Application of Numerical Methods in Engineering Problems Using MATLAB®

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