Nonlinear Problems of Engineering

Nonlinear Problems of Engineering

1st Edition - January 1, 1964

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  • Editor: William F. Ames
  • eBook ISBN: 9781483225814

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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.

Table of Contents

  • Contributors



    New Methods in Nonlinear Mechanics

    I. Introduction

    II. The Comparative Approach

    III. Classical Approach

    IV. Discussion

    V. The New Approach of Invariant Imbedding

    VI. Discussion

    VII. Variational Processes

    VIII. Geodesics

    IX. Dynamic Programming and the Calculus of Variations

    X. Approximation in Policy Space

    XI. Discussion


    Probability as a Science

    On Random Solutions of Nonlinear Integral Equations



    A Singular Case of Iteration of Analytic Functions: A Contribution to the Small-Divisor Problem

    I. The "Center Problem" in the Iteration of Analytic Functions

    II. Contexts Leading to Small-Divisor Series

    III. Generalities Regarding Iteration of Analytic Functions

    IV. Construction of Singular Iterations Zn+1 = f(Zn)

    V. Properties of Singular Iterations


    Networks of Inextensible Cords

    I. Introduction

    II. Pure Homogeneous Deformation

    III. Plane Strain of a Net—Displacement Boundary Conditions

    IV. Plane Strain of a Net—Force Boundary Conditions

    V. Further Developments


    On Integral Operators Generating Stream Functions of Compressible Fluids


    I. Partial Differential Equations Arising in the Theory of Compressible Fluids

    II. The Determination of the Stream Function of a Vortex in the Subsonic Region

    III. A Method for Generating Solutions of Equation (1.3.5)



    Some Problems Concerning Linear Differential Equations Made Nonlinear by Unknown or Moving Boundaries

    A. Melting or Solidification

    B. Consolidation of an Earth Dam

    C. Seepage through a Porous Dam

    D. Lubrication in a Journal Bearing, with Oil Cavitation


    General References

    Nonlinear Problems of Combined Conductive-Radiative Heat Transfer



    The Single Plate-Type Fin

    Radiant Interaction Between Fin and Tube Surfaces

    Radiant Interaction Between Fin Surfaces

    Radiant Interaction Between Fin and Tube and Between Neighboring Fins

    Concluding Remarks


    Statistical Problems Connected with the Solution of a Nonlinear Partial Differential Equation

    I. A Particular Nonlinear Partial Differential Equation and Its Solution by Means of a Geometrical Construction

    II. Formulation of a Statistical Problem

    III. The Solution of the Auxiliary Differential Equation


    Melting Decelerating Bodies





    Concluding Remarks


    Thermal Radiation Effects on Hypersonic Flow Fields

    I. Introduction

    II. Fundamentals of Radiant Energy Transfer

    III. Fundamental Equations of Radiation Gas Dynamics

    IV. Solutions for Radiation Transfer Equation

    V. New Parameters of Radiation Gas Dynamics

    VI. Wave Motions in Radiation Gas Dynamics

    VII. Shock Waves in Radiation Gas Dynamics

    VIII. Jet Mixing in Radiation Gas Dynamics

    IX. Plane Couette Flow in Radiation Magnetogas Dynamics


    Mathematical Theory of Compressible Fluids


    List of Symbols

    1. Two-Dimensional Compressible Flow in the Physical Plane

    2. Two-Dimensional Compressible Flow in the Hodograph Plane

    3. Two-Dimensional Compressible Flow About a Closed Body in a Uniform Subsonic Flow

    4. Two-Dimensional Flow through the Sonic Line


    Problems in Nonlinear Nonmechanics


    Information and Communication

    Symbols and Symbolic Structure

    Handicaps and Communication

    Other Observations

    Concluding Remarks


    Nonlinear Problems in Ballistics



    Alternating Direction Methods for Solving Partial Difference Equations

    1. Introduction

    2. The Difference Equation

    3. The Linear System

    4. The Peaceman-Rachford Method

    5. The Cummutative Case

    6. Laminar Flow Problem

    7. Numerical Results and Conclusions


    Subject Index

Product details

  • No. of pages: 266
  • Language: English
  • Copyright: © Academic Press 1964
  • Published: January 1, 1964
  • Imprint: Academic Press
  • eBook ISBN: 9781483225814

About the Editor

William F. Ames

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