Application of Numerical Methods in Engineering Problems Using MATLAB®

✍ Scribed by M. S. H. Al-Furjan; M. Rabani Bidgoli; Reza Kolahchi; A. Farrokhian; M. R. Bayati

• Publisher: CRC Press
• Year: 2023
• Tongue: English
• Leaves: 297
• Category: Library

✦ Synopsis

Application of Numerical Methods in Engineering Problems using MATLAB(R) presents an analysis of structures using numerical methods and mathematical modeling. This structural analysis also includes beam, plate, and pipe elements, and also examines deflection and frequency, or buckling loads. The various engineering theories of beams/plates/shells are comprehensively presented, and the relationships between stress and strain, and the governing equations of the structure are extracted. To solve governing equations with numerical methods, there are two general types, including methods based on derivatives or integrals. Derivative-based methods have the advantage of flexibility in modeling boundary conditions, low analysis time, and very high degree of accuracy. Therefore, the book explains numerical methods based on derivatives, especially the differential quadrature method. Features: Examines the application of numerical methods to obtain the deflection, frequency, and buckling loads Discusses the application of numerical methods for solving motion equations Includes numerous practical and applicable examples throughout

✦ Table of Contents

Cover
Half Title
Series
Title
Copyright
Contents
Preface to the First Edition
Foreword
About the Authors
Acknowledgments
Chapter 1 Basic Theories
1.1 Introduction
1.2 Strain–Displacement Equations
1.3 Beam Theories
1.3.1 Introduction
1.3.2 Preliminaries
1.3.3 Euler–Bernoulli Theory
1.3.4 Timoshenko Beam Theory
1.3.5 Sinusoidal Shear Deformation Theory
1.3.6 Hyperbolic Shear Deformation Beam Theory
1.3.7 Exponential Shear Deformation Beam Theory
1.4 Plate Theories
1.4.1 Classical Theory
1.4.2 First-Order Shear Deformation Theory
1.4.3 Reddy Theory
1.4.4 Sinusoidal Shear Deformation Theory
1.5 Shell Theories
1.5.1 Classical Shell Theory
1.5.2 FSDT or the Mindlin Theory
1.5.3 Reddy Theory
References
Chapter 2 Solution Methods
2.1 Analytical Methods
2.1.1 Navier Method
2.1.2 Galerkin Method
2.2 Numerical Methods for Space Domain
2.2.1 Differential Quadrature Method
2.2.2 Harmonic Differential Quadrature Method
2.2.3 Discrete Singular Convolution Method
2.2.4 Differential Cubature Method
2.3 Numerical Methods for Time Domain
2.3.1 Newmark Method
2.3.2 Poincaré–Lindstedt Method
2.3.3 Multiple Scale Method
2.3.4 First-Order Two-Scale Expansion Method
2.3.5 Second-Order Three-Time Scale Expansion Method
References
Chapter 3 Buckling of Nanoparticle-Reinforced Beams Exposed to Fire
3.1 Introduction
3.2 Mathematical Modeling
3.2.1 Energy Method
3.2.2 Hamilton’s Principle
3.3 Mori–Tanaka Rule
3.4 Numerical Results
3.4.1 Accuracy of DQM
3.4.2 Validation
3.4.3 Effect of Different Parameters
References
Chapter 4 Dynamic Response of Nanofiber-Reinforced Beams Subjected to Seismic Ground Excitation
4.1 Introduction
4.2 Mathematical Model
4.3 Mori–Tanaka Model
4.4 Energy Method
4.5 Numerical Results
4.5.1 Convergence of HDQM
4.5.2 Validation of Results
4.5.3 Effect of an NFRP Layer on the Dynamic Response
4.5.4 Effect of Carbon Nanofibers on the Dynamic Response
4.5.5 Effect of Geometric Parameters of a Beam on the Dynamic Response
4.5.6 Effect of Boundary Conditions on Dynamic Response
References
Chapter 5 Buckling Analysis of Plates Reinforced with Graphene Platelets
5.1 Introduction
5.2 Kinematics of Different Theories
5.3 Motion Equation
5.4 Numerical Result and Discussion
References
Chapter 6 Vibration Analysis of Agglomerated Nanoparticle-Reinforced Plates
6.1 Introduction
6.2 Mathematical Modeling
6.2.1 Stress–Strain Relations
6.2.2 Energy Method
6.3 Numerical Results and Discussion
6.3.1 Validation
6.3.2 Effects of Different Parameters
References
Chapter 7 Vibration Analysis of Plates with an NFRP Layer
7.1 Introduction
7.2 Stress–Strain Relations
7.3 Energy Method
7.4 Numerical Results and Discussion
References
Chapter 8 Vibration Analysis of Plates Reinforced with Nanoparticles and a Piezoelectric Layer
8.1 Introduction
8.2 Constitutive Equations of Piezoelectric Material
8.3 Energy Method
8.4 Numerical Results and Discussion
References
Chapter 9 Forced Vibration Analysis of Plates Reinforced with Nanoparticles
9.1 Introduction
9.2 Mathematical Modeling
9.3 Numerical Results and Discussion
9.3.1 Convergence of Numerical Method
9.3.2 Validation
9.3.3 Effects of Different Parameters
References
Chapter 10 Seismic Analysis of Plates Reinforced by Nanoparticles
10.1 Introduction
10.2 Stress–Strain Relations
10.3 Numerical Results and Discussion
10.3.1 Convergence of DQM
10.3.2 Validation of Results
10.3.3 Effect of the Magnetic Field
10.3.4 Effect of AL2O3 Nanoparticles
10.3.5 Effect of Concrete Plate Length
10.3.6 Effect of Boundary Conditions on the Dynamic Response
References
Chapter 11 Stress Analysis of Shells Reinforced with Nanoparticles
11.1 Introduction
11.2 Governing Equations
11.3 Numerical Results and Discussion
References
Chapter 12 Earthquake Response of Submerged Nanocomposite Shells Conveying Fluid
12.1 Introduction
12.2 Mathematical Modeling
12.3 Numerical Results and Discussion
12.3.1 Validation
12.3.2 Convergence of the Present Method
12.3.3 Effects of Various Parameters
References
Chapter 13 Vibration and Instability Analysis of Shells Reinforced by Nanoparticles
13.1 Introduction
13.2 Formulation
13.3 Numerical Results and Discussion
13.3.1 DQM Convergence
13.3.2 Effects of Different Parameters
References
Chapter 14 Dynamic Response of Nanocomposite Shells Covered with a Piezoelectric Layer
14.1 Introduction
14.2 Geometry of the Problem
14.3 Constitutive Equations
14.3.1 Piezoelectric Layer
14.3.2 Nanocomposite Pipe
14.4 Energy Method
14.5 Hamilton’s Principle
14.6 Numerical Results
14.6.1 Verification
14.6.2 Convergence of the Numerical Method
14.6.3 Effects of Various Parameters
References
Appendix A: The MATLAB Code for Chapter 4
Appendix B: The MATLAB Code for Chapter 6
Appendix C: The MATLAB Code for Chapter 7
Appendix D: The MATLAB Code for Chapter 8
Appendix E: The MATLAB Code for Chapter 11
Appendix F: The MATLAB Code for Chapter 12
Index