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A textbook intended to be used in senior undergraduate course on engineering, physics, computer science, or other scientific field. Introduces techniques by which engineers and scientists can obtain numerical results to difficult problems that cannot be solved by simple computational formulas. One section is for students who will need some computational ability but will not necessarily have to solve physical equations; another introduces the basic computational tools of physics; a third contains advanced topics of possible interest to researchers in wave propagation, deformable-body dynamics, compressible fluid flow, and biomechanics. The CD-ROM contains the FORTRAN code used to solve the example problems. Annotation c. by Book News, Inc., Portland, Or.

This book is an introduction to computational mechanics, proceeding from basic computational tools to advanced computational procedures and applications. Emphasis is placed on the numerical techniques and how they form the bases for algorithms. Numerous worked examples in structural mechanics, heat transfer, fluid flow, and biomechanics are given with the numerical codes to illustrate how the methods are applied. A concluding section addresses advanced applications in such areas as finite volume methods and biomechanics.
Preface xiii
Acknowledgment xv
PART 1 BASIC COMPUTATIONAL TOOLS
Linear Systems and Matrices
3(24)
Nomenclature
3(1)
Introduction
4(1)
Matrix Formalities
4(4)
Index Notation
4(2)
Matrix Notation
6(2)
Condition of Matrix Systems
8(2)
Techniques for Matrix Solution
10(11)
Direct Methods
10(8)
Iterative Methods
18(3)
Mixed Boundary Conditions
21(1)
Conclusion
22(5)
Further Reading
22(1)
Problems
22(5)
Nonlinear Systems
27(20)
Nomenclature
27(1)
Introduction
28(1)
Scalar Equations
28(10)
Method of Successive Approximations
28(3)
Bisection Method
31(2)
Method of False Position (regula falsi Method)
33(4)
Locally Convergent Methods
37(1)
Matrix Equations
38(3)
Matrix Newton-Raphson Method
38(2)
Approximate Jacobian Formulation
40(1)
Conclusion
41(6)
Reference
42(1)
Further Reading
42(1)
Problems
42(5)
Approximation, Interpolation, and Curve Fitting
47(30)
Nomenclature
47(1)
Introduction
47(1)
Polynomial Curve Fit
48(4)
Chebyshev Polynomial Fit
52(4)
Least-Squares Polynomial Fit
56(4)
Least-Squares Chebyshev Polynomial Fit
60(1)
Fourier Series of Discrete Systems
61(3)
Spline Functions
64(8)
Piecewise Linear Splines
64(2)
Piecewise Cubic Splines
66(6)
Conclusion
72(5)
Further Reading
73(1)
Problems
74(3)
Numerical Integration
77(18)
Nomenclature
77(1)
Introduction
77(1)
Simple Integration Formulas
78(4)
Integration of Cubic Splines
82(1)
Gauss-Legendre Integration
83(4)
Comparison of Methodologies
87(1)
Conclusion
88(7)
Further Reading
88(1)
Problems
89(6)
PART 2 COMPUTATIONAL TOOLS FOR APPLICATIONS
Finite-Difference Techniques
95(14)
Nomenclature
95(1)
Introduction
95(1)
Simple Modeling Formulas
96(3)
Error and Mesh Considerations
99(2)
Backward Differences
101(5)
Forward Differences
106(1)
Central Differences
106(1)
Conclusion
107(2)
Further Reading
108(1)
Problems
108(1)
Initial-Value Problems
109(22)
Nomenclature
109(1)
Introduction
109(1)
Initial Increments with a Taylor Series
110(2)
Taylor Series Method for Implicit Systems
112(1)
Runge--Kutta Method
112(4)
Euler Forward-Integration Method
116(3)
Modified Euler Method
119(3)
Optimum Step-Size Considerations
122(1)
Milne Method
123(2)
Conclusion
125(6)
Further Reading
126(1)
Problems
126(5)
Ordinary Differential Equations
131(14)
Nomenclature
131(1)
Introduction
131(1)
Iterative Solutions of Boundary-Value Problems
132(1)
Matrix Solutions of Linear Boundary-Value Problems
133(5)
Example in Heat Transfer
133(3)
Example in Structural Mechanics
136(2)
Matrix Solutions of Nonlinear Boundary-Value Problems
138(4)
Conclusion
142(3)
Further Reading
142(1)
Problems
142(3)
Partial Differential Equations
145(20)
Nomenclature
145(1)
Introduction
146(1)
Classification of Partial Differential Equations
146(1)
Modeling of Partial Differential Equations
147(1)
Example in Heat Conduction
148(5)
Example in Structural Mechanics
153(7)
Conclusion
160(5)
Further Reading
160(1)
Problems
160(5)
Energy Methods and Minimization
165(24)
Nomenclature
165(1)
Introduction
166(1)
Calculus of Variations
167(3)
Higher-Order Functionals
170(2)
Examples in Structural Analysis
172(3)
Rayleigh-Ritz Method
175(2)
Heat Transfer Formulations
177(4)
Conclusion
181(8)
Further Reading
182(1)
Problems
182(7)
Finite-Element Methods
189(26)
Nomenclature
189(1)
Introduction
189(1)
Philosophy of Element Selection
190(1)
Structural Finite-Element Analysis
191(9)
Other Structural Finite-Element Method Approximations
200(3)
Finite-Element Structural Example
203(2)
Thermal Finite-Element Analysis
205(4)
Example in Heat Transfer
209(1)
Conclusion
210(5)
References
210(1)
Further Reading
210(1)
Problems
211(4)
Dynamic Methods in Applied Mechanics
215(20)
Nomenclature
215(1)
Introduction
215(1)
Lumped-Parameter Systems
216(6)
Modal Extraction by Lumped Parameters
222(1)
Modal Extraction by Finite Elements
223(3)
Dynamic Analysis by Finite-Element Methods
226(2)
Conclusion
228(7)
References
229(1)
Further Reading
229(1)
Problems
229(6)
PART 3 ADVANCED COMPUTATIONAL TOOLS
Method of Characteristics
235(20)
Nomenclature
235(1)
Introduction
236(1)
Classification of Partial Differential Equations
236(3)
Investigations in Engineering
239(1)
Applications in Structural Analysis
240(8)
Continuous Functions
240(4)
Discontinuities in the Variables
244(4)
Application in Fluid Mechanics
248(2)
Conclusion
250(5)
References
250(1)
Further Reading
250(1)
Problems
250(5)
Finite-Volume Methods
255(18)
Nomenclature
255(1)
Introduction
256(1)
Direct Analysis
257(7)
Dynamic Analysis of a Spherical Cavity
260(2)
Dynamic Analysis of a Timoshenko Beam
262(2)
Control Volume Analysis in Fluid Flow
264(4)
Conclusion
268(5)
References
268(1)
Further Reading
269(1)
Problems
269(4)
Biomechanical Applications
273(20)
Introduction
273(1)
Analysis of Orthodontic Appliances
273(3)
Prediction of Tooth Movement
276(12)
Orthopedic Applications of the Finite-Element Method
288(2)
Conclusion
290(3)
References
291(2)
Index 293
Koenig, Herbert