two commonly used probabilistic distribution types are given in table form. Studies on the computational accuracy and efforts show that a good balance in computer capacity is achieved at present. It should be noted that it's a non-gradient and non-intrusive algorithm with strong portability. For the sake of validating the procedure, three numerical examples concerning a mathematical function with analytical expression, structural design of a straight wing, and flutter analysis of a composite wing are used to show the effectiveness of the guided stochastic collocation method.展开更多
The vibrations of beams on a nonlinear elastic foundation were analyzed considering the effects of transverse shear deformation and the rotational inertia of beams. A weak form quadrature element method （QEM） is use...The vibrations of beams on a nonlinear elastic foundation were analyzed considering the effects of transverse shear deformation and the rotational inertia of beams. A weak form quadrature element method （QEM） is used for the vibration analysis. The fundamental frequencies of beams are presented for various slenderness ratios and nonlinear foundation parameters for both slender and short beams. The results for slender beams compare well with finite element results. The analysis shows that the transverse shear deformation and the nonlinear foundation parameter significantly affect the fundamental frequency of the beams.展开更多
By comparing the cross Sections for left-and right-handed electrons scattered from various unpolarized nuclear targets,the small parity-violating asymmetry can be measured.These asymmetry data probe a wide variety of ...By comparing the cross Sections for left-and right-handed electrons scattered from various unpolarized nuclear targets,the small parity-violating asymmetry can be measured.These asymmetry data probe a wide variety of important topies,including searches for new fundamental interactions and important features of nuclear structure that cannot be studied with other probes.A special feature of these experiments is that the results are interpreted with remarkably few theoretical uncertainties,which justifies pushing the experiments to the highest possible precision.To measure the small asymmetries accurately,a number of novel experimental techniques have been developed.展开更多
In order to overcome the possible singularity associated with the Point Interpolation Method(PIM),the Radial Point Interpolation Method(RPIM)was proposed by G.R.Liu.Radial basis functions(RBF)was used in RPIM as basis...In order to overcome the possible singularity associated with the Point Interpolation Method(PIM),the Radial Point Interpolation Method(RPIM)was proposed by G.R.Liu.Radial basis functions(RBF)was used in RPIM as basis functions for interpolation.All these radial basis functions include shape parameters.The choice of these shape parameters has been and stays a problematic theme in RBF approximation and interpolation theory.The object of this study is to contribute to the analysis of how these shape parameters affect the accuracy of the radial PIM.The RPIM is studied based on the global Galerkin weak form performed using two integration technics:classical Gaussian integration and the strain smoothing integration scheme.The numerical performance of this method is tested on their behavior on curve fitting,and on three elastic mechanical problems with regular or irregular nodes distributions.A range of recommended shape parameters is obtained from the analysis of different error indexes and also the condition number of the matrix system.All resulting RPIM methods perform very well in term of numerical computation.The Smoothed Radial Point Interpolation Method(SRPIM)shows a higher accuracy,especially in a situation of distorted node scheme.展开更多
Unused mechanical energies can be found in numerous ambient vibration sources in industry including rotating equipment,vehicles,aircraft,piping systems,fluid flow,and even external movement of the human body.A portion...Unused mechanical energies can be found in numerous ambient vibration sources in industry including rotating equipment,vehicles,aircraft,piping systems,fluid flow,and even external movement of the human body.A portion of the vibrational energy can be recovered using piezoelectric transduction and stored for subsequent smart system utilization for applications including powering wireless sensor devices for health condition monitoring of rotating machines and defence communication technology.The vibration environment in the considered application areas is varied and often changes over time and can have components in three perpendicular directions,simultaneously or singularly.This paper presents the development of analytical methods for modeling of self-powered cantilevered piezoelectric bimorph beams with tip mass under simultaneous longitudinal and transverse input base motions utilizing the weak and strong forms of Hamiltonian’s principle and space-and time-dependent eigenfunction series which were further formulated using orthonormalization.The reduced constitutive electromechanical equations of the cantilevered piezoelectric bimorph were subsequently analyzed using Laplace transforms and frequency analysis to give multi-mode frequency response functions(FRFs).The validation between theoretical and experimental results at the single mode of eigenfunction solutions reduced from multi-mode FRFs is also given.展开更多
基金Supported by the National Natural Science Foundation of China (10971224)the Hebei Natural ScienceFoundation (07M003)
文摘In this paper, we give the definition of weak WT2-class of differential forms, and then obtain its weak reverse Holder inequality. As an application, we give an alternative proof of the higher integrability result of weakly A-harmonic tensors due to B. Stroffolini.
基金Project(51508562)supported by the National Natural Science Foundation of ChinaProject(ZK18-03-49)supported by the Scientific Research Program of National University of Defense Technology,China
文摘Flexural and eigen-buckling analyses for rectangular steel-concrete partially composite plates(PCPs)with interlayer slip under simply supported and clamped boundary conditions are conducted using the weak form quadrature element method(QEM).Both of the derivatives and integrals in the variational description of a problem to be solved are directly evaluated by the aid of identical numerical interpolation points in the weak form QEM.The effectiveness of the presented numerical model is validated by comparing numerical results of the weak form QEM with those from FEM or analytic solution.It can be observed that only one quadrature element is fully competent for flexural and eigen-buckling analysis of a rectangular partially composite plate with shear connection stiffness commonly used.The numerical integration order of quadrature element can be adjusted neatly to meet the convergence requirement.The quadrature element model presented here is an effective and promising tool for further analysis of steel-concrete PCPs under more general circumstances.Parametric studies on the shear connection stiffness and length-width ratio of the plate are also presented.It is shown that the flexural deflections and the critical buckling loads of PCPs are significantly affected by the shear connection stiffness when its value is within a certain range.
基金supported by the National Natural Science Foundation of China(Nos.12202148,12172136)the Natural Science Foundation of Guangdong Province(No.2021A1515010279)+1 种基金the National Science Fund for Distinguished Young Scholar(No.11925203)the Science and Technology Project of Guangzhou(No.202102020656).
文摘This paper presents a weak form quadrature element formulation in the analysis of nonlinear bifurcation and post-buckling of cylindrical composite stiffened laminates subjected to transverse loads.A total Lagrangian updating scheme is used in combination with arc-length method,and the branch-switching method is adopted to identify the whole post-buckling procedure of the laminates.The formulation of the shell model and beam model are based on the basic concept of Ahmad.The coincidence of discrete nodes and integration points in quadrature element endows it with compactness and conciseness in the nonlinear buckling analysis of the cylindrical stiffened laminates.Several numerical examples are firstly presented to verify the effectiveness and accuracy of present formulation.Parametric studies on the effects of the height-to-breadth ratio,lamination schemes,positions,distribution,number of the stiffeners on the bifurcation and post-buckling behavior are performed.
文摘This paper investigates the empirical validity of the Weak Form Efficient Market Hypothesis for American, European and Asian stock markets. Random Walk Hypothesis is used to prove weak form efficiency in American, European and Asian stock indices. ADF and PP Unit Root Tests have been used to test unit root in time series of daily data of American, European and Asian stock indices. Results show that sample of stock markets are weak-form efficient in terms of the Random Walk Hypothesis.
文摘A planar nonlinear weak form quadrature beam element of arbitrary number of axial nodes is proposed on the basis of the absolute nodal coordinate formulation (ANCF). Elastic forces of the element are established through geometrically exact beam theory, resulting in good consistency with classical beam theory. Two examples with strong geometrical nonlinearity are presented to verify the effec-tiveness of the formulation.
文摘The meshless local Petrov_Galerkin (MLPG) method for solving the bending problem of the thin plate were presented and discussed. The method used the moving least_squares approximation to interpolate the solution variables, and employed a local symmetric weak form. The present method was a truly meshless one as it did not need a finite element or boundary element mesh, either for purpose of interpolation of the solution, or for the integration of the energy. All integrals could be easily evaluated over regularly shaped domains (in general, spheres in three_dimensional problems) and their boundaries. The essential boundary conditions were enforced by the penalty method. Several numerical examples were presented to illustrate the implementation and performance of the present method. The numerical examples presented show that high accuracy can be achieved for arbitrary grid geometries for clamped and simply_supported edge conditions. No post processing procedure is required to computer the strain and stress, since the original solution from the present method, using the moving least squares approximation, is already smooth enough.
基金The authors are grateful to the two reviewers for carefully reading this paper and for their comments and suggestions which have highly improved the paper.
文摘The main aim of this paper is to analyze the numerical method based upon the spectral element technique for the numerical solution of the fractional advection-diffusion equa-tion.The time variable has been discretized by a second-order finite difference procedure.The stability and the convergence of the semi-discrete formula have been proven.Then,the spatial variable of the main PDEs is approximated by the spectral element method.The convergence order of the fully discrete scheme is studied.The basis functions of the spectral element method are based upon a class of Legendre polynomials.The numerical experiments confirm the theoretical results.
基金supported by Natural Science Foundation of Shanxi Province(Grant No.20210302124388).
文摘In this paper,we considered the improved element-free Galerkin(IEFG)method for solving 2D anisotropic steadystate heat conduction problems.The improved moving least-squares(IMLS)approximation is used to establish the trial function,and the penalty method is applied to enforce the boundary conditions,thus the final discretized equations of the IEFG method for anisotropic steady-state heat conduction problems can be obtained by combining with the corresponding Galerkin weak form.The influences of node distribution,weight functions,scale parameters and penalty factors on the computational accuracy of the IEFG method are analyzed respectively,and these numerical solutions show that less computational resources are spent when using the IEFG method.
基金supported by the National Natural Science Foundation of China (Grant Nos.51178247 and 50778104)the National High Technology Research and Development Program of China (Grant No.2009AA04Z401)
文摘The recently proposed weak form quadrature element method （QEM） is applied to flexural and vibrational analysis of thin plates The integrals involved in the variational description of a thin plate are evaluated by an efficient numerical scheme and the par- tial derivatives at the integration sampling points are then approximated using differential quadrature analogs. Neither the grid pattern nor the number of nodes is fixed, being adjustable according to convergence need. The C~ continuity conditions char- acterizing the thin plate theory are discussed and the robustness of the weak form quadrature element for thin plates against shape distortion is examined. Examples are presented and comparisons with analytical solutions and the results of the finite element method are made to demonstrate the convergence and computational efficiency of the weak form quadrature element method. It is shown that the present formulation is applicable to thin plates with varying thickness as well as uniform plates.
基金supported by the Defense Industrial Technology Development Program(Grant Nos.A2120110001 and B2120110011)the National Natural Science Foundation of China(Grant No.A020317)
文摘This paper presents a novel stochastic collocation method based on the equivalent weak form of multivariate function integral to quantify and manage uncertainties in complex mechanical systems. The proposed method, which combines the advantages of the response surface method and the traditional stochastic collocation method, only sets integral points at the guide lines of the response surface. The statistics, in an engineering problem with many uncertain parameters, are then transformed into a linear combination of simple functions' statistics. Furthermore, the issue of determining a simple method to solve the weight-factor sets is discussed in detail. The weight-factor sets of two commonly used probabilistic distribution types are given in table form. Studies on the computational accuracy and efforts show that a good balance in computer capacity is achieved at present. It should be noted that it's a non-gradient and non-intrusive algorithm with strong portability. For the sake of validating the procedure, three numerical examples concerning a mathematical function with analytical expression, structural design of a straight wing, and flutter analysis of a composite wing are used to show the effectiveness of the guided stochastic collocation method.
基金Supported by the Tsinghua Fundamental Research Foundation (No. JCXX2005069)the National Natural Science Foundation of China (No. 50778104)
文摘The vibrations of beams on a nonlinear elastic foundation were analyzed considering the effects of transverse shear deformation and the rotational inertia of beams. A weak form quadrature element method （QEM） is used for the vibration analysis. The fundamental frequencies of beams are presented for various slenderness ratios and nonlinear foundation parameters for both slender and short beams. The results for slender beams compare well with finite element results. The analysis shows that the transverse shear deformation and the nonlinear foundation parameter significantly affect the fundamental frequency of the beams.
基金Department of Energy(DOE)under grants DE-FG02-84ER40146(PAS)DE-FG02-07ER41522(KDP).
文摘By comparing the cross Sections for left-and right-handed electrons scattered from various unpolarized nuclear targets,the small parity-violating asymmetry can be measured.These asymmetry data probe a wide variety of important topies,including searches for new fundamental interactions and important features of nuclear structure that cannot be studied with other probes.A special feature of these experiments is that the results are interpreted with remarkably few theoretical uncertainties,which justifies pushing the experiments to the highest possible precision.To measure the small asymmetries accurately,a number of novel experimental techniques have been developed.
文摘In order to overcome the possible singularity associated with the Point Interpolation Method(PIM),the Radial Point Interpolation Method(RPIM)was proposed by G.R.Liu.Radial basis functions(RBF)was used in RPIM as basis functions for interpolation.All these radial basis functions include shape parameters.The choice of these shape parameters has been and stays a problematic theme in RBF approximation and interpolation theory.The object of this study is to contribute to the analysis of how these shape parameters affect the accuracy of the radial PIM.The RPIM is studied based on the global Galerkin weak form performed using two integration technics:classical Gaussian integration and the strain smoothing integration scheme.The numerical performance of this method is tested on their behavior on curve fitting,and on three elastic mechanical problems with regular or irregular nodes distributions.A range of recommended shape parameters is obtained from the analysis of different error indexes and also the condition number of the matrix system.All resulting RPIM methods perform very well in term of numerical computation.The Smoothed Radial Point Interpolation Method(SRPIM)shows a higher accuracy,especially in a situation of distorted node scheme.
文摘Unused mechanical energies can be found in numerous ambient vibration sources in industry including rotating equipment,vehicles,aircraft,piping systems,fluid flow,and even external movement of the human body.A portion of the vibrational energy can be recovered using piezoelectric transduction and stored for subsequent smart system utilization for applications including powering wireless sensor devices for health condition monitoring of rotating machines and defence communication technology.The vibration environment in the considered application areas is varied and often changes over time and can have components in three perpendicular directions,simultaneously or singularly.This paper presents the development of analytical methods for modeling of self-powered cantilevered piezoelectric bimorph beams with tip mass under simultaneous longitudinal and transverse input base motions utilizing the weak and strong forms of Hamiltonian’s principle and space-and time-dependent eigenfunction series which were further formulated using orthonormalization.The reduced constitutive electromechanical equations of the cantilevered piezoelectric bimorph were subsequently analyzed using Laplace transforms and frequency analysis to give multi-mode frequency response functions(FRFs).The validation between theoretical and experimental results at the single mode of eigenfunction solutions reduced from multi-mode FRFs is also given.
