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Differential Quadrature and Its Application in Engineering

  • Book
  • © 2000

Overview

Authors:
  1. Chang Shu

    1. Department of Mechanical & Production Engineering, National University of Singapore, Singapore

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  • Fortran programs attached allow easy practical application of the methods in the book

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Mathematical Fundamentals of Differential Quadrature Method: Linear Vector Space Analysis and Function Approximation

    • Chang Shu
    Pages 1-24

  3. Polynomial-based Differential Quadrature (PDQ)

    • Chang Shu
    Pages 25-68

  4. Fourier Expansion-based Differential Quadrature (FDQ)

    • Chang Shu
    Pages 69-94

  5. Some Properties of DQ Weighting Coefficient Matrices

    • Chang Shu
    Pages 95-122

  6. Solution Techniques for DQ Resultant Equations

    • Chang Shu
    Pages 123-152

  7. Application of Differential Quadrature Method to Solve Incompressible Navier-Stokes Equations

    • Chang Shu
    Pages 153-185

  8. Application of Differential Quadrature Method to Structural and Vibration Analysis

    • Chang Shu
    Pages 186-223

  9. Miscellaneous Applications of Differential Quadrature Method

    • Chang Shu
    Pages 224-244

  10. Application of Differential Quadrature to Complex Problems

    • Chang Shu
    Pages 245-266

  11. Generalized Integral Quadrature (GIQ) and Its Application to Solve Boundary Layer Equations

    • Chang Shu
    Pages 267-323

  12. Back Matter

    Pages 288-340
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Keywords

About this book

In the past few years, the differential quadrature method has been applied extensively in engineering. This book, aimed primarily at practising engineers, scientists and graduate students, gives a systematic description of the mathematical fundamentals of differential quadrature and its detailed implementation in solving Helmholtz problems and problems of flow, structure and vibration. Differential quadrature provides a global approach to numerical discretization, which approximates the derivatives by a linear weighted sum of all the functional values in the whole domain. Following the analysis of function approximation and the analysis of a linear vector space, it is shown in the book that the weighting coefficients of the polynomial-based, Fourier expansion-based, and exponential-based differential quadrature methods can be computed explicitly. It is also demonstrated that the polynomial-based differential quadrature method is equivalent to the highest-order finite difference scheme. Furthermore, the relationship between differential quadrature and conventional spectral collocation is analysed.
The book contains material on:
- Linear Vector Space Analysis and the Approximation of a Function;
- Polynomial-, Fourier Expansion- and Exponential-based Differential Quadrature;
- Differential Quadrature Weighting Coefficient Matrices;
- Solution of Differential Quadrature-resultant Equations;
- The Solution of Incompressible Navier-Stokes and Helmholtz Equations;
- Structural and Vibrational Analysis Applications;
- Generalized Integral Quadrature and its Application in the Solution of Boundary Layer Equations.
Three FORTRAN programs for simulation of driven cavity flow, vibration analysis of plate and Helmholtz eigenvalue problems respectively, are appended. These sample programs should give the reader a better understanding of differential quadrature and can easily be modified to solve the readers own engineering problems.

Authors and Affiliations

  • Department of Mechanical & Production Engineering, National University of Singapore, Singapore

    Chang Shu

Bibliographic Information

  • Book Title: Differential Quadrature and Its Application in Engineering

  • Authors: Chang Shu

  • DOI: https://doi.org/10.1007/978-1-4471-0407-0

  • Publisher: Springer London

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag London 2000

  • Hardcover ISBN: 978-1-85233-209-9Published: 14 January 2000

  • Softcover ISBN: 978-1-4471-1132-0Published: 12 October 2012

  • eBook ISBN: 978-1-4471-0407-0Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XVI, 340

  • Topics: Mathematical and Computational Engineering, Analysis

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