Contact Problems

The legacy of L.A. Galin

By: L. A. Galin, G.M.L. Gladwell (Editor)

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Hardcover | 24 September 2008

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332 Pages

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23.39 x 15.6 x 1.91

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L.A. Galin's book on contact problems is a remarkable work. Actually there are two books: the first, published in 1953 deals with contact problems in the classical theory of elasticity; this is the one that was translated into English in 1961. The second book, published in 1980, included the first, and then had new sections on contact problems for viscoelastic materials, and rough contact problems; this section has not previously been translated into English.

In this new translation, the original text and the mathematical analysis have been completely revised, new material has been added, and the material appearing in the 1980 Russian translation has been completely rewritten.

In addition there are three essays by students of Galin, bringing the analysis up to date.

Industry Reviews

From the reviews:

"This book, edited by G. M. L. Gladwell, is essentially a summary of the life-long contributions of Professor L. A. Galin to the discipline of Contact Mechanics. ... the book is a very welcome addition to the literature in the steadily growing Mathematical Theory of Contact Mechanics. Professor G. M. L. Gladwell should be complemented on the considerable effort and time he put into this fine book, and the contributions of Galin's students bring the results of this classical approach up to date." (Meir Shillor, Mathematical Reviews, Issue 2012 e)

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Non-Fiction Science Physics Classical Mathematics Dynamics & Statics Mathematics Calculus & Mathematical Analysis Differential Calculus & Equations Engineering & Technology Mechanical Engineering & Materials Mechanical Engineering Materials Science

Mechanics of Solids

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Published: 25th November 2010

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Editor's Preface	p. ix
Biographical Sketch of L.A. Galin	p. xi
A Review of Research before 1953	p. 1
Introduction	p. 1
Frictionless Plane Problems	p. 1
Plane Adhesive Contact Problems	p. 3
Plane Frictional Contact Problems	p. 4
Plane Contact between Two Elastic Bodies	p. 5
Three-Dimensional Contact Problems	p. 7
Plane Elasticity Theory	p. 11
The Fundamental Equations	p. 11
Stresses and Displacements in a Semi-Infinite Elastic Plane	p. 21
Plane Static Isotropic Contact Problems	p. 33
Boundary Conditions for Plane Contact Problems	p. 33
The Riemann-Hilbert Problem for the Half-Plane	p. 35
Frictionless Punch Problems - Introduction	p. 39
Frictionless Punch Problems - Theory	p. 41
Examples of Frictionless Problems	p. 44
Frictional Punch Problems - Theory	p. 49
Frictional Punch Problems - Examples	p. 51
Sliding Contact with Coulomb Friction	p. 55
A Two-Punch Problem	p. 58
Moving Punches, and Anisotropic Media	p. 61
Introduction	p. 61
Dynamic Plane Isotropic Elasticity Theory	p. 62
Displacement - Stress Relations	p. 64
Boundary Value Problems for a Moving Punch	p. 66
Complex Variable Formulation for a Plane Anisotropic Elastic Body	p. 67
Contact Problems for an Anisotropic Half-Plane	p. 70
Stick-Slip Contact	p. 74
Contact of Two Elastic Bodies	p. 87
Contact Problems in Three Dimensions	p. 91
The Papkovich-Neuber Solution	p. 91
Solutions of Laplace's Equation in Certain Curvilinear Coordinates	p. 95
Circular Punches	p. 98
The Green's Function for the Exterior of a Circular Disc	p. 101
Axisymmetric Frictionless Contact Problems	p. 105
Axisymmetric Contact with Prescribed Contact Region	p. 112
Loading Outside a Circular Punch	p. 112
Axi-Symmetric Contact Problems with Friction	p. 115
A Punch of Elliptic Cross-Section	p. 120
Forces and Moments on an Elliptical Punch	p. 131
A Punch of Arbitrary Cross-Section	p. 133
The Pressure of a Wedge-Shaped Punch with Plane Base	p. 136
A Slender Beam on an Elastic Body	p. 136
Contact of Two Elastic Bodies	p. 144
Contact between a Rigid Punch and a Clamped Plate	p. 145
Viscoelasticity, Wear and Roughness	p. 153
Introduction	p. 153
The Laplace Transform	p. 153
2-D Orthotropic Viscoelastic Bodies	p. 155
Adhesive Contact for a Viscoelastic Half-Plane	p. 157
Viscoelastic Rolling Contact	p. 165
The Limiting Case of Rolling of a Cylinder on a Viscoelastic Base	p. 177
Contact Problems in the Presence of Wear	p. 183
Axisymmetric Contact Problems in the Presence of Wear	p. 186
Plane Contact Problems for Rough Elastic Bodies	p. 190
Contact Problems for Rough Axisymmetric Elastic Bodies	p. 195
References	p. 199
Index	p. 205
Development of Galin's Research in Contact Mechanics	p. 207
Two-Dimensional Sliding Contact of Elastic Bodies	p. 207
Problem Formulation	p. 207
Contact Problem for a Cylinder	p. 210
Contact Problem for a Flat Punch	p. 212
Contact Problem with Partial Slip for the Inclined Punch with Rounded Edges	p. 217
Problem Formulation	p. 218
Contact Pressure Analysis	p. 220
Shear Stress Analysis	p. 225
Tensile Stress Analysis	p. 230
Results and Discussions	p. 232
Conclusions	p. 236
Appendix	p. 237
Three-Dimensional Sliding Contact of Elastic Bodies	p. 238
The Friction Law Has the Form [sigma subscript xz] = [rho]p	p. 239
The Friction Law Has the Form [sigma subscript xz] = [tau subscript 0] + [rho]p	p. 242
Periodic Contact Problem	p. 244
One-Level Model	p. 245
Principle of Localization	p. 248
System of Indenters of Various Heights	p. 250
Stress Field Analysis	p. 252
Hertz Type Contact Problems for Power-Law Shaped Bodies	p. 261
Introduction	p. 261
Hertz Type Contact Problems for rigid Indenters	p. 261
Formulation of a Hertz Type Contact Problem	p. 262
Frictionless Axisymmetric Contact	p. 264
The Galin Solution for Frictionless Axisymmetric Contact	p. 264
The Sneddon Representation of the Galin solution	p. 264
The Galin Solution for Monomial Punches	p. 266
A Solution for Polynomial Punches	p. 267
Axisymmetric Contact Problems with Molecular Adhesion	p. 267
Adhesive (No-Slip) Axisymmetric Contact Problems	p. 270
Two-Dimensional Problem for a Punch with Horizontal Base	p. 270
Axisymmetric Adhesive Contact Problems for Curved Punches	p. 271
The Mossakovskii Solution for Adhesive Contact	p. 271
Solution to the Problem for Punches of Monomial Shape	p. 273
Self-Similar Contact Problems	p. 275
Similarity Transformations for Hertz Type Contact Problems	p. 277
Punches Described by Homogeneous Functions	p. 279
Punches Described by Parametric-Homogeneous Functions	p. 280
Hardness Measurements and Depth-Sensing Techniques	p. 283
Brief History of Hardness Measurements	p. 283
Depth-Sensing Techniques	p. 285
Adhesive (No-Slip) Indentation	p. 287
Similarity Considerations of 3D Indentation	p. 293
Further Developments of Galin's Stick-Slip Problem	p. 293
Introduction	p. 293
The Stick-Slip Problem in Galin's Formulation	p. 294
Refinements of Galin's Solution	p. 294
Solution of the Galin Stick-Slip Problem Due to Antipov and Arutyunyan	p. 298
Solution to the Galin Stick-Slip Problem Due to Spence	p. 303
Extensions to the Stick-Slip Contact Problem	p. 306
Arbitrary Load	p. 306
A Periodic System of Punches	p. 307
Self-Similarity Approach in Stick-Slip Contact Problems	p. 307
Table of Contents provided by Ingram. All Rights Reserved.

Contact Problems

The legacy of L.A. Galin

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

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