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Differential Quadrature Method (differential + quadrature_method)

Distribution by Scientific Domains

Engineering	83%

Selected Abstracts

DQ-based simulation of weakly nonlinear heat conduction processes

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2008
S. Tomasiello
Abstract In this paper, an explicit form for the numerical solution of problems in the space,time domain by using quadrature rules is proposed. The compact form of the shape functions recently proposed by the author is useful to the scope. Numerical solutions for the time-dependent one-dimensional nonlinear heat conduction problem are calculated by means of the iterative differential quadrature method, a method proposed by the author and based on quadrature rules. The accuracy of the solution and stability analysis show good performance of the approach. Copyright © 2007 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]

New approaches in application of differential quadrature method to fourth-order differential equations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 2 2005
Xinwei Wang
Abstract Various methods to apply multiple boundary conditions in the differential quadrature method are summarized and discussed. Two of them are new approaches appearing for the first time. Numerical examples demonstrate the accuracy of the new methods in applying multiple boundary conditions. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Stability and accuracy of the iterative differential quadrature method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2003
Stefania Tomasiello
Abstract In this paper the stability and accuracy of an iterative method based on differential quadrature rules will be discussed. The method has already been proposed by the author in a previous work, where its good performance has been shown. Nevertheless, discussion about stability and accuracy remained open. An answer to this question will be provided in this paper, where the conditional stability of the method will be pointed out, in addition to an examination of the possible errors which arise under certain conditions. The discussion will be preceded by an overview of the method and its foundations, i.e. the differential quadrature rules, and followed by a numerical case which shows how the method behaves when applied to reduce continuous systems to two-degree-of-freedom systems in the non-linear range. In particular, here the case of oscillators coupled in non-linear terms will be treated. The numerical results, used to draw Poincaré maps, will be compared with those obtained by using the Runge,Kutta method with a high precision goal. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Performance and numerical behavior of the second-order scheme of precise time-step integration for transient dynamic analysis

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2007
Hang Ma
Abstract Spurious high-frequency responses resulting from spatial discretization in time-step algorithms for structural dynamic analysis have long been an issue of concern in the framework of traditional finite difference methods. Such algorithms should be not only numerically dissipative in a controllable manner, but also unconditionally stable so that the time-step size can be governed solely by the accuracy requirement. In this article, the issue is considered in the framework of the second-order scheme of the precise integration method (PIM). Taking the Newmark-, method as a reference, the performance and numerical behavior of the second-order PIM for elasto-dynamic impact-response problems are studied in detail. In this analysis, the differential quadrature method is used for spatial discretization. The effects of spatial discretization, numerical damping, and time step on solution accuracy are explored by analyzing longitudinal vibrations of a shock-excited rod with rectangular, half-triangular, and Heaviside step impact. Both the analysis and numerical tests show that under the framework of the PIM, the spatial discretization used here can provide a reasonable number of model types for any given error tolerance. In the analysis of dynamic response, an appropriate spatial discretization scheme for a given structure is usually required in order to obtain an accurate and meaningful numerical solution, especially for describing the fine details of traction responses with sharp changes. Under the framework of the PIM, the numerical damping that is often required in traditional integration schemes is found to be unnecessary, and there is no restriction on the size of time steps, because the PIM can usually produce results with machine-like precision and is an unconditionally stable explicit method. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 [source]