Inverse differential quadrature method and its application in engineering / Saheed O. Ojo... [and 3 others].

Format:

Book

Author/Creator:

Ojo, Saheed O., author.

Contributor:

Wiley InterScience (Online service)

Series:

Wiley-ASME Press series

Language:

English

Subjects (All):

Engineering mathematics.

Differential equations--Numerical solutions.

Differential equations.

Physical Description:

1 online resource.

Place of Publication:

Hoboken, New Jersey : John Wiley & Sons, Inc. ; [New York, New York] : ASME Press, 2025.

Contents:

Cover

Half Title Page

Title Page

Copyright

Contents

Preface

Nomenclature

Acronyms

Acknowledgments

1: Introduction

1.1 Introduction

1.2 Overview of Numerical Approximation Methods

1.3 Numerical Approximation

1.4 Spectral Methods

1.4.1 Galerkin and Tau Approach

1.4.2 Collocation Approach

1.5 Differential Quadrature Method

1.5.1 Determination of Weighting Coefficients

1.5.2 DQM Implementation of Dual Boundary Conditions

1.6 Errors Incurred in Numerical Differentiation

1.7 Indirect Approximation Approach

1.8 Conclusion

References

2: Inverse Differential Quadrature Method

2.1 Introduction

2.2 Brief Description of DQM Formulation

2.3 Inverse Differential Quadrature Method

2.3.1 First-order iDQM-by-integration

2.3.2 Higher-order iDQM-by-integration

2.3.3 Computational Aspects of iDQM-by-integration

2.3.4 First-order iDQM-by-inversion

2.3.5 Higher-order iDQM-by-inversion

2.3.6 Proof of ym = m!ˆD( ym)1

2.4 iDQM Error Formulation

2.4.1 Error Formulation of iDQM-by-integration

2.4.2 Error of iDQM-by-inversion

2.4.3 Comparison of iDQM Error with DQM Error

2.5 Two-dimensional iDQM

2.5.1 First-order iDQM

2.5.2 Second-order iDQM

2.5.3 Higher-order iDQM

2.6 Discretisation of ODEs and PDEs

2.6.1 One-dimensional iDQM Discretisation

2.6.2 Two-dimensional iDQM Discretisation

2.7 Numerical Examples

2.7.1 Approximation of a Function and Its Derivatives

2.7.2 Numerical Solution of Euler Cantilever Beam (ODE

2.7.3 Solution of Simply Supported Isotropic Plate Under Sinusoidally Distributed Load (PDE)

2.7.4 Error Analysis (Measure of Numerical Accuracy

2.7.5 Error Propagation (Measure of Numerical Stability

2.8 Conclusion

3: Application to Beam Structures

3.1 Introduction

3.2 Euler Beam

3.2.1 Euler Beam Formulation

3.2.2 iDQM Discretisation

3.2.3 Static Solution of Euler Beam

3.2.4 Buckling Solution of Euler Beam

3.2.5 Free Vibration Solution of Euler Beam

3.3 Timoshenko Curved Laminated Beam

3.3.1 Timoshenko Beam Formulation for Laminated Curved Beams

3.3.2 iDQM Discretisation

3.3.3 Static Analysis of Laminated Beams

3.3.3.1 Static Solution of Laminated Curved Beams

3.3.3.2 Static Solution of VS Straight Beams

3.3.4 Transient and Free Vibration Analyses of Laminated Curved Beams

3.3.4.1 Free Vibration Solution of Laminated Curved Beams

3.3.4.2 Transient Solution of Laminated Curved Beams

3.4 UF Beam

3.4.1 Strong Unified Formulation

3.4.2 iDQM Discretisation

3.4.3 Static Analysis of 3D Laminated Beams

3.4.3.1 Static Solution of 3D Symmetric Cross-ply Laminated Beam

3.4.3.2 Static Solution of 3D Non-symmetric Cross-ply Laminated Beam

3.4.3.3 Static Solution of 3D Sandwich Laminated Beam

3.4.4 Buckling Analysis of 3D Laminated Beams

Notes:

Second place of publication from the publisher's website.

Electronic reproduction. Hoboken, N.J. Available via World Wide Web.

Description based on online resource; title from digital title page (viewed on October 07, 2025).

Other Format:

Print version :

ISBN:

9781394254132

139425413X

9781394254156

1394254156

9781394254149

1394254148

Publisher Number:

90104200386

CIPO000302844

Access Restriction:

Restricted for use by site license.