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E-raamat: Introduction to Integrative Engineering: A Computational Approach to Biomedical Problems

(Clemson University, South Carolina, USA)
  • Formaat: 446 pages
  • Ilmumisaeg: 03-Mar-2017
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781315388458
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Introduction to Integrative Engineering: A Computational Approach to Biomedical ProblemsSuurem pilt
  • Formaat: 446 pages
  • Ilmumisaeg: 03-Mar-2017
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781315388458
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This textbook is designed for an introductory course at undergraduate and graduate levels for bioengineering students. It provides a systematic way of examining bioengineering problems in a multidisciplinary computational approach. The book introduces basic concepts of multidiscipline-based computational modeling methods, provides detailed step-by-step techniques to build a model with consideration of underlying multiphysics, and discusses many important aspects of a modeling approach including results interpretation, validation, and assessment.

Preface xv
Acknowledgments xix
Author xxi
I Readying the Integrative Mindset 1(12)
1 From Compartmentalized Disciplines to Transdiscipline
3(10)
1.1 Reductive Specialization for the Twentieth Century
3(1)
1.2 Integrative Problem Solving for the Twenty-First Century
4(1)
1.3 Jack of All Trades, Master of None?
5(1)
1.4 Venturing Out of Our Comfort Zones
6(1)
1.5 Difference in Learning That and Learning How
7(1)
1.6 Connecting the Dots
8(1)
1.7 Borrowing Zen's Way of Seeing the World with the Assistance of Computational Modeling
8(1)
1.8 Seeking Convergence beyond Engineering
9(1)
1.9 Exercises
10(1)
Recommended Readings
11(2)
II Cracking Open the Blackbox of Computational Modeling 13(314)
2 Engineering Problems and Partial Differential Equations
15(24)
2.1 Brief Review of Differential Equations
15(4)
2.1.1 Ordinary versus partial differential equations
15(1)
2.1.2 Order of differential equations
16(1)
2.1.3 Linear versus nonlinear differential equations
16(1)
2.1.4 Constant versus nonconstant coefficients
16(1)
2.1.5 Dimension of differential equations
17(1)
2.1.6 Time-dependent and -independent differential equations
17(1)
2.1.7 Initial and boundary conditions
18(1)
2.2 Connecting PDEs to the Engineering World
19(8)
2.2.1 Some differential notations
19(5)
2.2.1.1 V operator
19(1)
2.2.1.2 Gradient of a field
20(1)
2.2.1.3 Dot product and divergence of a field
21(1)
2.2.1.4 Cross product and curl of a field
22(2)
2.2.1.5 Laplacian of a field
24(1)
2.2.2 Common engineering problems and their governing PDEs
24(3)
2.3 Brief Review of Matrix Algebra
27(6)
2.3.1 Row and column vectors
27(1)
2.3.2 Addition and subtraction
27(1)
2.3.3 Multiplication by a scalar
28(1)
2.3.4 Matrix-matrix multiplication
28(1)
2.3.5 Transposition
29(1)
2.3.6 Differentiation and integration
29(1)
2.3.7 Square matrix
29(1)
2.3.8 Diagonal matrix
30(1)
2.3.9 Identity matrix
30(1)
2.3.10 Symmetric matrix
30(1)
2.3.11 Determinant
30(1)
2.3.12 Matrix inversion
31(1)
2.3.13 Matrix partition
31(1)
2.3.14 Matrix calculation using MATLAB
31(2)
2.3.15 Making plots using MATLAB
33(1)
2.4 Exercises
33(4)
Recommended Readings
37(2)
3 Where Do Differential Equations Come From?
39(12)
3.1 PDE for a Hanging Bar
39(2)
3.2 PDE for a Vibrating String
41(2)
3.3 PDE for Heat Transfer
43(1)
3.4 PDE for Mass Diffusion
44(2)
3.5 PDE for Beam Structures
46(3)
3.6 Commonality in PDEs for Different Problems
49(1)
3.7 Exercises
49(1)
Recommended Readings
50(1)
4 Approximate Solutions to Differential Equations
51(12)
4.1 Approximate Solutions
51(2)
4.2 Approximate Solutions by Weighted Integral
53(1)
4.3 How Good Are Approximate Solutions?
54(3)
4.4 Influence of Weight Functions
57(2)
4.5 Exercises
59(2)
Recommended Readings
61(2)
5 Discretization of Physical Domains
63(56)
5.1 Dividing Physical Domains into Small Elements
63(2)
5.2 Nodal Connectivity and Degrees of Freedom
65(2)
5.3 Linking Nodal DOF to Polynomial Functions
67(4)
5.3.1 1D elements
67(2)
5.3.2 2D elements
69(2)
5.4 Choice of Polynomial Terms
71(4)
5.4.1 Pascal triangle
72(1)
5.4.2 Pascal pyramid and 3D elements
73(2)
5.5 Shape Functions
75(6)
5.6 Lagrange Interpolation Formulas
81(23)
5.6.1 Lagrange formula for 1D elements
82(2)
5.6.2 Lagrange formula for 2D quadrilateral elements
84(3)
5.6.3 Shape functions for serendipity elements
87(3)
5.6.4 Lagrange formulas for 2D triangular elements
90(7)
5.6.4.1 Area coordinates for triangles
90(3)
5.6.4.2 Lagrange formulas for 2D triangular elements
93(4)
5.6.5 Lagrange formula for 3D hexahedral elements
97(2)
5.6.6 Lagrange formulas for 3D tetrahedral elements
99(5)
5.6.6.1 Volume coordinates for tetrahedrons
99(2)
5.6.6.2 Lagrange formulas for 3D tetrahedral elements
101(3)
5.7 Hermite Interpolation
104(6)
5.7.1 Hermite interpolation formulas
104(2)
5.7.2 Shape functions for beam elements
106(4)
5.7.3 Plate and shell elements
110(1)
5.8 Interpolation of Field Quantities in a Matrix Form
110(3)
5.9 Exercises
113(4)
Recommended Readings
117(2)
6 Solving Differential Equations Computationally
119(44)
6.1 Differential Equations in Strong and Weak Forms
120(1)
6.2 FEM Formulation Using the Galerkin Method
121(5)
6.2.1 Elementary [ Ke] matrix
122(2)
6.2.2 Volumetric and point loads or constraints
124(2)
6.3 Single-Element Structure
126(1)
6.4 From Elementary to Global through Assembly
127(2)
6.4.1 Global [ K] matrix
128(1)
6.5 Bar Elements for 1D Problems
129(6)
6.6 Bar Elements for 2D and 3D Truss Structures
135(12)
6.6.1 2D truss structures
135(6)
6.6.2 3D truss structures
141(6)
6.7 FEM Formulation for Beams
147(6)
6.7.1 Weak-form PDE for beams
147(1)
6.7.2 FEM formulation
148(5)
6.8 The Essence of FEM
153(1)
6.9 Exercises
154(8)
Recommended Readings
162(1)
7 Scalar Field Problems in Higher Dimensions
163(18)
7.1 FEM Formulation for 2D Scalar Field Problems
163(6)
7.1.1 FEM formulation
163(3)
7.1.2 Elementary [ Ke] matrix
166(3)
7.2 Types of 2D Scalar Field Problems
169(1)
7.3 FEM Formulation for 3D Scalar Field Problems
170(6)
7.3.1 FEM formulation
170(2)
7.3.2 Elementary [ Ke] matrix
172(4)
7.4 Types of 3D Scalar Field Problems
176(1)
7.5 Exercises
176(3)
Recommended Readings
179(2)
8 Vector Field Problems in Higher Dimensions
181(24)
8.1 3D Solid Mechanics Problems
181(12)
8.1.1 Free-body diagram and PDEs of equilibrium
181(2)
8.1.2 Weighted integral of residual
183(4)
8.1.3 FEM formulation
187(2)
8.1.4 Elementary [ Ke] matrix for solid mechanics problems
189(4)
8.2 2D Solid Mechanics Problems
193(8)
8.2.1 Plane stress situation
193(1)
8.2.2 Plane strain situation
194(2)
8.2.3 FEM formulation for 2D solid mechanics
196(5)
8.3 Exercises
201(3)
Recommended Readings
204(1)
9 Axisymmetric Scalar and Vector Field Problems
205(16)
9.1 Axisymmetric Scalar Field Problems
205(6)
9.1.1 PDE in cylindrical coordinates
205(1)
9.1.2 Axisymmetry and FEM formulation
206(5)
9.2 Axisymmetric Vector Field Problems
211(7)
9.2.1 PDEs of equilibrium in cylindrical coordinates
211(3)
9.2.2 FEM formulation for axisymmetric solid mechanics
214(4)
9.3 Exercises
218(2)
Recommended Readings
220(1)
10 Isoparametric Elements
221(48)
10.1 Isoparametric Elements for Slender Structures
221(7)
10.1.1 Shape and mapping functions for bar elements
221(3)
10.1.1.1 The 2-node isoparametric bar element
221(2)
10.1.1.2 The 3-node isoparametric bar element
223(1)
10.1.1.3 ne-Node isoparametric bar element
223(1)
10.1.2 Elementary [ Ke] matrix for bar elements
224(2)
10.1.3 Shape and mapping functions for beam elements
226(1)
10.1.4 Elementary [ Ke] matrix for beam elements
227(1)
10.2 Isoparametric Elements for 2D Structures
228(19)
10.2.1 Shape and mapping functions
229(2)
10.2.1.1 The 4-node isoparametric square element
229(1)
10.2.1.2 ne-Node isoparametric square element
230(1)
10.2.1.3 The 3-node isoparametric triangular element
230(1)
10.2.1.4 ne-Node isoparametric triangular element
231(1)
10.2.2 Elementary [ Ke] matrix for scalar field problems
231(7)
10.2.2.1 The 4-node quadrilateral elements
233(1)
10.2.2.2 The 3-node isoparametric triangular elements
233(3)
10.2.2.3 Axisymmetric situation
236(2)
10.2.3 Elementary [ Ke] matrix for vector field problems
238(9)
10.2.3.1 Axisymmetric situation
243(4)
10.3 Isoparametric Elements for 3D Structures
247(16)
10.3.1 Shape and mapping functions
248(2)
10.3.1.1 The 8-node isoparametric hexahedral element
248(1)
10.3.1.2 ne-Node isoparametric hexahedral element
249(1)
10.3.1.3 The 4-node isoparametric tetrahedral element
249(1)
10.3.1.4 ne-Node isoparametric tetrahedral element
250(1)
10.3.2 Elementary [ Ke] matrix for scalar field problems
250(6)
10.3.3 Elementary [ Ke] matrix for vector field problems
256(7)
10.4 Exercises
263(4)
Recommended Readings
267(2)
11 Gauss Quadrature and Numerical Integration
269(28)
11.1 Gauss Quadrature
270(5)
11.1.1 A 1-point Gauss quadrature
270(1)
11.1.2 A 2-point Gauss quadrature
271(1)
11.1.3 A 3-point Gauss quadrature
272(3)
11.1.4 Locations and weights of Gauss points
275(1)
11.2 Gauss Quadrature for 2D Quadrilateral Elements
275(5)
11.2.1 A 2-point Gauss quadrature
276(1)
11.2.2 A 3-point Gauss quadrature
277(3)
11.3 Gauss Quadrature for 2D Triangular Elements
280(5)
11.3.1 Locations and weights of Gauss points
281(2)
11.3.2 Integration in area coordinates
283(2)
11.4 Gauss Quadrature for 3D Hexahedral Elements
285(1)
11.5 Gauss Quadrature for 3D Tetrahedral Elements
286(3)
11.5.1 Integration in volume coordinates
287(2)
11.6 Exercises
289(6)
Recommended Readings
295(2)
12 Dealing with Generalized PDEs
297(16)
12.1 A General Form PDE and Its Matrix Equation
297(7)
12.1.1 Elementary mass matrix: consistent and lumped
298(4)
12.1.2 Elementary damping matrix
302(1)
12.1.3 Elementary absorption matrix
303(1)
12.1.4 Elementary convection matrix
303(1)
12.2 Solving the General Matrix Equation
304(1)
12.3 Eigenvalues, Eigenvectors, and Free Vibration
305(5)
12.3.1 Eigenvalues and eigenvectors
305(1)
12.3.2 Free vibration
306(4)
12.4 Exercises
310(2)
Recommended Readings
312(1)
13 Errors in FEM Results
313(14)
13.1 Modeling Errors
314(1)
13.1.1 Domain approximation error
314(1)
13.1.2 Field variable approximation error
314(1)
13.1.3 Quadrature and arithmetic error
315(1)
13.2 Convergence of FEM Solutions
315(9)
13.2.1 Effect of mesh refinement: h-convergence
319(3)
13.2.2 Effect of element discretization order: p-convergence
322(1)
13.2.3 Effect of quadrature points
323(1)
13.3 Exercises
324(2)
Recommended Reading
326(1)
III Developing Hands-On Modeling Skills 327(60)
14 A Quick Tour of the COMSOL Modeling Environment
329(22)
14.1 COMSOL Starting Screen
330(1)
14.2 Making Initial Selections Step-By-Step
330(3)
14.2.1 Selecting spacial dimension
330(2)
14.2.2 Selecting proper physics modules
332(1)
14.2.3 Selecting a proper type of study
332(1)
14.3 Getting Familiar with the Modeling Environment
333(4)
14.3.1 Model Builder window
334(1)
14.3.2 Settings window
334(3)
14.3.3 Graphics window
337(1)
14.4 A Practical Sense of Building Proper Models
337(2)
14.5 Modeling Example: Tuning the Sound of Music
339(8)
14.5.1 Tuning a string by adjusting string tension
340(5)
14.5.2 Changing pitches using strings of different sizes
345(1)
14.5.3 Taking advantage of COMSOL tutorials
346(1)
14.6 Taking Advantage of COMSOL's Geometric Parameterization Capability
347(4)
15 A Glimpse of the ABAQUS and ANSYS User Interfaces
351(10)
15.1 ABAQUS Modeling Environment
351(3)
15.1.1 Model tree in ABAQUS
351(2)
15.1.2 Module in ABAQUS
353(1)
15.2 ANSYS Modeling Environment
354(4)
15.2.1 Main Menu in ANSYS
355(3)
15.3 Practice, Practice, Practice
358(3)
16 Dealing with Problems of Biomedical and Regulatory Interest
361(26)
16.1 Computational Bioengineering'
361(3)
16.1.1 Problems of musculoskeletal concerns
362(1)
16.1.2 Problems of circulatory concerns
363(1)
16.1.3 Problems of cancer development and treatment
363(1)
16.1.4 Other types of bioengineering problems
363(1)
16.2 Some Practical Issues in Image-Based Modeling
364(5)
16.2.1 image scanning and segmentation
365(1)
16.2.2 Importing and meshing the CAD geometry
366(1)
16.2.3 Further mechanical analysis
367(2)
16.3 Computational Modeling for Enhancing the Test Standards and Regulatory Processes
369(9)
16.3.1 Testing the femoral stem of a hip implant
369(1)
16.3.2 Setting up the round-robin test
370(2)
16.3.3 Testing the femoral component of a knee implant
372(2)
16.3.4 Testing of a spinal implant assembly
374(2)
16.3.5 Calling for clinically relevant and predictive modeling
376(2)
16.4 Examining the Transient Hypoxia Condition in Cornea due to Contact Lens Wear
378(4)
16.5 Examining the pH Drop in a Titanium Crevice due to Corrosion
382(4)
16.6 What to Expect in Future Editions
386(1)
IV Useful Knowledge 387(26)
A Mechanics of Materials
389(14)
A.1 Terms: Linear, Nonlinear, Elastic, and Plastic
389(1)
A.2 Describing Materials' Various Properties
389(2)
A.3 Linear, Nonlinear, Elastic, and Plastic Behavior in a Single Material
391(1)
A.4 Example of Nonlinear Elastic Behavior
392(2)
A.5 Pseudoelastic, Hyperelastic, and Viscoelastic
394(1)
A.6 Loading Modes, Stress States, and Mohr's Circle
394(4)
A.7 von Mises Stress or Principal Stress?
398(2)
A.8 Trajectories of Tension and Compression Lines
400(3)
B Useful Mathematic Knowledge
403(10)
B.1 Dot Product
403(1)
B.2 Cross Product
404(2)
B.3 Taylor and Maclaurin Series
406(1)
B.4 Proof of dA = det[ J]Adri
406(1)
B.5 Proof of dV = det[ J]AdriA
407(2)
B.6 Lagrange Multipliers
409(4)
Index 413
Guigen Zhang, Ph.D., is Professor of Bioengineering and Professor of Electri- cal and Computer Engineering at Clemson University. He is also the Executive Director of the Institute for Biological Interfaces of Engineering, a research and education/training institute designated by the South Carolina Commission on Higher Education. Professor Zhang is a fellow of the American Institute for Medical and Biological Engineering (AIMBE). He has published extensively in the areas of biosensors, biomechanics, biomaterials and computational modeling. Over the years, his research has been funded by diverse funding sources ranging from federal agencies such as National Institutes for Health and National Science Foundation, to private foundations like the Bill and Melinda Gates Foundation, to venture groups and state-level startup funds, as well as industries in the health-care, semiconductors, and data-storage sectors. Professor Zhang holds numerous patents in nanotechnology-enhanced structures and biosensors. Aside from his services on the editorial boards of numerous scientific journals, Pro- fessor Zhang is also active in serving leadership roles in professional societies. He is currently the Executive Editor of the Biomaterials Forum of the Society For Biomaterials (SFB), and President of the Institute of Biological Engineer- ing (IBE), a professional society that supports the community of scientists and engineers who are at the forefront of creating new linkages between biology and engineering and seeking new opportunities through Biology-Inspired engineering.
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