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
This paper, based on the hi sto rical background of CLT(communicative language teaching), mainly addresses the k ey issues concerning the weak form of CLT. This is an area few people have paid attention to in the past...This paper, based on the hi sto rical background of CLT(communicative language teaching), mainly addresses the k ey issues concerning the weak form of CLT. This is an area few people have paid attention to in the past few years in China. Therefore, its main concepts and f e atures are discussed with relevance to literature and an empirical study on four novice teachers of English. Finally, the research shows that the weak form of CLT is being conducted in Chinese secondary schools.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
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
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
The Meshless Local Petrov-Galerkin (MLPG) with Laplace transform is used for solving partial differential equation. Local weak form is developed using the weighted residual method locally from the dynamic partial diff...The Meshless Local Petrov-Galerkin (MLPG) with Laplace transform is used for solving partial differential equation. Local weak form is developed using the weighted residual method locally from the dynamic partial differential equation and using the moving least square (MLS) method to construct shape function. This method is a more effective alternative than the finite element method for computer modelling and simulation of problems in engineering;however, the accuracy of the present method depends on a number of parameters deriving from local weak form and different subdomains. In this paper, the meshless local Petrov-Galerkin (MLPG) formulation is proposed for forced vibration analysis. First, the results are presented for different values of as, and aq?with regular distribution of nodes nt=55. After, the results are presented with fixed values of?as?and aq?for different time-step.展开更多
高耸结构P-Δ效应的传统分析方法一般难以考虑时变轴力作用,有可能会低估P-Δ效应对结构安全性的影响.本文应用求积单元法(weak form quadrature element method,QEM),针对分布质量结构体系和含有集中质量的结构体系分别建立Hermite型...高耸结构P-Δ效应的传统分析方法一般难以考虑时变轴力作用,有可能会低估P-Δ效应对结构安全性的影响.本文应用求积单元法(weak form quadrature element method,QEM),针对分布质量结构体系和含有集中质量的结构体系分别建立Hermite型求积单元模型,发展了一种高耸结构P-Δ效应高阶精确分析方法.该方法能够应用于具有突变质量的结构体系,可处理任意轴向荷载引起的动力P-Δ效应问题,无需迭代计算即可获得高精度的P-Δ效应解答,同时能准确地揭示竖向荷载以及时变轴力对高耸结构特性的影响规律.通过对3个不同类型案例的比较分析,验证了本文方法的可行性和准确性.数值分析结果表明,本文方法可以实现高精度的P-Δ效应分析,对于质量均匀分布和含有集中质量的结构体系仅需使用一个求积单元即可获得非常精确的动态响应结果.展开更多
Bell’s theorem determines the number of representations of a positive integer in terms of the ternary quadratic forms x2+by2+cz2 with b,c {1,2,4,8}. This number depends only on the number of representations of an int...Bell’s theorem determines the number of representations of a positive integer in terms of the ternary quadratic forms x2+by2+cz2 with b,c {1,2,4,8}. This number depends only on the number of representations of an integer as a sum of three squares. We present a modern elementary proof of Bell’s theorem that is based on three standard Ramanujan theta function identities and a set of five so-called three-square identities by Hurwitz. We use Bell’s theorem and a slight extension of it to find explicit and finite computable expressions for Tunnel’s congruent number criterion. It is known that this criterion settles the congruent number problem under the weak Birch-Swinnerton-Dyer conjecture. Moreover, we present for the first time an unconditional proof that a square-free number n 3(mod 8) is not congruent.展开更多
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This paper, based on the hi sto rical background of CLT(communicative language teaching), mainly addresses the k ey issues concerning the weak form of CLT. This is an area few people have paid attention to in the past few years in China. Therefore, its main concepts and f e atures are discussed with relevance to literature and an empirical study on four novice teachers of English. Finally, the research shows that the weak form of CLT is being conducted in Chinese secondary schools.
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 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.
文摘The Meshless Local Petrov-Galerkin (MLPG) with Laplace transform is used for solving partial differential equation. Local weak form is developed using the weighted residual method locally from the dynamic partial differential equation and using the moving least square (MLS) method to construct shape function. This method is a more effective alternative than the finite element method for computer modelling and simulation of problems in engineering;however, the accuracy of the present method depends on a number of parameters deriving from local weak form and different subdomains. In this paper, the meshless local Petrov-Galerkin (MLPG) formulation is proposed for forced vibration analysis. First, the results are presented for different values of as, and aq?with regular distribution of nodes nt=55. After, the results are presented with fixed values of?as?and aq?for different time-step.
文摘高耸结构P-Δ效应的传统分析方法一般难以考虑时变轴力作用,有可能会低估P-Δ效应对结构安全性的影响.本文应用求积单元法(weak form quadrature element method,QEM),针对分布质量结构体系和含有集中质量的结构体系分别建立Hermite型求积单元模型,发展了一种高耸结构P-Δ效应高阶精确分析方法.该方法能够应用于具有突变质量的结构体系,可处理任意轴向荷载引起的动力P-Δ效应问题,无需迭代计算即可获得高精度的P-Δ效应解答,同时能准确地揭示竖向荷载以及时变轴力对高耸结构特性的影响规律.通过对3个不同类型案例的比较分析,验证了本文方法的可行性和准确性.数值分析结果表明,本文方法可以实现高精度的P-Δ效应分析,对于质量均匀分布和含有集中质量的结构体系仅需使用一个求积单元即可获得非常精确的动态响应结果.
文摘Bell’s theorem determines the number of representations of a positive integer in terms of the ternary quadratic forms x2+by2+cz2 with b,c {1,2,4,8}. This number depends only on the number of representations of an integer as a sum of three squares. We present a modern elementary proof of Bell’s theorem that is based on three standard Ramanujan theta function identities and a set of five so-called three-square identities by Hurwitz. We use Bell’s theorem and a slight extension of it to find explicit and finite computable expressions for Tunnel’s congruent number criterion. It is known that this criterion settles the congruent number problem under the weak Birch-Swinnerton-Dyer conjecture. Moreover, we present for the first time an unconditional proof that a square-free number n 3(mod 8) is not congruent.
