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El. knyga: Computational Nondestructive Evaluation Handbook: Ultrasound Modeling Techniques

, (University of South Carolina)
  • Formatas: 584 pages
  • Išleidimo metai: 01-Jun-2020
  • Leidėjas: CRC Press
  • Kalba: eng
  • ISBN-13: 9780429853128
Kitos knygos pagal šią temą:
Computational Nondestructive Evaluation Handbook: Ultrasound Modeling TechniquesDidesnis paveikslėlis
  • Formatas: 584 pages
  • Išleidimo metai: 01-Jun-2020
  • Leidėjas: CRC Press
  • Kalba: eng
  • ISBN-13: 9780429853128
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Introducing computational wave propagation methods developed over 40 years of research, this comprehensive book offers a computational approach to NDE of isotropic, anisotropic, and functionally graded materials. It discusses recent methods to enable enhanced computational efficiency for anisotropic materials. It offers an overview of the need for and uses of NDE simulation. The content provides a basic understanding of ultrasonic wave propagation through continuum mechanics and detailed discussions on the mathematical techniques of six computational methods to simulate NDE experiments. In this book, the pros and cons of each individual method are discussed and guidelines for selecting specific simulation methods for specific NDE scenarios are offered.











Covers ultrasonic CNDE fundamentals to provide understanding of NDE simulation methods





Offers a catalog of effective CNDE methods to evaluate and compare





Provides exercises on real-life NDE problems with mathematical steps





Discusses CNDE for common material types, including isotropic, anisotropic, and functionally graded materials





Presents readers with practical knowledge on ultrasonic CNDE methods

This work is an invaluable resource for researchers, advanced students, and industry professionals across materials, mechanical, civil, and aerospace engineering, and anyone seeking to enhance their understanding of computational approaches for advanced material evaluation methods.

Recenzijos

This book is an invaluable addition to technical libraries in Computational Nondestructive Evaluation (NDE), as it is focused on the computational methods for NDE modeling and simulation, providing discussion of a variety of commonly used methods. Given the complexity of the subject, the authors have dedicated their first seven chapters to paving the way toward understanding. They discuss experimental methods for nondestructive testing of materials, basics of continuum mechanics, and wave propagation theory. The book [ also] includes numerous clear illustrations as well as many numerical solved examples. Graduate students and researchers already specialized for work in this field would fully benefit from this book."

--S. D. El Wakil, emeritus, University of Massachusetts Dartmouth, CHOICE, June 2021

Preface xxi
About the Author xxiii
Chapter 1 Computational Nondestructive Evaluation (CNDE)
1(28)
1.1 Introduction
1(11)
1.1.1 Various NDE Methods
2(4)
1.1.2 Computational Ultrasonic NDE
6(6)
1.2 Physics and Apparatus for Ultrasonic Technique
12(7)
1.2.1 Ultrasonic NDE
12(1)
1.2.2 Ultrasonic in situ NDE or SHM Method
13(3)
1.2.3 Ultrasonic NDE/SHM of Metals vs. Composites
16(3)
1.3 Historical Background of CNDE
19(4)
1.4 Overview of the
Chapters
23(1)
1.5 Summary
24(5)
Chapter 2 Vector Fields and Tensor Analysis
29(28)
2.1 Understanding Vectors
29(3)
2.2 A Brief Review of Index Notation
32(2)
2.2.1 Dot Product of Two Vectors
32(1)
2.2.2 Cross Product of Two Vectors
33(1)
2.3 Understanding the Vector Field
34(5)
2.3.1 Gradient Operator
36(1)
2.3.2 Divergence of a Vector Field
37(1)
2.3.3 Curl of a Vector Field
38(1)
2.4 Concept of Tensor and Tensor Analysis in Brief
39(3)
2.4.1 First-Order and Second-Order Tensors
39(2)
2.4.2 Transformation Laws of Tensors
41(1)
2.5 Covariant, Contravariant Tensors, and Jacobian Matrix
42(4)
2.5.1 Transformation of Scalar and Vector Objects and Covariant Vectors
42(2)
2.5.2 Transformation of Basis, Contravariant Vectors, and Jacobian
44(2)
2.6 Examples on Index Notations
46(6)
2.7 Summary
52(1)
2.8 Appendix
53(4)
2.8.1 Divergence Theorem
53(1)
2.8.2 Stokes Theorem
54(3)
Chapter 3 Mechanics of Continua
57(44)
3.1 Coordinate System
57(4)
3.1.1 Lagrangian Coordinate or Material Coordinate System
59(1)
3.1.2 Eulerian Coordinate or Spatial Coordinate System
59(2)
3.2 Motion of a Deformable Body
61(5)
3.2.1 Material Derivatives
62(1)
3.2.1.1 Material Derivative of Displacement Gradient
63(1)
3.2.1.2 Material Derivative of Jacobian
63(1)
3.2.1.3 Material Derivative of Square of an Arc Length
64(1)
3.2.1.4 Material Derivative of Element of an Area
64(1)
3.2.1.5 Material Derivatives of Line () and Surface () Integral of a Scalar Field φ
64(1)
3.2.1.6 Material Derivatives of Surface () Integral of a Vector Field
65(1)
3.2.2 Path Lines and Stream Lines
65(1)
3.3 Deformation and Strain in a Deformable Body
66(4)
3.3.1 Cauchy's and Green's Deformation Tensor
68(1)
3.3.2 Description of Strain in a Deformable body
69(1)
3.3.3 Strain in terms of Displacement
69(1)
3.4 Mass, Momentum, and Energy
70(2)
3.4.1 Mass of a Body
70(1)
3.4.2 Momentum of a Deformable Body
71(1)
3.4.3 Angular Momentum of a Deformable Body
71(1)
3.4.4 Kinetic Energy Stored in a Deformable Body
71(1)
3.5 Fundamental Axiom of Continuum Mechanics
72(2)
3.5.1 Axiom 1: Principle of Conservation of Mass
72(1)
3.5.2 Axiom 2: Principle of Balance of Momentum
73(1)
3.5.3 Axiom 3: Principle of Balance of Angular Momentum
73(1)
3.5.4 Axiom 4: Principle of Conservation of Energy
73(1)
3.6 Internal Stress State in a Deformable Body
74(2)
3.7 External and Internal Load on a Deformable Body
76(1)
3.8 Fundamental Elastodynamic Equation
77(2)
3.9 Thermodynamics of Continua
79(5)
3.9.1 Conservation of Local Energy
79(2)
3.9.2 Conservation of Mechanical Energy (Kinetic, Internal, and Potential Energy)
81(1)
3.9.3 Internal Energy and Strain Energy
82(2)
3.10 Constitutive Law of Continua
84(5)
3.10.1 Materials with One Plane of Symmetry: Monoclinic Materials
87(1)
3.10.2 Materials with Two Planes of Symmetry: Orthotropic Materials
88(1)
3.10.3 Materials with Three Planes of Symmetry and One Plane of Isotropy: Transversely Isotropic Materials
88(1)
3.10.4 Materials with Three Planes and Three Axes of Symmetry: Isotropic Materials
89(1)
3.11 Appendix
89(9)
3.11.1 Important Equations in Cartesian Coordinate System
89(2)
3.11.2 Important Equations in Cylindrical Coordinate System
91(1)
3.11.2.1 Transformation to Cylindrical Coordinate System
91(2)
3.11.2.2 Gradient Operator in Cylindrical Coordinate System
93(1)
3.11.2.3 Strain-Displacement Relation in Cylindrical Coordinate System
94(1)
3.11.2.4 Governing Differential Equations of Motion in Cylindrical Coordinate System
94(1)
3.11.3 Important Equations in Spherical Coordinate System
95(1)
3.11.3.1 Gradient Operator in Spherical Coordinate System
95(1)
3.11.3.2 Strain-Displacement Relation in Spherical Coordinate System
96(1)
3.11.3.3 Governing Differential Equations of Motion in Spherical Coordinate System
96(1)
3.11.4 Fundamental Concept of Classical Mechanics
97(1)
3.12 Summary
98(3)
Chapter 4 Acoustic and Ultrasonic Waves in Elastic Media
101(68)
4.1 Basic Terminologies in Wave Propagation
101(7)
4.1.1 Wave Fronts, Rays, and Plane Waves
101(1)
4.1.2 Phase Wave Velocity
102(1)
4.1.3 Plane Harmonic Wave
103(2)
4.1.4 Wave Groups and Group Wave Velocity
105(1)
4.1.5 Wave Dispersion
106(2)
4.2 Wave Propagation in Fluid Media
108(3)
4.2.1 Pressure Potential in Fluid
109(2)
4.2.2 Generalized Wave Potential in Fluid
111(1)
4.3 Wave Propagation in Bulk Isotropic Solid Media
111(19)
4.3.1 Navier's Equation of Motion
111(2)
4.3.2 Solving Navier's Equation of Motion: Solution of Wave Propagation in Isotropic Solids
113(1)
4.3.2.1 Helmholtz Decomposition
113(1)
4.3.2.2 Navier's Equation of Motion to Helmholtz Equation
114(1)
4.3.2.3 Generalized Wave Potentials in Isotropic Solids
115(1)
4.3.2.4 Longitudinal Waves and Shear Waves in Isotropic Solids
116(2)
4.3.2.5 In Plane and Out of Plane Shear Waves in Isotropic Solids
118(2)
4.3.2.6 Wave Potentials for P, SV, and SH Waves and Their Relation
120(1)
4.3.3 Wave Interactions at the Bulk Isotropic Interfaces
121(1)
4.3.3.1 P-Wave Incident at the Interface
122(5)
4.3.3.2 SH-Wave Incident at the Interface
127(3)
4.4 Wave Propagation in Bulk Anisotropic Solid Media
130(25)
4.4.1 Governing Elastodynamic Equation in Anisotropic Media
135(3)
4.4.2 Wave Modes in all Possible Directions of Wave Propagation in 3D
138(1)
4.4.2.1 Comparison between Isotropic and Anisotropic Slowness Profiles
138(4)
4.4.2.2 Slowness Profiles for Monoclinic Material
142(1)
4.4.2.3 Slowness Profiles for Fully Orthotropic Material
142(5)
4.4.2.4 Slowness Profiles for Transversely Isotropic
147(1)
4.4.3 Wave Interactions at the Bulk Anisotropic Interfaces
147(1)
4.4.3.1 Geometrical Understanding of Reflection and Refraction in Anisotropic Solid
147(8)
4.5 Appendix
155(12)
4.5.1 Energy Flux & Group Velocity
155(2)
4.5.2 Integral Approach to Obtain Governing Elastodynamic Equation based on Classical Mechanics
157(2)
4.5.3 Understanding the Snell's Law in Isotropic and Anisotropic Media
159(1)
4.5.3.1 Snell's Law at Isotropic Material Interface
159(2)
4.5.3.2 Snell's Law at Anisotropic Material Interface
161(4)
4.5.4 Slowness, Group Velocity and Steering Angle
165(2)
4.6 Summary
167(2)
Chapter 5 Wave Propagation in Bounded Structures
169(64)
5.1 Basic Understanding of Guided Waves and its Application in NDE
169(5)
5.2 Guided Waves in Isotropic Plates using Classical Approach
174(31)
5.2.1 Guided SH Wave Modes in Isotropic Plate
174(4)
5.2.2 Guided Rayleigh-Lamb Wave Modes in Isotropic Plate
178(7)
5.2.3 Generalized Guided Wave Modes in Isotropic Plate with Perturbed Geometry
185(1)
5.2.3.1 Motivation
185(4)
5.2.3.2 Generalized Formulation
189(3)
5.2.3.3 Boundary Conditions
192(5)
5.2.3.4 Discussions on Generalized Rayleigh Lamb and SH Modes
197(5)
5.2.4 Exercise: Guided Waves in Isotropic Plate with Experimental NDE Situations
202(3)
5.3 Guided Waves Propagation in Anisotropic Plates
205(16)
5.3.1 Analytical Approach for Single-Layered General Anisotropic Plate
205(4)
5.3.2 Analytical Approach for Multilayered General Anisotropic Plate
209(1)
5.3.3 Semianalytical Approach for Single- and Multilayered Anisotropic Plates
210(3)
5.3.3.1 Hamilton's Principle and the Governing Equation
213(2)
5.3.3.2 Discretization of Plate Thickness
215(1)
5.3.3.3 Element Strain Equation
215(1)
5.3.3.4 Governing Wave Equation
216(2)
5.3.3.5 Eigen Value Problem: Wave Dispersion Solution and Phase Velocity
218(1)
5.3.3.6 Dispersion Behavior
219(1)
5.3.3.7 Group Velocity of Propagating Wave Modes
219(2)
5.4 Guided Wave Propagation in Cylindrical Rods and Pipes
221(8)
5.4.1 Torsional Wave Modes in Cylindrical Wave Guides
228(1)
5.4.2 Exercise: Longitudinal and Flexural Wave Modes in Cylindrical Structures
229(1)
5.4.2.1 Longitudinal Wave
229(1)
5.4.2.2 Flexural Wave
229(1)
5.5 Summary
229(4)
Chapter 6 Overview of Basic Numerical Methods and Parallel Computing
233(36)
6.1 Understanding Error
233(1)
6.2 Error Propagation: Taylor Series
234(5)
6.2.1 Taylor Series Expansion
234(3)
6.2.2 Stability Condition
237(1)
6.2.3 Summary from Error Propagation
238(1)
6.3 Finite Difference Method (FDM)
239(4)
6.3.1 FD Formula with O(Δx2)
241(1)
6.3.2 BD Formula with O(Δx2)
242(1)
6.3.3 CD Formula with O(Δx2)
242(1)
6.3.4 CD Formula with O(Δx4)
242(1)
6.4 Time Integration: Explicit FDM Solution of Differential Equations
243(4)
6.5 Time Integration: Explicit Solution of Multidegrees-of-Freedom System
247(4)
6.5.1 Explicit Solution Algorithm for Multidegrees-of-Freedom System [ 3]
248(1)
6.5.2 Runge-Kutta (RK4) Algorithm for Multidegrees-of-Freedom System
249(2)
6.6 Time Integration: Implicit FDM Solution of Differential Equations
251(6)
6.6.1 Implicit Solution Algorithm (Houbolt Method) [ 3, 4]
252(1)
6.6.2 Implicit Newmark β Method
253(3)
6.6.3 Implicit Wilson θ Method
256(1)
6.7 Velocity Verlet Integration Scheme
257(1)
6.8 Overview of Parallel Computing for CNDE
258(11)
6.8.1 What is Parallel Computing
258(1)
6.8.2 Historical Background of Parallel Computing
259(1)
6.8.3 Serial vs. Parallel Computing for CNDE
260(1)
6.8.4 Methods for Parallel Programs
260(1)
6.8.4.1 Task-Parallelism
261(1)
6.8.4.2 Data-Parallelism
261(1)
6.8.4.3 Simple Example of Parallelization
261(1)
6.8.5 Understanding the Patterns in Parallel Program Structure
262(1)
6.8.6 Types of Parallel Hardware
262(1)
6.8.6.1 Single Instruction, Single Data (SISD)
262(1)
6.8.6.2 Single Instruction, Multiple Data (SIMD)
262(1)
6.8.6.3 Multiple Instructions, Single Data (MISD)
262(1)
6.8.6.4 Multiple Instructions, Multiple Data (MIMD)
263(1)
6.8.7 Type of Parallel Software
263(1)
6.8.7.1 Parallel Programming Languages
263(1)
6.8.7.2 Automatic Parallelization
263(1)
6.8.8 CPU vs GPU Parallel Computing
264(1)
6.8.8.1 CPU Parallel Computing using OpenMP
265(1)
6.8.8.2 GPU Parallel Computing using CUDA
265(4)
Chapter 7 Distributed Point Source Method for CNDE
269(130)
7.1 Basic Philosophy of Distributed Point Source Method (DPSM)
269(7)
7.1.1 DPSM and Other Methods
269(1)
7.1.2 Characteristics of DPSM Sources, Active and Passive
270(4)
7.1.3 Synthesis of Ultrasonic Field by Multiple Point Sources
274(2)
7.2 Modeling Ultrasonic Transducer in a Fluid
276(13)
7.2.1 Elastodynamic Green's Function in Fluid
277(1)
7.2.1.1 Reciprocal and Causal Green's Function from Green's Formula
277(1)
7.2.1.2 Generalized Equation for Green's Function
278(2)
7.2.1.3 Solution of Green's Function with Spherical Wave Front, Huygens' Principle
280(2)
7.2.2 DPSM in Lieu of Surface Integral Technique
282(2)
7.2.2.1 Computing Pressure and Velocity Field: Mathematical Expressions
284(2)
7.2.2.2 Computing Pressure and Velocity Field: Matrix Formulation
286(3)
7.2.2.3 Case Study: Modeling Pressure Field in Front of a Transducer
289(1)
7.3 Modeling Ultrasonic Wave Field in Isotropic Solids
289(17)
7.3.1 Elastodynamic Displacement and Stress Green's Functions in Isotropic Solids
290(1)
7.3.1.1 Elemental Point Source in Solid
290(1)
7.3.1.2 Navier's Equation of Motion with Body Force
291(1)
7.3.1.3 Point Source Excitation in a Solid
292(2)
7.3.1.4 Formulation of Displacement Green's Function
294(1)
7.3.1.5 Formulation of Stress Green's Function
295(1)
7.3.1.6 Detailed Expressions for Displacement and Stress Green's Functions
296(1)
7.3.1.7 Differentiation of Displacement Green's Function with respect to x1, x2, x3
297(4)
7.3.2 Computation of Displacements and Stresses in the Solid for Multiple Point Sources
301(1)
7.3.2.1 Displacement and Stresses at a Single Point
301(2)
7.3.2.2 Displacement and Stresses at a Multiple Points: Matrix Formulation
303(2)
7.3.2.3 Matrix Representation of Fluid Displacements
305(1)
7.4 CNDE Case Studies for Isotropic Solids using DPSM
306(18)
7.4.1 Computational Wave field Modeling at Fluid-Solid Interface [ 4]
306(1)
7.4.1.1 NDE Problem Statement
306(1)
7.4.1.2 Matrix formulation
307(1)
7.4.1.3 Boundary Conditions
308(1)
7.4.1.4 Solution
308(1)
7.4.1.5 Numerical Results Near Fluid Solid Interface
309(4)
7.4.2 Computational Wave Field Modeling in a Solid Plate Immersed in Fluid [ 3]
313(1)
7.4.2.1 NDE Problem Statement
313(2)
7.4.2.2 Matrix Formulation and Boundary Conditions
315(2)
7.4.2.3 Solution
317(1)
7.4.2.4 Numerical Results: Ultrasonic Fields in Solid Plate
317(3)
7.4.3 Computational Wave Field Modeling in a Solid Plate with Inclusion or Crack [ 16]
320(1)
7.4.3.1 Problem Geometry
320(2)
7.4.3.2 Matrix Formulation: Boundary and Continuity Conditions
322(1)
7.4.3.3 Solution
323(1)
7.4.3.4 Numerical Results: Ultrasonic Fields in Solid Plate with Horizontal Crack
323(1)
7.5 Modeling Ultrasonic Field in Anisotropic Solids (e.g., Composites)
324(17)
7.5.1 Elastodynamic Displacement and Stress Green's Function in General Anisotropic Solids
325(1)
7.5.2 Exact Mathematical Expression for the Green's Function
326(1)
7.5.2.1 Radon Transform Approach: Solution of Elastodynamic Green's Function
327(7)
7.5.2.2 Fourier Transform Approach: Solution of Elastodynamic Green's Function
334(3)
7.5.2.3 Comparison of Green's Function: Fourier vs. Radon Transform
337(3)
7.5.2.4 Relation between Radon Transform and Fourier Transform
340(1)
7.6 CNDE Case Studies for Anisotropic Solids using DPSM
341(16)
7.6.1 Numerical Computation of Wave Field in Anisotropic Half-space
342(2)
7.6.1.1 Verification of Boundary Condition and Convergence
344(1)
7.6.1.2 Computed Wave Field in Anisotropic Solids
345(2)
7.6.2 Numerical Computation of Wave Field in Anisotropic Plate
347(4)
7.6.2.1 Computed Wave Field in Anisotropic Plate
351(6)
7.7 Enhancing the Computational Efficiency of DPSM for Anisotropic Solids
357(4)
7.7.1 Symmetry Informed Sequential Mapping of Anisotropic Green's function (SISMAG)
357(1)
7.7.1.1 SISMAG Step 1
357(2)
7.7.1.2 SISMAG Step 2
359(1)
7.7.1.3 SISMAG Step 3
360(1)
7.8 Computation of Wave Fields in Multilayered Anisotropic Solids
361(7)
7.8.1 Wave Field Modeling in Pristine 4-ply Composite Plate
365(1)
7.8.2 Wave Field Modeling in Degraded 4-ply Composite Plate
365(1)
7.8.2.1 Material Degradation
365(1)
7.8.2.2 Wave Field in 4 ply Composite Plate with 0° and 90° Degraded Plies
366(2)
7.9 Computation of Wave Fields in the Presence of Delamination in Composite
368(10)
7.9.1 Delamination in DPSM
368(1)
7.9.2 Incorporation of Delamination Formulation in DPSM for CNDE
369(5)
7.9.3 Wave Field Modeling of (0/0) 2-ply Plate with Delamination
374(2)
7.9.4 Wave Field Modeling of (90/0) 2-ply Plate with Delami nation
376(2)
7.10 Implementation of DPSM in Computer Code for Automation
378(9)
7.10.1 Automation for Pristine and Degraded N-layered Media
378(1)
7.10.1.1 Digitization of Layer Stacking Sequence
378(1)
7.10.1.2 Calculation of Christoffel Solution based on n Unique Layers
379(1)
7.10.1.3 Calculation of Solid Components based on n Unique Layers
379(1)
7.10.1.4 Automated DPSM Matrix based on Digitized Stacking Sequence
379(2)
7.10.2 Automation for N-layered Plate with Delamination
381(1)
7.10.2.1 Delamination Sequence
381(1)
7.10.2.2 Calculation of Solid Components based on n Unique Layers
382(1)
7.10.2.3 Automated Population of DPSM Matrix based on Delamination Sequence
382(5)
7.11 Implementation of Parallel Computing for DPSM
387(2)
7.12 Appendix
389(10)
7.12.1 Effect of microscale Voids on Cijkl matrix
389(2)
7.12.2 Distribution of Point Sources with Convergence
391(1)
7.12.3 Flow Chart for the DPSM Algorithm
392(7)
Chapter 8 Elastodynamic Finite Integration Technique
399(32)
8.1 Introduction
399(2)
8.1.1 Finite Integration Technique
400(1)
8.2 Acoustic Finite Integration Technique
401(3)
8.2.1 Mathematical Equations: AFIT
401(2)
8.2.2 Step Size and Stability Conditions
403(1)
8.2.3 Initial Conditions and Boundary Conditions
403(1)
8.3 Elastodynamic Finite Integration Technique
404(13)
8.3.1 Mathematical Equations: Isotropic EFIT
405(2)
8.3.2 Mathematical Equations: Anisotropic EFIT
407(3)
8.3.3 Grid Sizing and Stability Requirements
410(1)
8.3.4 Boundary Conditions
410(3)
8.3.5 Initial Conditions for Ultrasound Excitation
413(1)
8.3.5.1 Normal Incidence Example
413(1)
8.3.5.2 Shear Excitation Example
414(1)
8.3.5.3 Angled Incidence Example
415(1)
8.3.6 Computational Implementation
415(2)
8.4 Examples
417(10)
8.4.1 Bulk Wave Angled Incidence with Arbitrary Backwall
417(3)
8.4.2 Lamb Waves in an Aluminum Plate
420(1)
8.4.3 Guided Waves in a Cross-ply Composite Plate
420(7)
8.5 Summary
427(4)
Chapter 9 Local Interaction Simulation Approach
431(22)
9.1 Introduction
431(1)
9.2 Mathematical Equations: LISA
432(6)
9.3 Grid Sizing and Stability Requirements
438(1)
9.4 Boundary Conditions
438(1)
9.5 Initial Conditions for Ultrasound Excitation
439(3)
9.5.1 Displacement Excitation
440(1)
9.5.2 Electromechanical Model of Actuation
440(2)
9.6 Computational Implementation
442(2)
9.7 Examples
444(5)
9.7.1 Guided Waves in an Isotropic Plate
444(1)
9.7.2 Guided Waves in Composite Plates
444(4)
9.7.3 Guided Waves in Rail Track
448(1)
9.8 Summary
449(4)
Chapter 10 Spectral Element Method for CNDE
453(58)
10.1 Introduction
453(3)
10.1.1 A Comparative Analysis of FEM and SEM
454(2)
10.1.2 Classification of SEM
456(1)
10.2 Mathematical Formulation of SEM
456(20)
10.2.1 Application of Hamiltonian Principle
457(6)
10.2.2 Application of Weighted Residual Method
463(8)
10.2.3 Spectral Shape Function
471(2)
10.2.3.1 Lobatto Polynomials
473(1)
10.2.3.2 Laguerre Polynomials
473(1)
10.2.3.3 Chebyshev Polynomials
474(1)
10.2.4 Lobatto Integration Quadrature
474(2)
10.7 Modeling Piezoelectric Effect using SEM
476(2)
10.8 Implementation of SEM in CNDE Computation
478(16)
10.8.1 Setting up Initial Parameters
479(1)
10.8.2 Discretization of the Problem Domain
479(2)
10.8.3 Determination Global Mass and Stiffness Matrix
481(1)
10.8.3.1 Local Stiffness Matrix
481(1)
10.8.3.2 Material Properties
482(1)
10.8.3.3 Shape Functions
482(1)
10.8.3.4 First Derivate of the Shape Functions
483(1)
10.8.3.5 Weighting Function
483(1)
10.8.3.6 Coordinate Transformation
484(2)
10.8.3.7 Assembly of Local Stiffness Matrix into a Global Stiffness Matrix
486(6)
10.8.4 Necessary Variables and Flowchart
492(2)
10.9 CNDE Case Studies at Low Frequencies (<~1 MHz)
494(3)
10.9.1 Propagation of Elastic Waves in an Angle Bar [ 6]
494(2)
10.9.2 Propagation of Elastic Waves in a Half-pipe, Aluminum Shell Structure [ 6]
496(1)
10.10 CNDE Case Studies at High Frequencies (>~1 MHz)
497(7)
10.10.1 Pulse-echo Simulation at 1 MHz
498(5)
10.10.2 Pulse-echo Simulation at 5 MHz
503(1)
10.11 Experimental Validation
504(2)
10.12 Appendix
506(3)
10.12.1 Electrical Boundary Conditions for Piezoelectric Crystal
506(1)
10.12.1.1 Condition 1: Piezoelectric Sensor in Closed Circuit
507(1)
10.12.1.2 Condition 2: Piezoelectric Sensor in an Open Circuit
507(1)
10.12.1.3 Condition 3: Actuator
508(1)
10.13 Summary
509(2)
Chapter 11 Perielastodynamic Simulation Method for CNDE
511(40)
11.1 Introduction
511(2)
11.2 Fundamental of Peridynamic Approach
513(6)
11.2.1 Fundamentals of Bond-based Peridynamic Theory
514(2)
11.2.2 Peridynamic Constitutive Model
516(1)
11.2.3 Bond Constant Estimation in Isotropic Material
517(2)
11.3 Fundamentals of Perielastodynamic Simulations
519(2)
11.3.1 Perielastodynamic Spatial and Temporal Discretization
519(1)
11.3.2 Numerical Time Integration
520(1)
11.4 CNDE Case Study: Modeling Guided Waves in Isotropic Plate
521(12)
11.4.1 Problem Statement
521(2)
11.4.2 Dispersion Behavior and Wave Tuning
523(2)
11.4.3 Discretization of Perielastodynamic Problem Domain
525(1)
11.4.4 Numerical Computation and Results
526(1)
11.4.4.1 Displacement Filed Presentation
526(1)
11.4.4.2 Vector Field Representation of the Guided Wave Modes
527(4)
11.4.4.3 Fourier Analysis of the Sensor Signals
531(2)
11.5 CNDE Case Study: Wave-Damage Interaction in Isotropic Plate
533(14)
11.5.1 CNDE of a Plate with Hole: Comment on the Sensor Placement
533(3)
11.5.2 CNDE of a Plate with Crack with Experimental Validation
536(5)
11.5.2.1 Experimental Design for the Validation of Perielastodynamic
541(1)
11.5.2.2 Other Computational Method for Verification of Perielastodynamic
541(2)
11.5.2.3 Verification and Validation of Perielastodynamic Simulation
543(2)
11.5.2.4 Wave Field Computation with Cracks and Comparisons
545(2)
11.6 Summary
547(4)
Index 551
Sourav Banerjee, Cara A.C. Leckey
Daugiau apie elektronines knygas Daugiau apie elektronines knygas
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