Inverse Differential Quadrature Method and Its Application in Engineering.

Format:

Book

Author/Creator:

Ojo, Saheed O.

Contributor:

Khalid, Hasan M.

Chanda, Aniket G.

Weaver, Paul M.

Series:

Wiley-ASME Press Series

Language:

English

Physical Description:

1 online resource (370 pages)

Edition:

1st ed.

Place of Publication:

Newark : John Wiley & Sons, Incorporated, 2025.

Summary:

Inverse Differential Quadrature Method and its Application in Engineering Authoritative reference introducing iDQM as a numerical tool to accurately perform high fidelity analyses efficiently for solving problems in engineering governed by higher-order ordinary and partial differential equations.

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

3.4.4.1 Buckling Solution of 3D Laminated Beams

3.4.4.2 Buckling Solution of 3D VS Laminated Beams

3.4.5 Free Vibration Analysis of 3D Laminated Beams

3.4.5.1 Free Vibration Solution of 3D Laminated Beams

3.4.5.2 Free Vibration Solution of 3D VS Laminated Beams

3.5 Conclusion

4: Application to Plate Structures

4.1 Introduction

4.2 FSDT Formulation for Laminated Plate

4.3 iDQM Discretisation

4.4 Bending Analysis

4.4.1 Static Solution of Laminated Plates

4.4.2 Convergence Analysis

4.5 Buckling Analysis

4.5.1 Buckling Solution of Laminated Plates

4.5.2 Convergence Analysis

4.6 Free Vibration Analysis of Arbitrary-shaped Plates

4.6.1 Geometric Mapping

4.6.2 Transformed Discretised Equations

4.6.3 Free Vibration of Square Plates

4.6.4 Free Vibration of Skew Plates.

4.6.4.1 Free Vibration of Isotropic Skew Plates

4.6.4.2 Free Vibration of Clamped-clamped Composite Skew Plates

4.6.5 Free Vibration of Circular Plates

4.6.5.1 Free Vibration of Isotropic Circular Plates

4.6.5.2 Free Vibration of Composite Circular Plates

4.6.6 Free Vibration of Annular Sector Plates

4.6.6.1 Free Vibration of Isotropic Annular Sector Plates

4.6.6.2 Free Vibration of Laminated Annular Sector Plates

4.6.7 Convergence Analysis

4.7 Transient Analysis

4.7.1 Transient Analysis of Laminated Plates

4.7.1.1 Transient Analysis of Laminated Plates Under Step Load

4.7.1.2 Transient Analysis of Laminated Plates Under Arbitrary Loading Conditions

4.7.2 Convergence Analysis

4.8 Conclusion

5: Application to Shell Structures

5.1 Introduction

5.2 Shell Unified Formulation

5.2.1 Strong Shell Unified Formulation

5.2.2 iDQM Discretisation

5.2.3 Static Solution of Laminated Cylindrical and Spherical Shells

5.2.3.1 Static Analysis of Laminated Composite Spherical Shell Subject to Bi-sinusoidal Load-1

5.2.3.2 Static Analysis of Spherical Laminated Composite Shell Subject to Bi-sinusoidal Load-2

5.2.3.3 Static Analysis of Laminated Composite Cylindrical Shell Subject to Bi-sinusoidal Load

5.2.3.4 Static Analysis of Laminated Composite Cylindrical Shell in Cylindrical Bending

5.2.3.5 Static Analysis of Isotropic Sandwich Cylindrical Shell with Isotropic Face Sheets Subject to Bi-sinusoidal Load

5.2.4 Free Vibration Solution of Laminated Cylindrical and Spherical Shells

5.2.4.1 Free Vibration of Laminated Composite Spherical Shell with Various Deepness and Span-to-thickness Ratios

5.2.4.2 Free Vibration of Laminated Composite Cylindrical Shell with Various Deepness and Span-thickness Ratios

5.3 Conclusion

References.

6: Application to Multidomain Structures

6.1 Introduction

6.2 Multidomain iDQM for Beam Structures

6.2.1 Beam Formulation for a Subdomain

6.2.2 Assembly Procedure

6.2.3 Compatibility Conditions

6.2.4 Static Solution of Beam Under Point Load

6.3 Multidomain iDQM for Plate Structures

6.3.1 Plate Formulation for a Subdomain

6.3.2 Assembly Procedure

6.3.3 Compatibility Conditions

6.3.4 Solution of Bending of Plate Under a Patch Load

6.3.5 Solution of Bending of Plates Comprising Dissimilar Materials

6.3.6 Solution of Bending of Plate with Discontinuous Boundaries

6.4 Conclusion

7: Application to Nonlinear Problems

7.1 Introduction

7.2 One-dimensional Problems

7.2.1 Nonlinear Flexural Vibration of a Simply Supported Euler Beam

7.2.2 Nonlinear Flexural Vibration of SS Timoshenko Beam

7.2.3 Nonlinear Flexural Vibration of Clamped-clamped Timoshenko Beam

7.2.4 Steady-state Heat Conduction in Slab with Temperature-dependent Conductivity

7.2.5 One-dimensional Scalar Combustion Model

7.2.6 Soliton Solutions to the Korteweg-de Vries Equation

7.2.7 Solution of the Interaction Between Two Solitons

7.2.8 Solution of the Interaction Between Three Solitons

7.3 Two-dimensional Problems

7.3.1 Nonlinear Bending Analysis of Isotropic SS Square Plates

7.3.2 Nonlinear Bending Analysis of Isotropic Fully Clamped Square Plate

7.3.3 2D Scalar Combustion Model

7.4 Conclusion

8: Application to Miscellaneous Problems

8.1 Introduction

8.2 One-dimensional Problems

8.2.1 Thermomechanical Formulation for Laminated Beams

8.2.1.1 Static Analysis of Laminated Beams Subject to Thermal Load

8.2.1.2 Static Solution of Composite Beam Integrated with Piezoelectric Actuator Subject to Electromechanical Load

8.2.2 Solution of Chemical Reactor Equation.

8.2.3 1D Time-dependent Heat Diffusion in a Sphere

8.3 Two-dimensional Problems

8.3.1 Solution of Convection-diffusion Equation

8.3.2 Solution of Vorticity-stream Function Equations

8.3.3 Solution of Helmholtz Equation

8.4 Conclusion

9: Preconditioning of iDQM Systems of Equations

9.1 Introduction

9.2 iDQM Preconditioning

9.3 Preconditioning by Normalisation

9.3.1 Formulation for Linear Time-independent Systems

9.3.1.1 Static Response of Simply Supported Plate Under Sinusoidally Distributed Load

9.3.1.2 Static Response of SS Plate Under Uniformly Distributed Load

9.3.1.3 Stress Prediction of SS 3D Laminated Beam Under Sinusoidally Distributed Load

9.3.2 Formulation for Linear Second-order Time-dependent Systems

9.3.2.1 Transient Response of SS Timoshenko Beam Under Time-dependent Uniformly Distributed Load

9.3.3 Formulation for Nonlinear Systems

9.3.3.1 Geometrically Nonlinear Bending Analysis of SS Isotropic Plate under Large Uniform Pressure Load

9.3.3.2 Geometrically Nonlinear Bending Analysis of Clamped Isotropic Plate under Large Uniform Pressure Load

9.4 Preconditioning by Matrix Inversion

9.5 Preconditioning by Matrix Inversion and Normalisation

9.5.1 Separation of Constants and Normalisation (PMN-Method 1)

9.5.2 Separation of Constants and Boundaries and Normalisation (PMN-Method 2)

9.5.2.1 Buckling Analysis of SS Euler Beam

9.5.2.2 Buckling Solution of SS FSDT Plate

9.5.2.3 Free Vibration Analysis of SS Euler Beam

9.5.2.4 Free Vibration Analysis of SS FSDT Plate

9.6 Comparison of Computational Complexities of Preconditioning Methods

9.7 Conclusion

10: Discussion on iDQM Convergence

10.1 Introduction

10.2 Convergence Analysis

10.2.1 Convergence of iDQM for Static Analysis.

10.2.1.1 Convergence of Bending Solution for Euler Beam.

Notes:

Publisher supplied metadata and other sources.

Description based on publisher supplied metadata and other sources.

Other Format:

Print version:

ISBN:

1-394-25415-6

1-394-25413-X

OCLC:

1543510373