E-Book, Englisch, 340 Seiten, eBook
Shu Differential Quadrature and Its Application in Engineering
Erscheinungsjahr 2012
ISBN: 978-1-4471-0407-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 340 Seiten, eBook
ISBN: 978-1-4471-0407-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
Zielgruppe
Professional/practitioner
Autoren/Hrsg.
Weitere Infos & Material
1 Mathematical Fundamentals of Differential Quadrature Method: Linear Vector Space Analysis and Function Approximation.- 1.1 Introduction.- 1.2 Derivative Approximation by Differential Quadrature (DQ) Method.- 1.3 Analysis of A Linear Vector Space.- 1.4 Solution of Partial Differential Equations (PDEs) and Function Approximation.- 2 Polynomial-based Differential Quadrature (PDQ).- 2.1 Introduction.- 2.2 Computation of Weighting Coefficients for the First Order Derivative.- 2.3 Computation of Weighting Coefficients for the Second and Higher Order Derivatives.- 2.4 Error Analysis.- 2.5 Relationship Between PDQ and Other Approaches.- 2.6 Extension to the Multi-dimensional Case.- 2.7 Specific Results for Typical Grid Point Distributions.- 2.8 Generation of Low Order Finite Difference Schemes by PDQ.- 3 Fourier Expansion-based Differential Quadrature (FDQ).- 3.1 Introduction.- 3.2 Cosine Expansion-based Differential Quadrature (CDQ) for Even Functions.- 3.3 Sine Expansion-based Differential Quadrature (SDQ) for Odd Functions.- 3.4 Fourier Expansion-based Differential Quadrature (FDQ) for Any General function.- 3.5 Some Properties of Fourier Expansion-based Differential Quadrature.- 4 Some Properties of DQ Weighting Coefficient Matrices.- 4.1 Introduction.- 4.2 Determinant and Rank of DQ Weighting Coefficient Matrices.- 4.3 Structures and Properties of DQ Weighting Coefficient Matrices.- 4.4 Effect of Grid Point Distribution on Eigenvalues of DQ Discretization Matrices.- 4.5 Effect of Grid Point Distribution on Magnitude of DQ Weighting Coefficients.- 5 Solution Techniques for DQ Resultant Equations.- 5.1 Introduction.- 5.2 Solution Techniques for DQ Ordinary Differential Equations.- 5.3 Solution Techniques for DQ Algebraic Equations.- 5.4 Implementation of Boundary Conditions.- 5.5 Sample Applications of DQ Method.- 6 Application of Differential Quadrature Method to Solve Incompressible Navier-Stokes Equations.- 6.1 Introduction.- 6.2 Governing Equations.- 6.3 Solution of Vorticity-Stream Function Formulation.- 6.4 Solution of Incompressible Navier-Stokes Equations in Primitive Variable Form.- 7 Application of Differential Quadrature Method to Structural and Vibration Analysis.- 7.1 Introduction.- 7.2 Differential Quadrature Analysis of Beams.- 7.3 Differential Quadrature Analysis of Thin Plates.- 7.4 Differential Quadrature Analysis of Shells.- 8 Miscellaneous Applications of Differential Quadrature Method.- 8.1 Introduction.- 8.2 Application to Heat Transfer.- 8.3 Application to Chemical Reactor.- 8.4 Application to Lubrication Problems.- 8.5 Application to Waveguide Analysis.- 8.6 Solution of the Helmholtz Equation.- 8.7 Effect of Mesh Point Distribution on Accuracy of DQ Results.- 9 Application of Differential Quadrature to Complex Problems.- 9.1 Introduction.- 9.2 Multi-domain DQ Method.- 9.3 DQ Application in Curvilinear Coordinate System.- 9.4 Differential Cubature Method for Complex Problems.- 10 Generalized Integral Quadrature (GIQ) And Its Application to Solve Boundary Layer Equations.- 10.1 Introduction.- 10.2 Generalized Integral Quadrature (GIQ).- 10.3 DQ-GIQ Algorithm to Solve Boundary Layer Equations.- 10.4 Steady Boundary Layer Solutions.- 10.5 Unsteady Boundary Layer Solutions.- Appendices.- A. A Fortran Program for Simulation of Natural Convection in A Square Cavity.- B. A Fortran Program for Vibration Analysis of Rectangular Plates.- References.