Ames Nonlinear Problems of Engineering

1. Auflage 2014
ISBN: 978-1-4832-2581-4
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 266 Seiten, Web PDF

Nonlinear Problems of Engineering reviews certain nonlinear problems of engineering. This book provides a discussion of nonlinear problems that occur in four areas, namely, mathematical methods, fluid mechanics, mechanics of solids, and transport phenomena. Organized into 15 chapters, this book begins with an overview of some of the fundamental ideas of two mathematical theories, namely, invariant imbedding and dynamic programming. This text then explores nonlinear integral equations, which have long occupied a prominent place in mathematical analysis. Other chapters consider the phenomena associated with essentially divergent small-divisor series, such as may occur in the formal solution of differential equations that represent the oscillations of conservative dynamical systems. This book discusses as well the mechanics of idealized textiles consisting of inextensible filaments. The final chapter deals with the use of the Peaceman-Rachford alternating direction implicit method for solving the finite difference analogs of boundary value problems. This book is a valuable resource for engineers and mathematicians.

Autoren/Hrsg.

Ames, William F.

Inhaltsverzeichnis

1;Front Cover;1
2;Nonlinear
Problems of Engineering;4
3;Copyright Page;5
4;Table of Contents;12
5;Contributors;6
6;Foreword;8
7;Preface;10
8;Chapter 1.
New Methods in Nonlinear Mechanics;16
8.1;I. Introduction;16
8.2;II. The Comparative Approach;17
8.3;III. Classical Approach;17
8.4;IV. Discussion;19
8.5;V. The New Approach of Invariant
Imbedding;19
8.6;VI. Discussion;20
8.7;VII. Variational Processes;21
8.8;VIII. Geodesies;22
8.9;IX. Dynamic Programming and the Calculus of Variations;23
8.10;X. Approximation in Policy Space;24
8.11;XI. Discussion;25
8.12;References;25
9;Chapter
2. Probability as a Science;27
9.1;I.;27
9.2;II.;29
9.3;III.;32
9.4;IV.;33
10;Chapter 3.
On Random Solutions of Nonlinear Integral Equations ;38
10.1;Text;38
10.2;References;42
11;Chapter 4.
A Singular Case of Iteration of Analytic Functions: A Contribution to the Small-Divisor Problem;44
11.1;I. The "Center Problem" in the Iteration of Analytic Functions;44
11.2;II. Contexts Leading to Small-Divisor Series;48
11.3;III. Generalities Regarding Iteration of Analytic Functions;51
11.4;IV. Construction of Singular Iterations zn+1 = f(zn);57
11.5;V. Properties of Singular Iterations;60
11.6;References;65
12;Chapter 5 .
Networks of Inextensible Cords;66
12.1;I. Introduction;66
12.2;II. Pure Homogeneous Deformation;67
12.3;III. Plane Strain of a Net—Displacement Boundary Conditions;71
12.4;IV. Plane Strain of a Net—Force Boundary Conditions;74
12.5;V. Further Developments;77
12.6;Bibliography;79
13;Chapter 6.
On Integral Operators Generating Stream Functions of Compressible Fluids;80
13.1;Introduction;80
13.2;I. Partial Differential Equations Arising in the Theory of Compressible Fluids;82
13.3;II. The Determination of the Stream Function of a Vortex in the Subsonic Region;86
13.4;III. A Method for Generating Solutions of Equation (1.3.5);91
13.5;References;101
13.6;Bibliography;102
14;Chapter 7.
Some Problems Concerning Linear Differential Equations Made Nonlinear by Unknown or Moving Boundaries;105
14.1;A. Melting or Solidification;105
14.2;B. Consolidation of an Earth Dam;107
14.3;C. Seepage through a Porous Dam;110
14.4;D. Lubrication in a Journal Bearing, with Oil Cavitation;113
14.5;References;118
14.6;General References;118
15;Chapter 8.
Nonlinear Problems of Combined Conductive-Radiative Heat Transfer;119
15.1;Nomenclature;119
15.2;Introduction;119
15.3;The Single Plate-Type Fin;120
15.4;Radiant Interaction between Fin and Tube Surfaces;124
15.5;Radiant Interaction between Fin Surfaces;131
15.6;Radiant Interaction between Fin and Tube and between Neighboring Fins;135
15.7;Concluding Remarks;136
15.8;References;137
16;Chapter 9.
Statistical Problems Connected with the Solution of a Nonlinear Partial Differential Equation;138
16.1;I. A Particular Nonlinear Partial Differential Equation and Its Solution by Means of a Geometrical Construction;139
16.2;II. Formulation of a Statistical Problem;143
16.3;III. The Solution of the Auxiliary Differential Equation;149
16.4;Notes;151
17;Chapter 10.
Melting Decelerating Bodies;153
17.1;Introduction;153
17.2;Symbols;154
17.3;Analysis;157
17.4;Results;167
17.5;Concluding Remarks;175
17.6;References;176
18;Chapter 11.
Thermal Radiation Effects on Hypersonic Flow Fields;178
18.1;I. Introduction;178
18.2;II. Fundamentals of Radiant Energy Transfer;179
18.3;III. Fundamental Equations of Radiation Gas Dynamics;180
18.4;IV. Solutions for Radiation Transfer Equation;183
18.5;V. New Parameters of Radiation Gas Dynamics;185
18.6;VI. Wave Motions in Radiation Gas Dynamics;188
18.7;VII. Shock Waves in Radiation Gas Dynamics;189
18.8;VIII. Jet Mixing in Radiation Gas Dynamics;191
18.9;IX. Plane Couette Flow in Radiation Magnetogas Dynamics;194
18.10;References;198
19;Chapter 12.
Mathematical Theory of Compressible Fluids;199
19.1;Introduction;199
19.2;List of Symbols;200
19.3;1. Two-Dimensional Compressible Flow in the Physical Plane;201
19.4;2. Two-Dimensional Compressible Flow in the Hodograph Plane;204
19.5;3. Two-Dimensional Compressible Flow about a Closed Body in a Uniform Subsonic Flow;209
19.6;4. Two-Dimensional Flow through the Sonic Line;215
19.7;References;221
20;Chapter 13.
Problems in Nonlinear Nonmechanics;223
20.1;Introduction;223
20.2;Information and Communication;224
20.3;Symbols and Symbolic Structure;226
20.4;Handicaps and Communication;228
20.5;Other Observations;230
20.6;Concluding Remarks;231
20.7;References;231
21;Chapter 14.
Nonlinear Problems in Ballistics;232
21.1;Text;232
21.2;References;233
22;Chapter 15.
Alternating Direction Methods for Solving Partial Difference Equations;235
22.1;1. Introduction;235
22.2;2. The Difference Equation;236
22.3;3. The Linear System;238
22.4;4. The Peaceman-Rachford Method;239
22.5;5. The Cummutative Case;243
22.6;6. Laminar Flow Problem;248
22.7;7. Numerical Results and Conclusions;259
22.8;References;260
23;Subject Index;262