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Applied Mathematics and Mechanics(English Edition) 2004年第8期25卷 878-886页

作者：李晶晶程昌钧 Shanghai Institute of Applied Mathematics and Mechanics and Department of Mechanics Shanghai University Shanghai 200072 P.R.China

Based on the Reddy's theory of plates with the effect of higher-order shear deformations, the governing equations for bending of orthotropic plates with finite deformations were established. The differential quadrature (DQ) method of nonlinear analysis to the problem was presented. New DQ approach, presented by Wang and Bert (DQWB), is extended to handle the multiple boundary conditions of plates. The techniques were also further extended to simplify nonlinear computations. The numerical convergence and comparison of solutions were studied. The results show that the DQ method presented is very reliable and valid. Moreover, the influences of geometric and material parameters as well as the transverse shear deformations on nonlinear bending were investigated. Numerical results show the influence of the shear deformation on the static bending of orthotropic moderately thick plate is significant.

关键词： higher-order transverse shear deformation finite deformation differential quadrature method DQWB approach convergence and comparison study of solution

differential quadrature method TO STABILITY ANALYSIS OF PIPES CONVEYING FLUID WITH SPRING SUPPORT

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Acta Mechanica Solida Sinica 2000年第4期13卷 320-327页

作者： Ni Qiao Huang Yuying Huazhong Univ Sci & Technol Dept Mech Wuhan 430074 Peoples R China

It is a new attempt to extend the differential quadrature method(DQM) to stability analysis of the straight and curved centerlinepipes conveying fluid. Emphasis is placed on the study of theinfluences of several parameters on the critical flow *** to other methods, this method can more easily deal with thepipe with spring support at its boundaries and asks for much lesscomputing effort while giving ac- ceptable precision in the numericalresults.

关键词： pipes conveying fluid differential quadrature method critical flowvelocity

A MIXTURE differential quadrature method FOR SOLVING TWO-DIMENSIONAL INCOMPRESSIBLE NAVIER_STOKES EQUATIONS

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Applied Mathematics and Mechanics(English Edition) 1999年第12期20卷 1358-1366页

作者：孙建安朱正佑 Shanghai Institute of Applied Mathematics and Mechanics Shanghai P R China Department of Mathematics Shanghai University Shanghai P R China

differential quadrature method (DQM) is able to obtain highly accurate numerical solutions of differential equations just using a few grid points. But using purely differential quadrature method, good numerical solutions of two_dimensional incompressible Navier_Stokes equations can be obtained only for low Reynolds number flow and numerical solutions will not be convergent for high Reynolds number flow. For this reason, in this paper a combinative predicting_correcting numerical scheme for solving two_dimensional incompressible Navier_Stokes equations is presented by mixing upwind difference method into differential quadrature one. Using this scheme and pseudo_time_dependent algorithm, numerical solutions of high Reynolds number flow are obtained with only a few grid points. For example, 1∶1 and 1∶2 driven cavity flows are calculated and good numerical solutions are obtained.

关键词： numerical method differential quadrature method Navier_Stokes equations

Buckling analysis of nanobeams with exponentially varying stiffness by differential quadrature method

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Chinese Physics B 2017年第7期26卷 218-227页

作者： S Chakraverty Laxmi Behera Department of Mathematics National Institute of Technology Rourkela

We present the application of differential quadrature（DQ） method for the buckling analysis of nanobeams with exponentially varying stiffness based on four different beam theories of Euler-Bernoulli, Timoshenko, Reddy, and *** formulation is based on the nonlocal elasticity theory of Eringen. New results are presented for the guided and simply supported guided boundary conditions. Numerical results are obtained to investigate the effects of the nonlocal parameter,length-to-height ratio, boundary condition, and nonuniform parameter on the critical buckling load parameter. It is observed that the critical buckling load decreases with increase in the nonlocal parameter while the critical buckling load parameter increases with increase in the length-to-height ratio.

关键词： differential quadrature method exponentially varying stiffness different beam theories

Investigation of the Free Vibrations of Radial Functionally Graded Circular Cylindrical Beams Based on differential quadrature method

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Computer Modeling in Engineering & Sciences 2022年第7期132卷 23-41页

作者： Xiaojun Huang Liaojun Zhang Renyu Ge Hanbo Cui Zhedong Xu College of Water Conservancy and Hydropower Engineering Hohai UniversityNanjing210098China School of Architecture and Civil Engineering Anhui Polytechnic UniversityWuhu241000China

In the current research,an effective differential quadrature method(DQM)has been developed to solve natural frequency and vibration modal functions of circular section beams along radial functional *** on the high-order theory of transverse vibration of circular cross-section beams,lateral displacement equation was reconstructed neglecting circumferential shear *** equations coupled with deflection and rotation angles were derived based on elastic mechanics theory and further simplified into a constant coefficient differential equation with natural frequency as ***,differential quadrature method was applied to transform the eigenvalue problem of the derived differential equation into a set of algebraic equation eigenvalue *** frequencies of the free vibrations of cylindrical beams with circular cross-sections were calculated at one time,and corresponding modal functions were solved *** obtained numerical results indicated that the natural frequencies of functionally graded(FG)circular cylindrical beams obtained using differential quadrature method agreed with the results reported in related *** addition,influences of varying gradient parameters on the modal shapes of circular cylindrical beams were found to be strongly consistent with previous *** results further validated the feasibility and accuracy of the developed differential quadrature method in solving the transverse vibration of FG circular cross-section beams.

关键词： Functionally graded materials circular cylindrical beams natural frequency modal function differential quadrature method

Static Analysis of Doubly-Curved Shell Structures of Smart Materials and Arbitrary Shape Subjected to General Loads Employing Higher Order Theories and Generalized differential quadrature method

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Computer Modeling in Engineering & Sciences 2022年第12期133卷 719-798页

作者： Francesco Tornabene Matteo Viscoti Rossana Dimitri Department of Innovation Engineering School of EngineeringUniversity of SalentoLecce73100Italy

The article proposes an Equivalent Single Layer(ESL)formulation for the linear static analysis of arbitrarily-shaped shell structures subjected to general surface loads and boundary conditions.A parametrization of the physical domain is provided by employing a set of curvilinear principal *** generalized blendingmethodology accounts for a distortion of the structure so that disparate geometries can be *** layer of the stacking sequence has an arbitrary orientation and is modelled as a generally anisotropic *** addition,re-entrant auxetic three-dimensional honeycomb cells with soft-core behaviour are considered in the *** unknown variables are described employing a generalized displacement field and pre-determined through-the-thickness functions assessed in a unified ***,a weak assessment of the structural problem accounts for shape functions defined with an isogeometric approach starting fromthe computational *** has been proposed to define two-dimensional distributions of static surface *** the same way,boundary conditions with three-dimensional features are implemented along the shell edges employing linear *** fundamental relations are obtained from the stationary configuration of the total potential energy,and they are numerically tackled by employing the Generalized differential quadrature(GDQ)method,accounting for nonuniform computational *** the post-processing stage,an equilibrium-based recovery procedure allows the determination of the three-dimensional dispersion of the kinematic and static *** case studies have been presented,and a successful benchmark of different structural responses has been performed with respect to various refined theories.

关键词： 3D honeycomb anisotropic materials differential quadrature method general loads and constraints higher order theories linear static analysis weak formulation

Stability Analysis and Order Improvement for Time Domain differential quadrature method

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Advances in Applied Mathematics and Mechanics 2016年第1期8卷 128-144页

作者： Fangzong Wang Xiaobing Liao Xiong Xie College of Electrical Engineering&New Energy China Three Gorges UniversityYichang 443002China

The differential quadrature method has been widely used in scientific and engineering ***,for the basic characteristics of time domain differential quadrature method,such as numerical stability and calculation accuracy or order,it is still lack of systematic analysis *** this paper,according to the principle of differential quadrature method,it has been derived and proved that the weighting coefficients matrix of differential quadrature method meets the important V-transformation *** the equivalence of the differential quadrature method and the implicit Runge-Kutta method,it has been proved that the differential quadrature method is A-stable and s-stage s-order *** this basis,in order to further improve the accuracy of the time domain differential quadrature method,a class of improved differential quadrature method of s-stage 2s-order has been proposed by using undetermined coefficients method and Pad´e *** numerical results show that the proposed differential quadrature method is more precise than the traditional differential quadrature method.

关键词： differential quadrature method numerical stability order V-transformation Runge-Kutta method Pad´e approximations

Computation of one—dimensional consolidation of double layered ground using differential quadrature method

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Journal of Zhejiang University Science 2003年第2期4卷 195-201页

作者：王宏志陈云敏黄博 InstituteofGeotecfhnicalEngineering ZhejiangUniversityHangzhou310027China

The authors give the solution to the problem of one-dimensional conso l idation of double-layered ground with the use of the differential quadrature me t hod. Case studies showed that the computational results for pore-water pressure in soil layer agreed with those of analytical solution; and that in the computat ional results for the interface of soil layer also agreed with those of the anal ytical solution except for the small discrepancies during shortly after the star t of computation. The advantages of the solution presented in this paper are tha t compared with the analytical solution, it avoids the cumbersome work in solvin g the transcendental equation for eigenvalues, and in the case of the Laplace transform s olution, it can resolve the precision problem in the numerical solution of long time inverse Laplace transform. Because of the matrix form of the solution in th is paper, it is convenient for formulating computational program for engineering practice. The formulas for calculating double-layered ground consolidation may be easily extended to the case of multi-layered soils.

关键词： Double-layered ground One-dimensional consolidat ion differential quadrature method

differential quadrature method for Bending Problem of Plates with Transverse Shear Effects

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Journal of Shanghai University(English Edition) 2003年第3期7卷 228-233页

作者：李晶晶程昌钧 Shanghai Institute of Applied Mathematics and Mechanics and College of Sciences Shanghai University Shanghai 200072 China

A differential quadrature (DQ) method for orthotropic plates was proposed based on Reddy' s theory of plates with the effects of the higher-order transverse shear deformations. Wang-Bert's DQ approach was also further extended to handle the boundary conditions of plates. The computational convergence was studied, and the numerical results were obtained for different grid spacings and compared with the existing results. The results show that the DQ method is fairly reliable and effective.

关键词： differential quadrature method higher-order transverse shear deformation effect of grid spacing numerical convergence.

Free Vibration Analysis of Laminated Composite Beams Using differential quadrature method

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Tsinghua Science and Technology 2002年第6期7卷 567-573页

作者：冯丽娟钟宏志郝照平吴德隆 Department of Civil Engineering Tsinghua University Beijing 100084 China Beijing Institute of Astronautical Systems Engineering Beijing 100076 China

A higher-order theory for laminated composite beams is used to study the free vibration of laminated composite beams, and the differential quadrature method is employed to obtain the numerical solution of the governing differential equations. Free vibration analysis of beams with rectangular cross-section for various combinations of end conditions is studied. The results show that the differential quadrature method is reliable and accurate compared with other available results.

关键词： laminated composite beam free vibration differential quadrature method