Application of Numerical Methods in Engineering Problems Using MATLAB®

Description

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 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