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Differential Quadrature (differential + quadrature)

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Engineering100%

Terms modified by Differential Quadrature

  • differential quadrature method
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    Selected Abstracts

    DQEM analysis of out-of-plane deflection of non-prismatic curved beam structures considering the effect of shear deformation

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2008
    Chang-New Chen
    Abstract The development of differential quadrature element method (DQEM) out-of-plane deflection analysis model of curved non-prismatic beam structures considering the effect of shear deformation was carried out. The DQEM uses the differential quadrature (DQ) to discretize the governing differential equation defined on each element, the transition conditions defined on the inter-element boundary of two adjacent elements and the boundary conditions of the beam. Numerical results solved by the developed numerical algorithm are presented. The convergence of the developed DQEM analysis model is efficient. Copyright © 2006 John Wiley & Sons, Ltd. [source]

    An interpolation-based local differential quadrature method to solve partial differential equations using irregularly distributed nodes

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2008
    Hang Ma
    Abstract To circumvent the constraint in application of the conventional differential quadrature (DQ) method that the solution domain has to be a regular region, an interpolation-based local differential quadrature (LDQ) method is proposed in this paper. Instead of using regular nodes placed on mesh lines in the DQ method (DQM), irregularly distributed nodes are employed in the LDQ method. That is, any spatial derivative at a nodal point is approximated by a linear weighted sum of the functional values of irregularly distributed nodes in the local physical domain. The feature of the new approach lies in the fact that the weighting coefficients are determined by the quadrature rule over the irregularly distributed local supporting nodes with the aid of nodal interpolation techniques developed in the paper. Because of this distinctive feature, the LDQ method can be consistently applied to linear and nonlinear problems and is really a mesh-free method without the limitation in the solution domain of the conventional DQM. The effectiveness and efficiency of the method are validated by two simple numerical examples by solving boundary-value problems of a linear and a nonlinear partial differential equation. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    Application of a new differential quadrature methodology for free vibration analysis of plates

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2003
    G. Karami
    Abstract A new methodology is introduced in the differential quadrature (DQ) analysis of plate problems. The proposed approach is distinct from other DQ methods by employing the multiple boundary conditions in a different manner. For structural and plate problems, the methodology employs the displacement within the domain as the only degree of freedom, whereas along the boundaries the displacements as well as the second derivatives of the displacements with respect to the co-ordinate variable normal to the boundary in the computational domain are considered as the degrees of freedom for the problem. Employing such a procedure would facilitate the boundary conditions to be implemented exactly and conveniently. In order to demonstrate the capability of the new methodology, all cases of free vibration analysis of rectangular isotropic plates, in which the conventional DQ methods have had some sort of difficulty to arrive at a converged or accurate solution, are carried out. Excellent convergence behaviour and accuracy in comparison with exact results and/or results obtained by other approximate methods were obtained. The analogous DQ formulation for a general rectangular plate is derived and for each individual boundary condition the general format for imposing the given conditions is devised. It must be emphasized that the computational efforts of this new methodology are not more than for the conventional differential quadrature methods. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    Numerical study of grid distribution effect on accuracy of DQ analysis of beams and plates by error estimation of derivative approximation

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2001
    C. Shu
    Abstract The accuracy of global methods such as the differential quadrature (DQ) approach is usually sensitive to the grid point distribution. This paper is to numerically study the effect of grid point distribution on the accuracy of DQ solution for beams and plates. It was found that the stretching of grid towards the boundary can improve the accuracy of DQ solution, especially for coarse meshes. The optimal grid point distribution (corresponding to optimal stretching parameter) depends on the order of derivatives in the boundary condition and the number of grid points used. The optimal grid distribution may not be from the roots of orthogonal polynomials. This differs somewhat from the conventional analysis. This paper also proposes a simple and effective formulation for stretching the grid towards the boundary. The error distribution of derivative approximation is also studied, and used to analyze the effect of grid point distribution on accuracy of numerical solutions. Copyright © 2001 John Wiley & Sons, Ltd. [source]

    Numerical computation of three-dimensional incompressible Navier,Stokes equations in primitive variable form by DQ method

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2003
    C. Shu
    Abstract In this paper, the global method of differential quadrature (DQ) is applied to solve three-dimensional Navier,Stokes equations in primitive variable form on a non-staggered grid. Two numerical approaches were proposed in this work, which are based on the pressure correction process with DQ discretization. The essence in these approaches is the requirement that the continuity equation must be satisfied on the boundary. Meanwhile, suitable boundary condition for pressure correction equation was recommended. Through a test problem of three-dimensional driven cavity flow, the performance of two approaches was comparatively studied in terms of the accuracy. The numerical results were obtained for Reynolds numbers of 100, 200, 400 and 1000. The present results were compared well with available data in the literature. In this work, the grid-dependence study was done, and the benchmark solutions for the velocity profiles along the vertical and horizontal centrelines were given. Copyright © 2003 John Wiley & Sons, Ltd. [source]